From cb4c9bef025e58f98ddbb6cd0e5c4504f457d51c Mon Sep 17 00:00:00 2001 From: Jake Crawford Date: Mon, 28 Aug 2023 15:40:46 +0000 Subject: [PATCH] Merge pull request #1 from jjc2718/add_optimizers [ci skip] This build is based on https://github.com/greenelab/jake_dissertation/commit/3c54414f867d8b2fbddc5390e79b2142dfb8fe29. This commit was created by the following CI build and job: https://github.com/greenelab/jake_dissertation/commit/3c54414f867d8b2fbddc5390e79b2142dfb8fe29/checks https://github.com/greenelab/jake_dissertation/actions/runs/6001912086 --- citations.tsv | 30 +- manuscript.docx | Bin 0 -> 1586429 bytes manuscript.html | 689 ++-- manuscript.md | 461 +-- manuscript.pdf | Bin 209819 -> 1395427 bytes references.json | 7083 ++++++++++++++++++++++++++++++++-- spelling-error-locations.txt | 246 +- spelling-errors.txt | 105 +- variables.json | 80 +- 9 files changed, 7618 insertions(+), 1076 deletions(-) create mode 100644 manuscript.docx diff --git a/citations.tsv b/citations.tsv index ebb6a85..9dbf439 100644 --- a/citations.tsv +++ b/citations.tsv @@ -1,9 +1,25 @@ input_id dealiased_id standard_id short_id -doi:10.7554/eLife.32822 doi:10.7554/eLife.32822 doi:10.7554/elife.32822 IhliSZDo -pmc:PMC6103790 pmc:PMC6103790 pmc:PMC6103790 mSMVRkoc -pubmed:30718888 pubmed:30718888 pubmed:30718888 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-

Manuscript Title

+

Jake Crawford dissertation title

This manuscript -(permalink) +(permalink) was automatically generated -from greenelab/jake_dissertation@8c1a803 -on August 17, 2023. +from greenelab/jake_dissertation@3c54414 +on August 28, 2023.

Authors

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✉ — Correspondence possible via GitHub Issues -or email to -Jane Roe <jane.roe@whatever.edu>.

+

✉ — Correspondence possible via GitHub Issues

Abstract

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Chapter 1

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Two roads diverged in a wood, and I—
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Figures

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Chapter 2: optimization strongly influences model selection in transcriptomic prediction

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This chapter has been posted as a preprint on bioRxiv (https://www.biorxiv.org/content/10.1101/2023.06.26.546586v1) and submitted for publication at Bioinformatics Advances as “Optimizer’s dilemma: optimization strongly influences model selection in transcriptomic prediction”.

+

Contributions: I designed and ran the experiments, created the figures, wrote the initial draft of the manuscript, and edited the manuscript. Maria Chikina gave feedback on an initial version of the manuscript, gave guidance on experimental design, and edited the manuscript. Casey S. Greene gave feedback and guidance on experiments, and edited the manuscript.

+

Abstract

+

Motivation

+

Most models can be fit to data using various optimization approaches. +While model choice is frequently reported in machine-learning-based research, optimizers are not often noted. +We applied two different implementations of LASSO logistic regression implemented in Python’s scikit-learn package, using two different optimization approaches (coordinate descent and stochastic gradient descent), to predict driver mutation presence or absence from gene expression across 84 pan-cancer driver genes. +Across varying levels of regularization, we compared performance and model sparsity between optimizers.

+

Results

+

After model selection and tuning, we found that coordinate descent (implemented in the liblinear library) and SGD tended to perform comparably. +liblinear models required more extensive tuning of regularization strength, performing best for high model sparsities (more nonzero coefficients), but did not require selection of a learning rate parameter. +SGD models required tuning of the learning rate to perform well, but generally performed more robustly across different model sparsities as regularization strength decreased. +Given these tradeoffs, we believe that the choice of optimizers should be clearly reported as a part of the model selection and validation process, to allow readers and reviewers to better understand the context in which results have been generated.

+

Availability and implementation

+

The code used to carry out the analyses in this study is available at https://github.com/greenelab/pancancer-evaluation/tree/master/01_stratified_classification. Performance/regularization strength curves for all genes in the Vogelstein et al. 2013 dataset are available at https://doi.org/10.6084/m9.figshare.22728644.

+

Introduction

+

Gene expression profiles are widely used to classify samples or patients into relevant groups or categories, both preclinically [1,2] and clinically [3,4]. +To extract informative gene features and to perform classification, a diverse array of algorithms exist, and different algorithms perform well across varying datasets and tasks [1]. +Even within a given model class, multiple optimization methods can often be applied to find well-performing model parameters or to optimize a model’s loss function. +One commonly used example is logistic regression. +The widely used scikit-learn Python package for machine learning [5] provides two modules for fitting logistic regression classifiers: LogisticRegression, which uses the liblinear coordinate descent method [6] to find parameters that optimize the logistic loss function, and SGDClassifier, which uses stochastic gradient descent [7] to optimize the same loss function.

+

Using scikit-learn, we compared the liblinear (coordinate descent) and SGD optimization techniques for prediction of driver mutation status in tumor samples, across a wide variety of genes implicated in cancer initiation and development [8]. +We applied LASSO (L1-regularized) logistic regression, and tuned the strength of the regularization to compare model selection between optimizers. +We found that across a variety of models (i.e. varying regularization strengths), the training dynamics of the optimizers were considerably different: models fit using liblinear tended to perform best at fairly high regularization strengths (100-1000 nonzero features in the model) and overfit easily with low regularization strengths. +On the other hand, after tuning the learning rate, models fit using SGD tended to perform well across both higher and lower regularization strengths, and overfitting was less common.

+

Our results caution against viewing optimizer choice as a “black box” component of machine learning modeling. +The observation that LASSO logistic regression models fit using SGD tended to perform well for low levels of regularization, across diverse driver genes, runs counter to conventional wisdom in machine learning for high-dimensional data which generally states that explicit regularization and/or feature selection is necessary. +Comparing optimizers or model implementations directly is rare in applications of machine learning for genomics, and our work shows that this choice can affect generalization and interpretation properties of the model significantly. +Based on our results, we recommend considering the appropriate optimization approach carefully based on the goals of each individual analysis.

+

Methods

+

Data download and preprocessing

+

To generate binary mutated/non-mutated gene labels for our machine learning model, we used mutation calls for TCGA Pan-Cancer Atlas samples from MC3 [9] and copy number threshold calls from GISTIC2.0 [10]. +MC3 mutation calls were downloaded from the Genomic Data Commons (GDC) of the National Cancer Institute, at https://gdc.cancer.gov/about-data/publications/pancanatlas. +Thresholded copy number calls are from an older version of the GDC data and are available here: https://figshare.com/articles/dataset/TCGA_PanCanAtlas_Copy_Number_Data/6144122. +We removed hypermutated samples, defined as two or more standard deviations above the mean non-silent somatic mutation count, from our dataset to reduce the number of false positives (i.e., non-driver mutations). +Any sample with either a non-silent somatic variant or a copy number variation (copy number gain in the target gene for oncogenes and copy number loss in the target gene for tumor suppressor genes) was included in the positive set; all remaining samples were considered negative for mutation in the target gene.

+

RNA sequencing data for TCGA was downloaded from GDC at the same link provided above for the Pan-Cancer Atlas. +We discarded non-protein-coding genes and genes that failed to map and removed tumors that were measured from multiple sites. +After filtering to remove hypermutated samples and taking the intersection of samples with both mutation and gene expression data, 9074 total TCGA samples remained.

+

Cancer gene set construction

+

In order to study mutation status classification for a diverse set of cancer driver genes, we started with the set of 125 frequently altered genes from Vogelstein et al. [8] (all genes from Table S2A). +For each target gene, in order to ensure that the training dataset was reasonably balanced (i.e., that there would be enough mutated samples to train an effective classifier), we included only cancer types with at least 15 mutated samples and at least 5% mutated samples, which we refer to here as “valid” cancer types. +In some cases, this resulted in genes with no valid cancer types, which we dropped from the analysis. +Out of the 125 genes originally listed in the Vogelstein et al. cancer gene set, we retained 84 target genes after filtering for valid cancer types.

+

Classifier setup and optimizer comparison details

+

We trained logistic regression classifiers to predict whether or not a given sample had a mutational event in a given target gene using gene expression features as explanatory variables. +Based on our previous work, gene expression is generally effective for this problem across many target genes, although other -omics types can be equally effective in many cases [11]. +Our model was trained on gene expression data (X) to predict mutation presence or absence (y) in a target gene. +To control for varying mutation burden per sample and to adjust for potential cancer type-specific expression patterns, we included one-hot encoded cancer type and log10(sample mutation count) in the model as covariates. +Since gene expression datasets tend to have many dimensions and comparatively few samples, we used a LASSO penalty to perform feature selection [12]. +LASSO logistic regression has the advantage of generating sparse models (some or most coefficients are 0), as well as having a single tunable hyperparameter which can be easily interpreted as an indicator of regularization strength, or model complexity.

+

To compare model selection across optimizers, we first split the “valid” cancer types into train (75%) and test (25%) sets. +We then split the training data into “subtrain” (66% of the training set) data to train the model on, and “holdout” (33% of the training set) data to perform model selection, i.e. to use to select the best-performing regularization parameter, and the best-performing learning rate for SGD in the cases where multiple learning rates were considered. +In each case, these splits were stratified by cancer type, i.e. each split had as close as possible to equal proportions of each cancer type included in the dataset for the given driver gene.

+

LASSO parameter range selection and comparison between optimizers

+

The scikit-learn implementations of coordinate descent (in liblinear/LogisticRegression) and stochastic gradient descent (in SGDClassifier) use slightly different parameterizations of the LASSO regularization strength parameter. liblinear’s logistic regression solver optimizes the following loss function:

+

\[\hat{w} = \text{argmin}_{w} \ (C \cdot \ell(X, y; w)) + ||w||_1\]

+

where \(\ell(X, y; w)\) denotes the negative log-likelihood of the observed data \((X, y)\) given a particular choice of feature weights \(w\).SGDClassifier optimizes the following loss function:

+

\[\hat{w} = \text{argmin}_{w} \ \ell(X, y; w) + \alpha ||w||_1\]

+ +

which is equivalent with the exception of the LASSO parameter which is formulated slightly differently, as \(\alpha = \frac{1}{C}\). +The result of this slight difference in parameterization is that liblinear \(C\) values vary inversely with regularization strength (higher values = less regularization, or greater model complexity) and SGDClassifier \(\alpha\) values vary directly with regularization strength (lower values = less regularization, or greater model complexity).

+

For the liblinear optimizer, we trained models using \(C\) values evenly spaced on a logarithmic scale between (10-3, 107); i.e. the output of numpy.logspace(-3, 7, 21). +For the SGD optimizer, we trained models using the inverse range of \(\alpha\) values between (10-7, 103), or numpy.logspace(-7, 3, 21). +These hyperparameter ranges were intended to give evenly distributed coverage across genes that included “underfit” models (predicting only the mean or using very few features, poor performance on all datasets), “overfit” models (performing perfectly on training data but comparatively poorly on cross-validation and test data), and a wide variety of models in between that typically included the best fits to the cross-validation and test data.

+

For ease of visual comparison in our figures, we plot the SGD \(\alpha\) parameter directly, and the liblinear \(C\) parameter inversely (i.e. \(\frac{1}{C}\)). +This orients the x-axes of the relevant plots in the same direction: lower values represent lower regularization strength or higher model complexity, and higher values represent higher regularization strength or lower model complexity, for both optimizers.

+

SGD learning rate selection

+

scikit-learn’s SGDClassifier provides four built-in approaches to learning rate scheduling: constant (a single, constant learning rate), optimal (a learning rate with an initial value selected using a heuristic based on the regularization parameter and the data loss, that decreases across epochs), invscaling (a learning rate that decreases exponentially by epoch), and adaptive (a learning rate that starts at a constant value, which is divided by 5 each time the training loss fails to decrease for 5 straight epochs). +The optimal learning rate schedule is used by default.

+

When we compared these four approaches, we used a constant learning rate of 0.0005, and an initial learning rate of 0.1 for the adaptive and invscaling schedules. +We also tested a fifth approach that we called “constant_search”, in which we tested a range of constant learning rates in a grid search on a validation dataset, then evaluated the model on the test data using the best-performing constant learning rate by validation AUPR. +For the grid search, we used the following range of constant learning rates: {0.000005, 0.00001, 0.00005, 0.0001, 0.0005, 0.001, 0.01}. +Unless otherwise specified, results for SGD in the main paper figures used the constant_search approach, which performed the best in our comparison between schedulers.

+

Results

+

liblinear and SGD LASSO models perform comparably, but liblinear is sensitive to regularization strength

+

For each of the 125 driver genes from the Vogelstein et al. 2013 paper, we trained models to predict mutation status (presence or absence) from RNA-seq data, derived from the TCGA Pan-Cancer Atlas. +For each optimizer, we trained LASSO logistic regression models across a variety of regularization parameters (see Methods for parameter range details), achieving a variety of different levels of model sparsity (Supplementary Figure 4). +We repeated model fitting/evaluation across 4 cross-validation splits x 2 replicates (random seeds) for a total of 8 different models per parameter. +Cross-validation splits were stratified by cancer type.

+

Previous work has shown that pan-cancer classifiers of Ras mutation status are accurate and biologically informative [13]. +We first evaluated models for KRAS mutation prediction. +As model complexity increases (more nonzero coefficients) for the liblinear optimizer, we observed that performance increases then decreases, corresponding to overfitting for high model complexities/numbers of nonzero coefficients (Figure 1A). +On the other hand, for the SGD optimizer, we observed consistent performance as model complexity increases, with models having no nonzero coefficients performing comparably to the best (Figure 1B). +In this case, top performance for SGD (a regularization parameter of 10-1) is slightly better than top performance for liblinear (a regularization parameter of 1 / 3.16 x 102): we observed a mean test AUPR of 0.722 for SGD vs. mean AUPR of 0.692 for liblinear.

+

To determine how relative performance trends with liblinear tend to compare across the genes in the Vogelstein dataset at large, we looked at the difference in performance between optimizers for the best-performing models for each gene (Figure 1C). +The distribution is centered around 0 and more or less symmetrical, suggesting that across the gene set, liblinear and SGD tend to perform comparably to one another. +We saw that for 52/84 genes, performance for the best-performing model was better using SGD than liblinear, and for the other 32 genes performance was better using liblinear. +In order to quantify whether the overfitting tendencies (or lack thereof) also hold across the gene set, we plotted the difference in performance between the best-performing model and the largest (least regularized) model; classifiers with a large difference in performance exhibit strong overfitting, and classifiers with a small difference in performance do not overfit (Figure 1D). +For SGD, the least regularized models tend to perform comparably to the best-performing models, whereas for liblinear the distribution is wider suggesting that overfitting is more common.

+
-Figure 1: A square image at actual size and with a bottom caption. Loaded from the latest version of image on GitHub. - +Figure 1: A. Performance vs. inverse regularization parameter for KRAS mutation status prediction, using the liblinear coordinate descent optimizer. Dotted lines indicate top performance value of the opposite optimizer. B. Performance vs. regularization parameter for KRAS mutation status prediction, using the SGD optimizer. “Holdout” dataset is used for SGD learning rate selection, “test” data is completely held out from model selection and used for evaluation. C. Distribution of performance difference between best-performing model for liblinear and SGD optimizers, across all 84 genes in Vogelstein driver gene set. Positive numbers on the x-axis indicate better performance using liblinear, and negative numbers indicate better performance using SGD. D. Distribution of performance difference between best-performing model and largest (least regularized) model, for liblinear and SGD, across all 84 genes. Smaller numbers on the y-axis indicate less overfitting, and larger numbers indicate more overfitting. +
-
+

SGD is sensitive to learning rate selection

+

The SGD results shown in Figure 1 select the best-performing learning rate using a grid search on the holdout dataset, independently for each regularization parameter. +We also compared against other learning rate scheduling approaches implemented in scikit-learn (see Methods for implementation details and grid search specifications). +For KRAS mutation prediction, we observed that the choice of initial learning rate and scheduling approach affects performance significantly, and other approaches to selecting the learning rate performed poorly relative to liblinear (black dotted lines in Figure 2) and to the grid search. +We did not observe an improvement in performance over liblinear or the grid search for learning rate schedulers that decrease across epochs (Figure 2A, C, and D), nor did we see comparable performance when we selected a single constant learning rate for all levels of regularization without the preceding grid search (Figure 2B). +Notably, scikit-learn’s default “optimal” learning rate schedule performed relatively poorly for this problem, suggesting that tuning the learning rate and selecting a well-performing scheduler is a critical component of applying SGD successfully for this problem (Figure 2D). +We observed similar trends across all genes in the Vogelstein gene set, with other learning rate scheduling approaches performing poorly in aggregate relative to both liblinear and SGD with the learning rate grid search (Supplementary Figure 5).

+
-Figure 2: An image too wide to fit within page at full size. Loaded from a specific (hashed) version of the image on GitHub. - +Figure 2: A. Performance vs. regularization parameter for KRAS mutation prediction, using SGD optimizer with adaptive learning rate scheduler. Dotted line indicates top performance value using liblinear, from Figure 1A. B. Performance vs. regularization parameter, using SGD optimizer with constant learning rate scheduler and a learning rate of 0.0005. C. Performance vs. regularization parameter, using SGD optimizer with inverse scaling learning rate scheduler. D. Performance vs. regularization parameter, using SGD optimizer with “optimal” learning rate scheduler. +
-
+

liblinear and SGD result in different models, with varying loss dynamics

+

We sought to determine whether there was a difference in the sparsity of the models resulting from the different optimization schemes. +In general across all genes, the best-performing SGD models mostly tend to have many nonzero coefficients, but with a distinct positive tail, sometimes having few nonzero coefficients. +By contrast, the liblinear models are generally sparser with fewer than 2500 nonzero coefficients, out of ~16100 total input features, and a much narrower tail (Figure 3A). +The sum of the coefficient magnitudes, however, tends to be smaller on average across all levels of regularization for SGD than for liblinear (Figure 3B). +This effect is less pronounced for the other learning rate schedules shown in Figure 2, with the other options resulting in larger coefficient magnitudes (Supplementary Figure 6). +These results suggest that the models fit by liblinear and SGD navigate the tradeoff between bias and variance in slightly different ways: liblinear tends to produce sparser models (more zero coefficients) as regularization increases, but if the learning rate is properly tuned, SGD coefficients tend to have smaller overall magnitudes as regularization increases.

+

We also compared the components of the loss function across different levels of regularization between optimizers. +The LASSO logistic regression loss function can be broken down into a data-dependent component (the log-loss) and a parameter magnitude dependent component (the L1 penalty), which are added to get the total loss that is minimized by each optimizer; see Methods for additional details. +As regularization strength decreases for liblinear, the data loss collapses to near 0, and the L1 penalty dominates the overall loss (Figure 3C). +For SGD, on the other hand, the data loss decreases slightly as regularization strength decreases but remains relatively high (Figure 3D). +Other SGD learning rate schedules have similar loss curves to the liblinear results, although this does not result in improved classification performance (Supplementary Figure 7).

+
-Figure 3: A tall image with a specified height. Loaded from a specific (hashed) version of the image on GitHub. - +Figure 3: A. Distribution across genes of the number of nonzero coefficients included in best-performing LASSO logistic regression models. Violin plot density estimations are clipped at the ends of the observed data range, and boxes show the median/IQR. B. Distribution across genes of the sum of model coefficient weights for best-performing LASSO logistic regression models. C. Decomposition of loss function for models fit using liblinear across regularization levels. 0 values on the y-axis are rounded up to machine epsilon; i.e. 2.22 x 10-16. D. Decomposition of loss function for models fit using SGD across regularization levels. 0 values on the y-axis are rounded up to machine epsilon; i.e. 2.22 x 10-16. +
-
+

Discussion

+

Our work shows that optimizer choice presents tradeoffs in model selection for cancer transcriptomics. +We observed that LASSO logistic regression models for mutation status prediction fit using stochastic gradient descent were highly sensitive to learning rate tuning, but they tended to perform robustly across diverse levels of regularization and sparsity. +Coordinate descent implemented in liblinear did not require learning rate tuning, but generally performed best for a narrow range of fairly sparse models, overfitting as regularization strength decreased. +Tuning of regularization strength for liblinear, and learning rate (and regularization strength to a lesser degree) for SGD, are critical steps which must be considered as part of analysis pipelines. +The sensitivity we observed to these details highlights the importance of reporting exactly what optimizer was used, and how the relevant hyperparameters were selected, in studies that use machine learning models for transcriptomic data.

+

To our knowledge, the phenomenon we observed with SGD has not been documented in other applications of machine learning to genomic or transcriptomic data. +In recent years, however, the broader machine learning research community has identified and characterized implicit regularization for SGD in many settings, including overparametrized or feature-rich problems as is often the case in transcriptomics [14,15,16]. +The resistance we observed of SGD-optimized models to decreased performance on held-out data as model complexity increases is often termed “benign overfitting”: overfit models, in the sense that they fit the training data perfectly and perform worse on the test data, can still outperform models that do not fit the training data as well or that have stronger explicit regularization. +Benign overfitting has been attributed to optimization using SGD [16,17], and similar patterns have been observed for both linear models and deep neural networks [18,19].

+

Existing gene expression prediction benchmarks and pipelines typically use a single model implementation, and thus a single optimizer. +We recommend thinking critically about optimizer choice, but this can be challenging for researchers that are inexperienced with machine learning or unfamiliar with how certain models are fit under the hood. +For example, R’s glmnet package uses a cyclical coordinate descent algorithm to fit logistic regression models [20], which would presumably behave similarly to liblinear, but this is somewhat opaque in the glmnet documentation itself. +Increased transparency and documentation in popular machine learning packages with respect to optimization, especially for models that are difficult to fit or sensitive to hyperparameter settings, would benefit new and unfamiliar users.

+

Related to what we see in our SGD-optimized models, there exist other problems in gene expression analysis where using all available features is comparable to, or better than, using a subset. +For example, using the full gene set improves correlations between preclinical cancer models and their tissue of origin, as compared to selecting genes based on variability or tissue-specificity [21]. +On the other hand, when predicting cell line viability from gene expression profiles, selecting features by Pearson correlation improves performance over using all features, similar to our liblinear classifiers [22]. +In future work, it could be useful to explore if the coefficients found by liblinear and SGD emphasize the same pathways or functional gene sets, or if there are patterns to which mutation status classifiers (or other cancer transcriptomics classifiers) perform better with more/fewer nonzero coefficients.

+

Data and code availability

+

The data analyzed during this study were previously published as part of the TCGA Pan-Cancer Atlas project [23], and are available from the NIH NCI Genomic Data Commons (GDC). +The scripts used to download and preprocess the datasets for this study are available at https://github.com/greenelab/pancancer-evaluation/tree/master/00_process_data, and the code used to carry out the analyses in this study is available at https://github.com/greenelab/pancancer-evaluation/tree/master/01_stratified_classification, both under the open-source BSD 3-clause license. +Equivalent versions of Figure 1A and 1B for all 84 genes in the Vogelstein et al. 2013 gene set are available on Figshare at https://doi.org/10.6084/m9.figshare.22728644, under a CC0 license. +This manuscript was written using Manubot [24] and is available on GitHub at https://github.com/greenelab/optimizer-manuscript under the CC0-1.0 license. +This research was supported in part by the University of Pittsburgh Center for Research Computing through the resources provided. Specifically, this work used the HTC cluster, which is supported by NIH award number S10OD028483.

+

Supplementary Material

+
-Figure 4: A vector .svg image loaded from GitHub. The parameter sanitize=true is necessary to properly load SVGs hosted via GitHub URLs. White background specified to serve as a backdrop for transparent sections of the image. Note that if you want to export to Word (.docx), you need to download the image and reference it locally (e.g. content/images/vector.svg) instead of using a URL. - +Figure 4: Number of nonzero coefficients (model sparsity) across varying regularization parameter settings for KRAS mutation prediction using SGD and liblinear optimizers. +
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Bowling ScoresJaneJohnAliceBob
Game 1150187210105
Game 298202197102
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Digits 1-33Digits 34-66Digits 67-99Ref.
pi3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706piday.org
e2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642nasa.gov
+
+
+Figure 5: Distribution of performance difference between best-performing model for liblinear and SGD optimizers, across all 84 genes in Vogelstein driver gene set, for varying SGD learning rate schedulers. Positive numbers on the x-axis indicate better performance using liblinear, and negative numbers indicate better performance using SGD. + +
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SizeText ColorBackground Color
bigblueorange
smallblackwhite
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+Figure 6: Sum of absolute value of coefficients + 1 for KRAS mutation prediction using SGD and liblinear optimizers, with varying learning rate schedules for SGD. Similar to the figures in the main paper, the liblinear x-axis represents the inverse of the C regularization parameter; SGD x-axes represent the untransformed \alpha parameter. + +
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\[\int_0^\infty e^{-x^2} dx=\frac{\sqrt{\pi}}{2}\](1)

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Adding arbitrary HTML attributes to an element using Pandoc’s attribute syntax:

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Manubot Manubot Manubot Manubot Manubot. -Manubot Manubot Manubot Manubot. -Manubot Manubot Manubot. -Manubot Manubot. -Manubot.

+
+
+Figure 7: Decomposition of loss function into data loss and L1 penalty components for KRAS mutation prediction using SGD optimizer, across regularization levels, using varying learning rate schedulers. 0 values on the y-axis are rounded up to machine epsilon, i.e. 2.22 x 10-16. + +
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Adding arbitrary HTML attributes to an element with the Manubot attributes plugin (more flexible than Pandoc’s method in terms of which elements you can add attributes to):

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Manubot Manubot Manubot Manubot Manubot. -Manubot Manubot Manubot Manubot. -Manubot Manubot Manubot. -Manubot Manubot. -Manubot. -

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Available background colors for text, images, code, banners, etc:

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Using the Font Awesome icon set:

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diff --git a/manuscript.md b/manuscript.md index ec6ea2f..51d515c 100644 --- a/manuscript.md +++ b/manuscript.md @@ -1,14 +1,15 @@ --- -title: Manuscript Title +title: Jake Crawford dissertation title keywords: -- markdown -- publishing -- manubot +- gene-expression +- cancer-genomics +- machine-learning +- optimization +- domain-adaptation lang: en-US -date-meta: '2023-08-17' +date-meta: '2023-08-28' author-meta: -- John Doe -- Jane Roe +- Jake Crawford header-includes: | - - - - - - - - - + + + + + + + + + - - - - - - - - + + + + - - - + + + @@ -69,10 +66,10 @@ manubot-clear-requests-cache: false This manuscript -([permalink](https://greenelab.github.io/jake_dissertation/v/8c1a803748961dcf6b7e8ed4d5ec8f8ce6d5a2a9/)) +([permalink](https://greenelab.github.io/jake_dissertation/v/3c54414f867d8b2fbddc5390e79b2142dfb8fe29/)) was automatically generated -from [greenelab/jake_dissertation@8c1a803](https://github.com/greenelab/jake_dissertation/tree/8c1a803748961dcf6b7e8ed4d5ec8f8ce6d5a2a9) -on August 17, 2023. +from [greenelab/jake_dissertation@3c54414](https://github.com/greenelab/jake_dissertation/tree/3c54414f867d8b2fbddc5390e79b2142dfb8fe29) +on August 28, 2023. @@ -81,39 +78,22 @@ on August 17, 2023. -+ **John Doe** ++ **Jake Crawford**
![ORCID icon](images/orcid.svg){.inline_icon width=16 height=16} - [XXXX-XXXX-XXXX-XXXX](https://orcid.org/XXXX-XXXX-XXXX-XXXX) + [0000-0001-6207-0782](https://orcid.org/0000-0001-6207-0782) · ![GitHub icon](images/github.svg){.inline_icon width=16 height=16} - [johndoe](https://github.com/johndoe) + [jjc2718](https://github.com/jjc2718) · ![Twitter icon](images/twitter.svg){.inline_icon width=16 height=16} - [johndoe](https://twitter.com/johndoe) - · ![Mastodon icon](images/mastodon.svg){.inline_icon width=16 height=16} - [\@johndoe@mastodon.social](https://mastodon.social/@johndoe) + [jjc2718](https://twitter.com/jjc2718)
- Department of Something, University of Whatever - · Funded by Grant XXXXXXXX - - -+ **Jane Roe** - ^[✉](#correspondence)^
- ![ORCID icon](images/orcid.svg){.inline_icon width=16 height=16} - [XXXX-XXXX-XXXX-XXXX](https://orcid.org/XXXX-XXXX-XXXX-XXXX) - · ![GitHub icon](images/github.svg){.inline_icon width=16 height=16} - [janeroe](https://github.com/janeroe) -
- - Department of Something, University of Whatever; Department of Whatever, University of Something + Genomics and Computational Biology Graduate Group, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA ::: {#correspondence} ✉ — Correspondence possible via [GitHub Issues](https://github.com/greenelab/jake_dissertation/issues) -or email to -Jane Roe \. - ::: @@ -123,301 +103,242 @@ Jane Roe \. -This manuscript is a template (aka "rootstock") for [Manubot](https://manubot.org/ "Manubot"), a tool for writing scholarly manuscripts. -Use this template as a starting point for your manuscript. - -The rest of this document is a full list of formatting elements/features supported by Manubot. -Compare the input (`.md` files in the `/content` directory) to the output you see below. +## Chapter 1 -## Basic formatting +* Modeling strategies (copy existing review) -**Bold** __text__ +* Machine learning for cancer transcriptomics (add some new text) -[Semi-bold text]{.semibold} -[Centered text]{.center} +## Chapter 2: optimization strongly influences model selection in transcriptomic prediction -[Right-aligned text]{.right} +This chapter has been posted as a preprint on bioRxiv (https://www.biorxiv.org/content/10.1101/2023.06.26.546586v1) and submitted for publication at Bioinformatics Advances as "Optimizer’s dilemma: optimization strongly influences model selection in transcriptomic prediction". -*Italic* _text_ +_Contributions_: I designed and ran the experiments, created the figures, wrote the initial draft of the manuscript, and edited the manuscript. Maria Chikina gave feedback on an initial version of the manuscript, gave guidance on experimental design, and edited the manuscript. Casey S. Greene gave feedback and guidance on experiments, and edited the manuscript. -Combined *italics and __bold__* -~~Strikethrough~~ -1. Ordered list item -2. Ordered list item - a. Sub-item - b. Sub-item - i. Sub-sub-item -3. Ordered list item - a. Sub-item +### Abstract -- List item -- List item -- List item +#### Motivation -subscript: H~2~O is a liquid +Most models can be fit to data using various optimization approaches. +While model choice is frequently reported in machine-learning-based research, optimizers are not often noted. +We applied two different implementations of LASSO logistic regression implemented in Python's scikit-learn package, using two different optimization approaches (coordinate descent and stochastic gradient descent), to predict driver mutation presence or absence from gene expression across 84 pan-cancer driver genes. +Across varying levels of regularization, we compared performance and model sparsity between optimizers. -superscript: 2^10^ is 1024. +#### Results -[unicode superscripts](https://www.google.com/search?q=superscript+generator)⁰¹²³⁴⁵⁶⁷⁸⁹ +After model selection and tuning, we found that coordinate descent (implemented in the `liblinear` library) and SGD tended to perform comparably. +`liblinear` models required more extensive tuning of regularization strength, performing best for high model sparsities (more nonzero coefficients), but did not require selection of a learning rate parameter. +SGD models required tuning of the learning rate to perform well, but generally performed more robustly across different model sparsities as regularization strength decreased. +Given these tradeoffs, we believe that the choice of optimizers should be clearly reported as a part of the model selection and validation process, to allow readers and reviewers to better understand the context in which results have been generated. -[unicode subscripts](https://www.google.com/search?q=superscript+generator)₀₁₂₃₄₅₆₇₈₉ +#### Availability and implementation -A long paragraph of text. -Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. -Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. -Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. -Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. +The code used to carry out the analyses in this study is available at . Performance/regularization strength curves for all genes in the Vogelstein et al. 2013 dataset are available at . -Putting each sentence on its own line has numerous benefits with regard to [editing](https://asciidoctor.org/docs/asciidoc-recommended-practices/#one-sentence-per-line) and [version control](https://rhodesmill.org/brandon/2012/one-sentence-per-line/). -Line break without starting a new paragraph by putting -two spaces at end of line. +### Introduction -## Document organization +Gene expression profiles are widely used to classify samples or patients into relevant groups or categories, both preclinically [@doi:10.1371/journal.pcbi.1009926; @doi:10.1093/bioinformatics/btaa150] and clinically [@doi:10.1200/JCO.2008.18.1370; @doi:10/bp4rtw]. +To extract informative gene features and to perform classification, a diverse array of algorithms exist, and different algorithms perform well across varying datasets and tasks [@doi:10.1371/journal.pcbi.1009926]. +Even within a given model class, multiple optimization methods can often be applied to find well-performing model parameters or to optimize a model's loss function. +One commonly used example is logistic regression. +The widely used scikit-learn Python package for machine learning [@url:https://jmlr.org/papers/v12/pedregosa11a.html] provides two modules for fitting logistic regression classifiers: `LogisticRegression`, which uses the `liblinear` coordinate descent method [@url:https://www.jmlr.org/papers/v9/fan08a.html] to find parameters that optimize the logistic loss function, and `SGDClassifier`, which uses stochastic gradient descent [@online-learning] to optimize the same loss function. -Document section headings: +Using scikit-learn, we compared the `liblinear` (coordinate descent) and SGD optimization techniques for prediction of driver mutation status in tumor samples, across a wide variety of genes implicated in cancer initiation and development [@doi:10.1126/science.1235122]. +We applied LASSO (L1-regularized) logistic regression, and tuned the strength of the regularization to compare model selection between optimizers. +We found that across a variety of models (i.e. varying regularization strengths), the training dynamics of the optimizers were considerably different: models fit using `liblinear` tended to perform best at fairly high regularization strengths (100-1000 nonzero features in the model) and overfit easily with low regularization strengths. +On the other hand, after tuning the learning rate, models fit using SGD tended to perform well across both higher and lower regularization strengths, and overfitting was less common. -# Heading 1 +Our results caution against viewing optimizer choice as a "black box" component of machine learning modeling. +The observation that LASSO logistic regression models fit using SGD tended to perform well for low levels of regularization, across diverse driver genes, runs counter to conventional wisdom in machine learning for high-dimensional data which generally states that explicit regularization and/or feature selection is necessary. +Comparing optimizers or model implementations directly is rare in applications of machine learning for genomics, and our work shows that this choice can affect generalization and interpretation properties of the model significantly. +Based on our results, we recommend considering the appropriate optimization approach carefully based on the goals of each individual analysis. -## Heading 2 -### Heading 3 +### Methods -#### Heading 4 - -##### Heading 5 - -###### Heading 6 - -### A heading centered on its own printed page{.center .page_center} - - - -Horizontal rule: - ---- +#### Data download and preprocessing -`Heading 1`'s are recommended to be reserved for the title of the manuscript. +To generate binary mutated/non-mutated gene labels for our machine learning model, we used mutation calls for TCGA Pan-Cancer Atlas samples from MC3 [@doi:10.1016/j.cels.2018.03.002] and copy number threshold calls from GISTIC2.0 [@doi:10.1186/gb-2011-12-4-r41]. +MC3 mutation calls were downloaded from the Genomic Data Commons (GDC) of the National Cancer Institute, at . +Thresholded copy number calls are from an older version of the GDC data and are available here: . +We removed hypermutated samples, defined as two or more standard deviations above the mean non-silent somatic mutation count, from our dataset to reduce the number of false positives (i.e., non-driver mutations). +Any sample with either a non-silent somatic variant or a copy number variation (copy number gain in the target gene for oncogenes and copy number loss in the target gene for tumor suppressor genes) was included in the positive set; all remaining samples were considered negative for mutation in the target gene. -`Heading 2`'s are recommended for broad sections such as *Abstract*, *Methods*, *Conclusion*, etc. +RNA sequencing data for TCGA was downloaded from GDC at the same link provided above for the Pan-Cancer Atlas. +We discarded non-protein-coding genes and genes that failed to map and removed tumors that were measured from multiple sites. +After filtering to remove hypermutated samples and taking the intersection of samples with both mutation and gene expression data, 9074 total TCGA samples remained. -`Heading 3`'s and `Heading 4`'s are recommended for sub-sections. +#### Cancer gene set construction -## Links +In order to study mutation status classification for a diverse set of cancer driver genes, we started with the set of 125 frequently altered genes from Vogelstein et al. [@doi:10.1126/science.1235122] (all genes from Table S2A). +For each target gene, in order to ensure that the training dataset was reasonably balanced (i.e., that there would be enough mutated samples to train an effective classifier), we included only cancer types with at least 15 mutated samples and at least 5% mutated samples, which we refer to here as "valid" cancer types. +In some cases, this resulted in genes with no valid cancer types, which we dropped from the analysis. +Out of the 125 genes originally listed in the Vogelstein et al. cancer gene set, we retained 84 target genes after filtering for valid cancer types. -Bare URL link: +#### Classifier setup and optimizer comparison details -[Long link with lots of words and stuff and junk and bleep and blah and stuff and other stuff and more stuff yeah](https://manubot.org) +We trained logistic regression classifiers to predict whether or not a given sample had a mutational event in a given target gene using gene expression features as explanatory variables. +Based on our previous work, gene expression is generally effective for this problem across many target genes, although other -omics types can be equally effective in many cases [@doi:10.1186/s13059-022-02705-y]. +Our model was trained on gene expression data (X) to predict mutation presence or absence (y) in a target gene. +To control for varying mutation burden per sample and to adjust for potential cancer type-specific expression patterns, we included one-hot encoded cancer type and log~10~(sample mutation count) in the model as covariates. +Since gene expression datasets tend to have many dimensions and comparatively few samples, we used a LASSO penalty to perform feature selection [@doi:10.1111/j.2517-6161.1996.tb02080.x]. +LASSO logistic regression has the advantage of generating sparse models (some or most coefficients are 0), as well as having a single tunable hyperparameter which can be easily interpreted as an indicator of regularization strength, or model complexity. -[Link with text](https://manubot.org) +To compare model selection across optimizers, we first split the "valid" cancer types into train (75%) and test (25%) sets. +We then split the training data into "subtrain" (66% of the training set) data to train the model on, and "holdout" (33% of the training set) data to perform model selection, i.e. to use to select the best-performing regularization parameter, and the best-performing learning rate for SGD in the cases where multiple learning rates were considered. +In each case, these splits were stratified by cancer type, i.e. each split had as close as possible to equal proportions of each cancer type included in the dataset for the given driver gene. -[Link with hover text](https://manubot.org "Manubot Homepage") +#### LASSO parameter range selection and comparison between optimizers -[Link by reference][manubot homepage] +The scikit-learn implementations of coordinate descent (in `liblinear`/`LogisticRegression`) and stochastic gradient descent (in `SGDClassifier`) use slightly different parameterizations of the LASSO regularization strength parameter. `liblinear`'s logistic regression solver optimizes the following loss function: -[Manubot Homepage]: https://manubot.org +$$\hat{w} = \text{argmin}_{w} \ (C \cdot \ell(X, y; w)) + ||w||_1$$ -## Citations +where $\ell(X, y; w)$ denotes the negative log-likelihood of the observed data $(X, y)$ given a particular choice of feature weights $w$.`SGDClassifier` optimizes the following loss function: -Citation by DOI [@doi:10.7554/eLife.32822]. +$$\hat{w} = \text{argmin}_{w} \ \ell(X, y; w) + \alpha ||w||_1$$ -Citation by PubMed Central ID [@pmc:PMC6103790]. + -Citation by PubMed ID [@pubmed:30718888]. +which is equivalent with the exception of the LASSO parameter which is formulated slightly differently, as $\alpha = \frac{1}{C}$. +The result of this slight difference in parameterization is that `liblinear` $C$ values vary inversely with regularization strength (higher values = less regularization, or greater model complexity) and `SGDClassifier` $\alpha$ values vary directly with regularization strength (lower values = less regularization, or greater model complexity). -Citation by Wikidata ID [@wikidata:Q56458321]. +For the `liblinear` optimizer, we trained models using $C$ values evenly spaced on a logarithmic scale between (10^-3^, 10^7^); i.e. the output of `numpy.logspace(-3, 7, 21)`. +For the SGD optimizer, we trained models using the inverse range of $\alpha$ values between (10^-7^, 10^3^), or `numpy.logspace(-7, 3, 21)`. +These hyperparameter ranges were intended to give evenly distributed coverage across genes that included "underfit" models (predicting only the mean or using very few features, poor performance on all datasets), "overfit" models (performing perfectly on training data but comparatively poorly on cross-validation and test data), and a wide variety of models in between that typically included the best fits to the cross-validation and test data. -Citation by ISBN [@isbn:9780262517638]. +For ease of visual comparison in our figures, we plot the SGD $\alpha$ parameter directly, and the `liblinear` $C$ parameter inversely (i.e. $\frac{1}{C}$). +This orients the x-axes of the relevant plots in the same direction: lower values represent lower regularization strength or higher model complexity, and higher values represent higher regularization strength or lower model complexity, for both optimizers. -Citation by URL [@{https://greenelab.github.io/meta-review/}]. +#### SGD learning rate selection -Citation by alias [@deep-review]. +scikit-learn's `SGDClassifier` provides four built-in approaches to learning rate scheduling: `constant` (a single, constant learning rate), `optimal` (a learning rate with an initial value selected using a heuristic based on the regularization parameter and the data loss, that decreases across epochs), `invscaling` (a learning rate that decreases exponentially by epoch), and `adaptive` (a learning rate that starts at a constant value, which is divided by 5 each time the training loss fails to decrease for 5 straight epochs). +The `optimal` learning rate schedule is used by default. -Multiple citations can be put inside the same set of brackets [@doi:10.7554/eLife.32822; @deep-review; @isbn:9780262517638]. -Manubot plugins provide easier, more convenient visualization of and navigation between citations [@doi:10.1371/journal.pcbi.1007128; @pubmed:30718888; @pmc:PMC6103790; @deep-review]. +When we compared these four approaches, we used a constant learning rate of 0.0005, and an initial learning rate of 0.1 for the `adaptive` and `invscaling` schedules. +We also tested a fifth approach that we called "`constant_search`", in which we tested a range of constant learning rates in a grid search on a validation dataset, then evaluated the model on the test data using the best-performing constant learning rate by validation AUPR. +For the grid search, we used the following range of constant learning rates: {0.000005, 0.00001, 0.00005, 0.0001, 0.0005, 0.001, 0.01}. +Unless otherwise specified, results for SGD in the main paper figures used the `constant_search` approach, which performed the best in our comparison between schedulers. -Citation tags (i.e. aliases) can be defined in their own paragraphs using Markdown's reference link syntax: -[@deep-review]: doi:10.1098/rsif.2017.0387 -## Referencing figures, tables, equations +### Results -Figure @fig:square-image +#### `liblinear` and SGD LASSO models perform comparably, but `liblinear` is sensitive to regularization strength -Figure @fig:wide-image +For each of the 125 driver genes from the Vogelstein et al. 2013 paper, we trained models to predict mutation status (presence or absence) from RNA-seq data, derived from the TCGA Pan-Cancer Atlas. +For each optimizer, we trained LASSO logistic regression models across a variety of regularization parameters (see Methods for parameter range details), achieving a variety of different levels of model sparsity (Supplementary Figure {@fig:compare_sparsity}). +We repeated model fitting/evaluation across 4 cross-validation splits x 2 replicates (random seeds) for a total of 8 different models per parameter. +Cross-validation splits were stratified by cancer type. -Figure @fig:tall-image +Previous work has shown that pan-cancer classifiers of Ras mutation status are accurate and biologically informative [@doi:10.1016/j.celrep.2018.03.046]. +We first evaluated models for KRAS mutation prediction. +As model complexity increases (more nonzero coefficients) for the `liblinear` optimizer, we observed that performance increases then decreases, corresponding to overfitting for high model complexities/numbers of nonzero coefficients (Figure {@fig:optimizer_compare_mutations}A). +On the other hand, for the SGD optimizer, we observed consistent performance as model complexity increases, with models having no nonzero coefficients performing comparably to the best (Figure {@fig:optimizer_compare_mutations}B). +In this case, top performance for SGD (a regularization parameter of 10^-1^) is slightly better than top performance for `liblinear` (a regularization parameter of 1 / 3.16 x 10^2^): we observed a mean test AUPR of 0.722 for SGD vs. mean AUPR of 0.692 for `liblinear`. -Figure @fig:vector-image +To determine how relative performance trends with `liblinear` tend to compare across the genes in the Vogelstein dataset at large, we looked at the difference in performance between optimizers for the best-performing models for each gene (Figure {@fig:optimizer_compare_mutations}C). +The distribution is centered around 0 and more or less symmetrical, suggesting that across the gene set, `liblinear` and SGD tend to perform comparably to one another. +We saw that for 52/84 genes, performance for the best-performing model was better using SGD than `liblinear`, and for the other 32 genes performance was better using `liblinear`. +In order to quantify whether the overfitting tendencies (or lack thereof) also hold across the gene set, we plotted the difference in performance between the best-performing model and the largest (least regularized) model; classifiers with a large difference in performance exhibit strong overfitting, and classifiers with a small difference in performance do not overfit (Figure {@fig:optimizer_compare_mutations}D). +For SGD, the least regularized models tend to perform comparably to the best-performing models, whereas for `liblinear` the distribution is wider suggesting that overfitting is more common. -Table @tbl:bowling-scores - -Equation @eq:regular-equation - -Equation @eq:long-equation - -## Quotes and code - -> Quoted text - -> Quoted block of text -> -> Two roads diverged in a wood, and I— -> I took the one less traveled by, -> And that has made all the difference. - -Code `in the middle` of normal text, aka `inline code`. - -Code block with Python syntax highlighting: +![ +**A.** Performance vs. inverse regularization parameter for KRAS mutation status prediction, using the `liblinear` coordinate descent optimizer. Dotted lines indicate top performance value of the opposite optimizer. +**B.** Performance vs. regularization parameter for KRAS mutation status prediction, using the SGD optimizer. "Holdout" dataset is used for SGD learning rate selection, "test" data is completely held out from model selection and used for evaluation. +**C.** Distribution of performance difference between best-performing model for `liblinear` and SGD optimizers, across all 84 genes in Vogelstein driver gene set. Positive numbers on the x-axis indicate better performance using `liblinear`, and negative numbers indicate better performance using SGD. +**D.** Distribution of performance difference between best-performing model and largest (least regularized) model, for `liblinear` and SGD, across all 84 genes. Smaller numbers on the y-axis indicate less overfitting, and larger numbers indicate more overfitting. +](images/optimizers/figure_1.png){#fig:optimizer_compare_mutations width="100%"} -```python -from manubot.cite.doi import expand_short_doi +#### SGD is sensitive to learning rate selection -def test_expand_short_doi(): - doi = expand_short_doi("10/c3bp") - # a string too long to fit within page: - assert doi == "10.25313/2524-2695-2018-3-vliyanie-enhansera-copia-i-insulyatora-gypsy-na-sintez-ernk-modifikatsii-hromatina-i-svyazyvanie-insulyatornyh-belkov-vtransfetsirovannyh-geneticheskih-konstruktsiyah" -``` +The SGD results shown in Figure {@fig:optimizer_compare_mutations} select the best-performing learning rate using a grid search on the holdout dataset, independently for each regularization parameter. +We also compared against other learning rate scheduling approaches implemented in scikit-learn (see Methods for implementation details and grid search specifications). +For KRAS mutation prediction, we observed that the choice of initial learning rate and scheduling approach affects performance significantly, and other approaches to selecting the learning rate performed poorly relative to `liblinear` (black dotted lines in Figure {@fig:sgd_lr_schedulers}) and to the grid search. +We did not observe an improvement in performance over `liblinear` or the grid search for learning rate schedulers that decrease across epochs (Figure {@fig:sgd_lr_schedulers}A, C, and D), nor did we see comparable performance when we selected a single constant learning rate for all levels of regularization without the preceding grid search (Figure {@fig:sgd_lr_schedulers}B). +Notably, scikit-learn's default "optimal" learning rate schedule performed relatively poorly for this problem, suggesting that tuning the learning rate and selecting a well-performing scheduler is a critical component of applying SGD successfully for this problem (Figure {@fig:sgd_lr_schedulers}D). +We observed similar trends across all genes in the Vogelstein gene set, with other learning rate scheduling approaches performing poorly in aggregate relative to both `liblinear` and SGD with the learning rate grid search (Supplementary Figure {@fig:compare_all_lr}). -Code block with no syntax highlighting: +![ +**A.** Performance vs. regularization parameter for KRAS mutation prediction, using SGD optimizer with adaptive learning rate scheduler. Dotted line indicates top performance value using `liblinear`, from Figure {@fig:optimizer_compare_mutations}A. +**B.** Performance vs. regularization parameter, using SGD optimizer with constant learning rate scheduler and a learning rate of 0.0005. +**C.** Performance vs. regularization parameter, using SGD optimizer with inverse scaling learning rate scheduler. +**D.** Performance vs. regularization parameter, using SGD optimizer with "optimal" learning rate scheduler. +](images/optimizers/figure_2.png){#fig:sgd_lr_schedulers width="100%"} -``` -Exporting HTML manuscript -Exporting DOCX manuscript -Exporting PDF manuscript -``` +#### `liblinear` and SGD result in different models, with varying loss dynamics -## Figures +We sought to determine whether there was a difference in the sparsity of the models resulting from the different optimization schemes. +In general across all genes, the best-performing SGD models mostly tend to have many nonzero coefficients, but with a distinct positive tail, sometimes having few nonzero coefficients. +By contrast, the `liblinear` models are generally sparser with fewer than 2500 nonzero coefficients, out of ~16100 total input features, and a much narrower tail (Figure {@fig:optimizer_coefs}A). +The sum of the coefficient magnitudes, however, tends to be smaller on average across all levels of regularization for SGD than for `liblinear` (Figure {@fig:optimizer_coefs}B). +This effect is less pronounced for the other learning rate schedules shown in Figure {@fig:sgd_lr_schedulers}, with the other options resulting in larger coefficient magnitudes (Supplementary Figure {@fig:coef_weights_lr}). +These results suggest that the models fit by `liblinear` and SGD navigate the tradeoff between bias and variance in slightly different ways: `liblinear` tends to produce sparser models (more zero coefficients) as regularization increases, but if the learning rate is properly tuned, SGD coefficients tend to have smaller overall magnitudes as regularization increases. -![ -**A square image at actual size and with a bottom caption.** -Loaded from the latest version of image on GitHub. -](https://github.com/manubot/resources/raw/15493970f8882fce22bef829619d3fb37a613ba5/test/square.png "Square image"){#fig:square-image} -![ -**An image too wide to fit within page at full size.** -Loaded from a specific (hashed) version of the image on GitHub. -](https://github.com/manubot/resources/raw/15493970f8882fce22bef829619d3fb37a613ba5/test/wide.png "Wide image"){#fig:wide-image} +We also compared the components of the loss function across different levels of regularization between optimizers. +The LASSO logistic regression loss function can be broken down into a data-dependent component (the log-loss) and a parameter magnitude dependent component (the L1 penalty), which are added to get the total loss that is minimized by each optimizer; see Methods for additional details. +As regularization strength decreases for `liblinear`, the data loss collapses to near 0, and the L1 penalty dominates the overall loss (Figure {@fig:optimizer_coefs}C). +For SGD, on the other hand, the data loss decreases slightly as regularization strength decreases but remains relatively high (Figure {@fig:optimizer_coefs}D). +Other SGD learning rate schedules have similar loss curves to the `liblinear` results, although this does not result in improved classification performance (Supplementary Figure {@fig:loss_lr}). ![ -**A tall image with a specified height.** -Loaded from a specific (hashed) version of the image on GitHub. -](https://github.com/manubot/resources/raw/15493970f8882fce22bef829619d3fb37a613ba5/test/tall.png "Tall image"){#fig:tall-image height=3in} +**A.** Distribution across genes of the number of nonzero coefficients included in best-performing LASSO logistic regression models. Violin plot density estimations are clipped at the ends of the observed data range, and boxes show the median/IQR. +**B.** Distribution across genes of the sum of model coefficient weights for best-performing LASSO logistic regression models. +**C.** Decomposition of loss function for models fit using `liblinear` across regularization levels. 0 values on the y-axis are rounded up to machine epsilon; i.e. 2.22 x 10^-16^. +**D.** Decomposition of loss function for models fit using SGD across regularization levels. 0 values on the y-axis are rounded up to machine epsilon; i.e. 2.22 x 10^-16^. +](images/optimizers/figure_3.png){#fig:optimizer_coefs width="100%"} -![ -**A vector `.svg` image loaded from GitHub.** -The parameter `sanitize=true` is necessary to properly load SVGs hosted via GitHub URLs. -White background specified to serve as a backdrop for transparent sections of the image. -Note that if you want to export to Word (`.docx`), you need to download the image and reference it locally (e.g. `content/images/vector.svg`) instead of using a URL. -](https://raw.githubusercontent.com/manubot/resources/main/test/vector.svg?sanitize=true "Vector image"){#fig:vector-image height=2.5in .white} - -## Tables -| *Bowling Scores* | Jane | John | Alice | Bob | -|:-----------------|:-------------:|:-------------:|:-------------:|:-------------:| -| Game 1 | 150 | 187 | 210 | 105 | -| Game 2 | 98 | 202 | 197 | 102 | -| Game 3 | 123 | 180 | 238 | 134 | +### Discussion -Table: A table with a top caption and specified relative column widths. -{#tbl:bowling-scores} +Our work shows that optimizer choice presents tradeoffs in model selection for cancer transcriptomics. +We observed that LASSO logistic regression models for mutation status prediction fit using stochastic gradient descent were highly sensitive to learning rate tuning, but they tended to perform robustly across diverse levels of regularization and sparsity. +Coordinate descent implemented in `liblinear` did not require learning rate tuning, but generally performed best for a narrow range of fairly sparse models, overfitting as regularization strength decreased. +Tuning of regularization strength for `liblinear`, and learning rate (and regularization strength to a lesser degree) for SGD, are critical steps which must be considered as part of analysis pipelines. +The sensitivity we observed to these details highlights the importance of reporting exactly what optimizer was used, and how the relevant hyperparameters were selected, in studies that use machine learning models for transcriptomic data. -| | Digits 1-33 | Digits 34-66 | Digits 67-99 | Ref. | -|:--------|:-----------------------------------|:----------------------------------|:----------------------------------|:------------------------------------------------------------| -| pi | 3.14159265358979323846264338327950 | 288419716939937510582097494459230 | 781640628620899862803482534211706 | [`piday.org`](https://www.piday.org/million/) | -| e | 2.71828182845904523536028747135266 | 249775724709369995957496696762772 | 407663035354759457138217852516642 | [`nasa.gov`](https://apod.nasa.gov/htmltest/gifcity/e.2mil) | +To our knowledge, the phenomenon we observed with SGD has not been documented in other applications of machine learning to genomic or transcriptomic data. +In recent years, however, the broader machine learning research community has identified and characterized implicit regularization for SGD in many settings, including overparametrized or feature-rich problems as is often the case in transcriptomics [@arxiv:2108.04552; @arxiv:2003.06152; @url:http://proceedings.mlr.press/v134/zou21a.html]. +The resistance we observed of SGD-optimized models to decreased performance on held-out data as model complexity increases is often termed "benign overfitting": overfit models, in the sense that they fit the training data perfectly and perform worse on the test data, can still outperform models that do not fit the training data as well or that have stronger explicit regularization. +Benign overfitting has been attributed to optimization using SGD [@url:http://proceedings.mlr.press/v134/zou21a.html; @doi:10.1145/3446776], and similar patterns have been observed for both linear models and deep neural networks [@doi:10.1073/pnas.1907378117; @arxiv:1611.03530]. -Table: A table too wide to fit within page. -{#tbl:constant-digits} +Existing gene expression prediction benchmarks and pipelines typically use a single model implementation, and thus a single optimizer. +We recommend thinking critically about optimizer choice, but this can be challenging for researchers that are inexperienced with machine learning or unfamiliar with how certain models are fit under the hood. +For example, R's `glmnet` package uses a cyclical coordinate descent algorithm to fit logistic regression models [@doi:10.18637/jss.v033.i01], which would presumably behave similarly to `liblinear`, but this is somewhat opaque in the `glmnet` documentation itself. +Increased transparency and documentation in popular machine learning packages with respect to optimization, especially for models that are difficult to fit or sensitive to hyperparameter settings, would benefit new and unfamiliar users. -| | **Colors** | | -|:--------:|:--------------------------------:|:--------------------:| -| **Size** | **Text Color** | **Background Color** | -| big | blue | orange | -| small | black | white | -Table: A table with merged cells using the `attributes` plugin. -{#tbl: merged-cells} +Related to what we see in our SGD-optimized models, there exist other problems in gene expression analysis where using all available features is comparable to, or better than, using a subset. +For example, using the full gene set improves correlations between preclinical cancer models and their tissue of origin, as compared to selecting genes based on variability or tissue-specificity [@doi:10.1101/2023.04.11.536431]. +On the other hand, when predicting cell line viability from gene expression profiles, selecting features by Pearson correlation improves performance over using all features, similar to our `liblinear` classifiers [@doi:10.1101/2020.02.21.959627]. +In future work, it could be useful to explore if the coefficients found by `liblinear` and SGD emphasize the same pathways or functional gene sets, or if there are patterns to which mutation status classifiers (or other cancer transcriptomics classifiers) perform better with more/fewer nonzero coefficients. -## Equations -A LaTeX equation: +### Data and code availability -$$\int_0^\infty e^{-x^2} dx=\frac{\sqrt{\pi}}{2}$$ {#eq:regular-equation} +The data analyzed during this study were previously published as part of the TCGA Pan-Cancer Atlas project [@doi:10.1038/ng.2764], and are available from the NIH NCI Genomic Data Commons (GDC). +The scripts used to download and preprocess the datasets for this study are available at , and the code used to carry out the analyses in this study is available at , both under the open-source BSD 3-clause license. +Equivalent versions of Figure {@fig:optimizer_compare_mutations}A and {@fig:optimizer_compare_mutations}B for all 84 genes in the Vogelstein et al. 2013 gene set are available on Figshare at , under a CC0 license. +This manuscript was written using Manubot [@doi:10.1371/journal.pcbi.1007128] and is available on GitHub at under the CC0-1.0 license. +This research was supported in part by the University of Pittsburgh Center for Research Computing through the resources provided. Specifically, this work used the HTC cluster, which is supported by NIH award number S10OD028483. -An equation too long to fit within page: -$$x = a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s + t + u + v + w + x + y + z + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9$$ {#eq:long-equation} +### Supplementary Material -## Special +![Number of nonzero coefficients (model sparsity) across varying regularization parameter settings for KRAS mutation prediction using SGD and `liblinear` optimizers.](images/optimizers/supp_figure_1.png){#fig:compare_sparsity width="100%"} - [WARNING]{.semibold} _The following features are only supported and intended for `.html` and `.pdf` exports._ -_Journals are not likely to support them, and they may not display correctly when converted to other formats such as `.docx`._ +![Distribution of performance difference between best-performing model for `liblinear` and SGD optimizers, across all 84 genes in Vogelstein driver gene set, for varying SGD learning rate schedulers. Positive numbers on the x-axis indicate better performance using `liblinear`, and negative numbers indicate better performance using SGD.](images/optimizers/supp_figure_2.png){#fig:compare_all_lr width="100%" .page_break_before} -[Link styled as a button](https://manubot.org "Manubot Homepage"){.button} +![Sum of absolute value of coefficients + 1 for KRAS mutation prediction using SGD and `liblinear` optimizers, with varying learning rate schedules for SGD. Similar to the figures in the main paper, the `liblinear` x-axis represents the inverse of the $C$ regularization parameter; SGD x-axes represent the untransformed $\alpha$ parameter.](images/optimizers/supp_figure_3.png){#fig:coef_weights_lr width="100%" .page_break_before} -Adding arbitrary HTML attributes to an element using Pandoc's attribute syntax: +![Decomposition of loss function into data loss and L1 penalty components for KRAS mutation prediction using SGD optimizer, across regularization levels, using varying learning rate schedulers. 0 values on the y-axis are rounded up to machine epsilon, i.e. 2.22 x 10^-16^.](images/optimizers/supp_figure_4.png){#fig:loss_lr width="100%" .page_break_before} -::: {#some_id_1 .some_class style="background: #ad1457; color: white; margin-left: 40px;" title="a paragraph of text" data-color="white" disabled="true"} -Manubot Manubot Manubot Manubot Manubot. -Manubot Manubot Manubot Manubot. -Manubot Manubot Manubot. -Manubot Manubot. -Manubot. -::: -Adding arbitrary HTML attributes to an element with the Manubot `attributes` plugin (more flexible than Pandoc's method in terms of which elements you can add attributes to): - -Manubot Manubot Manubot Manubot Manubot. -Manubot Manubot Manubot Manubot. -Manubot Manubot Manubot. -Manubot Manubot. -Manubot. - - -Available background colors for text, images, code, banners, etc: - -`white`{.white} -`lightgrey`{.lightgrey} -`grey`{.grey} -`darkgrey`{.darkgrey} -`black`{.black} -`lightred`{.lightred} -`lightyellow`{.lightyellow} -`lightgreen`{.lightgreen} -`lightblue`{.lightblue} -`lightpurple`{.lightpurple} -`red`{.red} -`orange`{.orange} -`yellow`{.yellow} -`green`{.green} -`blue`{.blue} -`purple`{.purple} - -Using the [Font Awesome](https://fontawesome.com/) icon set: - - - - - - -[ - **Light Grey Banner**
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-useful for *warnings* - [manubot.org](https://manubot.org/) -]{.banner .lightred} ## References {.page_break_before} diff --git a/manuscript.pdf b/manuscript.pdf index c19bf34d821c48a06aae50d36fb16b4bc2a3cfe1..d00fca81f6d8bb102ae05f82a5cd567a7ed9a51b 100644 GIT binary patch literal 1395427 zcma%>V~l3O)9A;xZQHhO?r6uhZQJ(Fj&0kv&1Y=m?*Hb^MQ(EQ=5(byed_e7^oQ!| zUlqBMm;^mD0~-wa;sszIhM9+SqiEKGI{=N90%9i$aVumiJL{wrtEKDq{Ok6Bn%drKR)h$83my(*5)O)3X65H178UoerF*A~E;&_jBoH z@6Y11X4iJH`++K5#9`q9kZ-)q=G|=Xm!mi6+opkC??>_G_x&zsEAj(|)7IG8&)W%% ze8CbT)*E2*%DuNO_JN_n_w6B;r&G)_KBZ`P$kw1|=X;p@d+?@}@yB!0+a(kF@a{m6 zqf3dNkqSgK6ybFiJos2-aa$Hmp_jZ zG8u8I=jbIJTtfA5)}R8i-@wD%ZA8PpIJcWS=~4lTFqnfgiAQ^l^z>+PXs47S(d>?; z+UyWFCCMv`X@lj1pZU~hKK2rA85y7AdYj3S%VT2y>Q_)@3jge1G1wZPU)@>`C7{>b zj(*mj9jA1}lwLyDJzw~ z7a+XTl6YnkNL>@0>q3lL{T>`&_(S37eMKR>b7Eg|tc@BwR~I<4CL!uz`OnEib+2wf zcNRcKmQ7Y$y6$V!_zg3oo4$0s?krCm^>xjOesdc|Ac95b|LR#yFp28AP`b0>`lb47 zBrP?#6)dO;!dX>jw;^IuIxV^l#+I-yc^USnJ&|NdpFtlcig)9y+z?E8{7uDg`!1w} 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are capable of combining raw inputs into layers of intermediate features. These algorithms have recently shown impressive results across a variety of domains. Biology and medicine are data-rich disciplines, but the data are complex and often ill-understood. Hence, deep learning techniques may be particularly well suited to solve problems of these fields. We examine applications of deep learning to a variety of biomedical problems—patient classification, fundamental biological processes and treatment of patients—and discuss whether deep learning will be able to transform these tasks or if the biomedical sphere poses unique challenges. Following from an extensive literature review, we find that deep learning has yet to revolutionize biomedicine or definitively resolve any of the most pressing challenges in the field, but promising advances have been made on the prior state of the art. Even though improvements over previous baselines have been modest in general, the recent progress indicates that deep learning methods will provide valuable means for speeding up or aiding human investigation. Though progress has been made linking a specific neural network's prediction to input features, understanding how users should interpret these models to make testable hypotheses about the system under study remains an open challenge. Furthermore, the limited amount of labelled data for training presents problems in some domains, as do legal and privacy constraints on work with sensitive health records. Nonetheless, we foresee deep learning enabling changes at both bench and bedside with the potential to transform several areas of biology and medicine.", - "DOI": "10.1098/rsif.2017.0387", + "id": "1Cb94HrPD", + "URL": "https://arxiv.org/abs/1611.03530", + "number": "1611.03530", + "title": "Understanding deep learning requires rethinking generalization", + "issued": { + "date-parts": [ + [ + 2017, + 2, + 28 + ] + ] + }, + "author": [ + { + "given": "Chiyuan", + "family": "Zhang" + }, + { + "given": "Samy", + "family": "Bengio" + }, + { + "given": "Moritz", + "family": "Hardt" + }, + { + "given": "Benjamin", + "family": "Recht" + }, + { + "given": "Oriol", + "family": "Vinyals" + } + ], + "container-title": "arXiv", + "publisher": "arXiv", + "type": "report", + "abstract": " Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the model family, or to the regularization techniques used during training.\n Through extensive systematic experiments, we show how these traditional approaches fail to explain why large neural networks generalize well in practice. Specifically, our experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data. This phenomenon is qualitatively unaffected by explicit regularization, and occurs even if we replace the true images by completely unstructured random noise. We corroborate these experimental findings with a theoretical construction showing that simple depth two neural networks already have perfect finite sample expressivity as soon as the number of parameters exceeds the number of data points as it usually does in practice.\n We interpret our experimental findings by comparison with traditional models. ", + "note": "license: http://arxiv.org/licenses/nonexclusive-distrib/1.0/\nThis CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: arxiv:1611.03530" + }, + { + "id": "DIONdBGr", + "URL": "https://arxiv.org/abs/2003.06152", + "number": "2003.06152", + "title": "Can Implicit Bias Explain Generalization? Stochastic Convex Optimization as a Case Study", + "issued": { + "date-parts": [ + [ + 2020, + 12, + 23 + ] + ] + }, + "author": [ + { + "given": "Assaf", + "family": "Dauber" + }, + { + "given": "Meir", + "family": "Feder" + }, + { + "given": "Tomer", + "family": "Koren" + }, + { + "given": "Roi", + "family": "Livni" + } + ], + "container-title": "arXiv", + "publisher": "arXiv", + "type": "report", + "abstract": " The notion of implicit bias, or implicit regularization, has been suggested as a means to explain the surprising generalization ability of modern-days overparameterized learning algorithms. This notion refers to the tendency of the optimization algorithm towards a certain structured solution that often generalizes well. Recently, several papers have studied implicit regularization and were able to identify this phenomenon in various scenarios. We revisit this paradigm in arguably the simplest non-trivial setup, and study the implicit bias of Stochastic Gradient Descent (SGD) in the context of Stochastic Convex Optimization. As a first step, we provide a simple construction that rules out the existence of a \\emph{distribution-independent} implicit regularizer that governs the generalization ability of SGD. We then demonstrate a learning problem that rules out a very general class of \\emph{distribution-dependent} implicit regularizers from explaining generalization, which includes strongly convex regularizers as well as non-degenerate norm-based regularizations. Certain aspects of our constructions point out to significant difficulties in providing a comprehensive explanation of an algorithm's generalization performance by solely arguing about its implicit regularization properties. ", + "note": "license: http://arxiv.org/licenses/nonexclusive-distrib/1.0/\nThis CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: arxiv:2003.06152" + }, + { + "id": "kwgYU3iP", + "URL": "https://arxiv.org/abs/2108.04552", + "number": "2108.04552", + "title": "The Benefits of Implicit Regularization from SGD in Least Squares Problems", + "issued": { + "date-parts": [ + [ + 2022, + 7, + 12 + ] + ] + }, + "author": [ + { + "given": "Difan", + "family": "Zou" + }, + { + "given": "Jingfeng", + "family": "Wu" + }, + { + "given": "Vladimir", + "family": "Braverman" + }, + { + "given": "Quanquan", + "family": "Gu" + }, + { + "given": "Dean P.", + "family": "Foster" + }, + { + "given": "Sham M.", + "family": "Kakade" + } + ], + "container-title": "arXiv", + "publisher": "arXiv", + "type": "report", + "abstract": " Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to understand these issues in the simpler setting of linear regression (including both underparameterized and overparameterized regimes), where our goal is to make sharp instance-based comparisons of the implicit regularization afforded by (unregularized) average SGD with the explicit regularization of ridge regression. For a broad class of least squares problem instances (that are natural in high-dimensional settings), we show: (1) for every problem instance and for every ridge parameter, (unregularized) SGD, when provided with logarithmically more samples than that provided to the ridge algorithm, generalizes no worse than the ridge solution (provided SGD uses a tuned constant stepsize); (2) conversely, there exist instances (in this wide problem class) where optimally-tuned ridge regression requires quadratically more samples than SGD in order to have the same generalization performance. Taken together, our results show that, up to the logarithmic factors, the generalization performance of SGD is always no worse than that of ridge regression in a wide range of overparameterized problems, and, in fact, could be much better for some problem instances. More generally, our results show how algorithmic regularization has important consequences even in simpler (overparameterized) convex settings. ", + "note": "license: http://arxiv.org/licenses/nonexclusive-distrib/1.0/\nThis CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: arxiv:2108.04552" + }, + { + "publisher": "Elsevier BV", + "issue": "1", + "DOI": "10.1016/j.celrep.2018.03.046", + "type": "article-journal", + "page": "172-180.e3", + "source": "Crossref", + "title": "Machine Learning Detects Pan-cancer Ras Pathway Activation in The Cancer Genome Atlas", + "volume": "23", + "author": [ + { + "given": "Gregory P.", + "family": "Way" + }, + { + "given": "Francisco", + "family": "Sanchez-Vega" + }, + { + "given": "Konnor", + "family": "La" + }, + { + "given": "Joshua", + "family": "Armenia" + }, + { + "given": "Walid K.", + "family": "Chatila" + }, + { + "given": "Augustin", + "family": "Luna" + }, + { + "given": "Chris", + "family": "Sander" + }, + { + "given": "Andrew D.", + "family": "Cherniack" + }, + { + "given": "Marco", + "family": "Mina" + }, + { + "given": 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"family": "Ding" + }, + { + "given": "Catrina C.", + "family": "Fronick" + }, + { + "given": "Lucinda A.", + "family": "Fulton" + }, + { + "given": "Robert S.", + "family": "Fulton" + }, + { + "given": "Cyriac", + "family": "Kandoth" + }, + { + "given": "Elaine R.", + "family": "Mardis" + }, + { + "given": "Michael D.", + "family": "McLellan" + }, + { + "given": "Christopher A.", + "family": "Miller" + }, + { + "given": "Heather K.", + "family": "Schmidt" + }, + { + "given": "Richard K.", + "family": "Wilson" + }, + { + "given": "Daniel", + "family": "Crain" + }, + { + "given": "Erin", + "family": "Curley" + }, + { + "given": "Johanna", + "family": "Gardner" + }, + { + "given": "Kevin", + "family": "Lau" + }, + { + "given": "David", + "family": "Mallery" + }, + { + "given": "Scott", + "family": "Morris" + }, + { + "given": "Joseph", + "family": "Paulauskis" + }, + { + "given": "Robert", + "family": "Penny" + }, + { + "given": "Candace", + "family": "Shelton" + }, + { + "given": "Troy", 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"Fadlo", + "family": "Khuri" + }, + { + "given": "Kelly", + "family": "Magliocca" + }, + { + "given": "Shishir", + "family": "Maithel" + }, + { + "given": "Jeffrey J.", + "family": "Olson" + }, + { + "given": "Taofeek", + "family": "Owonikoko" + }, + { + "given": "Alan", + "family": "Pickens" + }, + { + "given": "Suresh", + "family": "Ramalingam" + }, + { + "given": "Dong M.", + "family": "Shin" + }, + { + "given": "Gabriel", + "family": "Sica" + }, + { + "given": "Erwin G.", + "family": "Van Meir" + }, + { + "given": "Hongzheng", + "family": "Zhang" + }, + { + "given": "Wil", + "family": "Eijckenboom" + }, + { + "given": "Ad", + "family": "Gillis" + }, + { + "given": "Esther", + "family": "Korpershoek" + }, + { + "given": "Leendert", + "family": "Looijenga" + }, + { + "given": "Wolter", + "family": "Oosterhuis" + }, + { + "given": "Hans", + "family": "Stoop" + }, + { + "given": "Kim E.", + "family": "van Kessel" + }, + { + "given": "Ellen C.", + "family": "Zwarthoff" + }, + { + "given": "Chiara", + "family": "Calatozzolo" + }, + { + "given": "Lucia", + "family": "Cuppini" + }, + { + "given": "Stefania", + "family": "Cuzzubbo" + }, + { + "given": "Francesco", + "family": "DiMeco" + }, + { + "given": "Gaetano", + "family": "Finocchiaro" + }, + { + "given": "Luca", + "family": "Mattei" + }, + { + "given": "Alessandro", + "family": "Perin" + }, + { + "given": "Bianca", + "family": "Pollo" + }, + { + "given": "Chu", + "family": "Chen" + }, + { + "given": "John", + "family": "Houck" + }, + { + "given": "Pawadee", + "family": "Lohavanichbutr" + }, + { + "given": "Arndt", + "family": "Hartmann" + }, + { + "given": "Christine", + "family": "Stoehr" + }, + { + "given": "Robert", + "family": "Stoehr" + }, + { + "given": "Helge", + "family": "Taubert" + }, + { + "given": "Sven", + "family": "Wach" + }, + { + "given": "Bernd", + "family": "Wullich" + }, + { + "given": "Witold", + "family": "Kycler" + }, + { + "given": "Dawid", + "family": "Murawa" + }, + { + "given": "Maciej", + "family": "Wiznerowicz" + }, + { + "given": "Ki", + "family": "Chung" + }, + { + "given": "W. Jeffrey", + "family": "Edenfield" + }, + { + "given": "Julie", + "family": "Martin" + }, + { + "given": "Eric", + "family": "Baudin" + }, + { + "given": "Glenn", + "family": "Bubley" + }, + { + "given": "Raphael", + "family": "Bueno" + }, + { + "given": "Assunta", + "family": "De Rienzo" + }, + { + "given": "William G.", + "family": "Richards" + }, + { + "given": "Steven", + "family": "Kalkanis" + }, + { + "given": "Tom", + "family": "Mikkelsen" + }, + { + "given": "Houtan", + "family": "Noushmehr" + }, + { + "given": "Lisa", + "family": "Scarpace" + }, + { + "given": "Nicolas", + "family": "Girard" + }, + { + "given": "Marta", + "family": "Aymerich" + }, + { + "given": "Elias", + "family": "Campo" + }, + { + "given": "Eva", + "family": "Giné" + }, + { + "given": "Armando López", + "family": "Guillermo" + }, + { + "given": "Nguyen", + "family": "Van Bang" + }, + { + "given": "Phan Thi", + "family": "Hanh" + }, + { + "given": "Bui Duc", + "family": "Phu" + }, + { + "given": "Yufang", + "family": "Tang" + }, + { + "given": "Howard", + "family": "Colman" + }, + { + "given": "Kimberley", + "family": "Evason" + }, + { + "given": "Peter R.", + "family": "Dottino" + }, + { + "given": "John A.", + "family": "Martignetti" + }, + { + "given": "Hani", + "family": "Gabra" + }, + { + "given": "Hartmut", + "family": "Juhl" + }, + { + "given": "Teniola", + "family": "Akeredolu" + }, + { + "given": "Serghei", + "family": "Stepa" + }, + { + "given": "Dave", + "family": "Hoon" + }, + { + "given": "Keunsoo", + "family": "Ahn" + }, + { + "given": "Koo Jeong", + "family": "Kang" + }, + { + "given": "Felix", + "family": "Beuschlein" + }, + { + "given": "Anne", + "family": "Breggia" + }, + { + "given": "Michael", + "family": "Birrer" + }, + { + "given": "Debra", + "family": "Bell" + }, + { + "given": "Mitesh", + "family": "Borad" + }, + { + "given": "Alan H.", + "family": "Bryce" + }, + { + "given": "Erik", + "family": "Castle" + }, + { + "given": "Vishal", + "family": "Chandan" + }, + { + "given": "John", + "family": "Cheville" + }, + { + "given": "John A.", + "family": "Copland" + }, + { + "given": "Michael", + "family": "Farnell" + }, + { + "given": "Thomas", + "family": "Flotte" + }, + { + "given": "Nasra", + "family": "Giama" + }, + { + "given": "Thai", + "family": "Ho" + }, + { + "given": "Michael", + "family": "Kendrick" + }, + { + "given": "Jean-Pierre", + "family": "Kocher" + }, + { + "given": "Karla", + "family": "Kopp" + }, + { + "given": "Catherine", + "family": "Moser" + }, + { + "given": "David", + "family": "Nagorney" + }, + { + "given": "Daniel", + "family": "O’Brien" + }, + { + "given": "Brian Patrick", + "family": "O’Neill" + }, + { + "given": "Tushar", + "family": "Patel" + }, + { + "given": "Gloria", + "family": "Petersen" + }, + { + "given": "Florencia", + "family": "Que" + }, + { + "given": "Michael", + "family": "Rivera" + }, + { + "given": "Lewis", + "family": "Roberts" + }, + { + "given": "Robert", + "family": "Smallridge" + }, + { + "given": "Thomas", + "family": "Smyrk" + }, + { + "given": "Melissa", + "family": "Stanton" + }, + { + "given": "R. Houston", + "family": "Thompson" + }, + { + "given": "Michael", + "family": "Torbenson" + }, + { + "given": "Ju Dong", + "family": "Yang" + }, + { + "given": "Lizhi", + "family": "Zhang" + }, + { + "given": "Fadi", + "family": "Brimo" + }, + { + "given": "Jaffer A.", + "family": "Ajani" + }, + { + "given": "Ana Maria", + "family": "Angulo Gonzalez" + }, + { + "given": "Carmen", + "family": "Behrens" + }, + { + "given": "Jolanta", + "family": "Bondaruk" + }, + { + "given": "Russell", + "family": "Broaddus" + }, + { + "given": "Bogdan", + "family": "Czerniak" + }, + { + "given": "Bita", + "family": "Esmaeli" + }, + { + "given": "Junya", + "family": "Fujimoto" + }, + { + "given": "Jeffrey", + "family": "Gershenwald" + }, + { + "given": "Charles", + "family": "Guo" + }, + { + "given": "Alexander J.", + "family": "Lazar" + }, + { + "given": "Christopher", + "family": "Logothetis" + }, + { + "given": "Funda", + "family": "Meric-Bernstam" + }, + { + "given": "Cesar", + "family": "Moran" + }, + { + "given": "Lois", + "family": "Ramondetta" + }, + { + "given": "David", + "family": "Rice" + }, + { + "given": "Anil", + "family": "Sood" + }, + { + "given": "Pheroze", + "family": "Tamboli" + }, + { + "given": "Timothy", + "family": "Thompson" + }, + { + "given": "Patricia", + "family": "Troncoso" + }, + { + "given": "Anne", + "family": "Tsao" + }, + { + "given": "Ignacio", + "family": "Wistuba" + }, + { + "given": "Candace", + "family": "Carter" + }, + { + "given": "Lauren", + "family": "Haydu" + }, + { + "given": "Peter", + "family": "Hersey" + }, + { + "given": "Valerie", + "family": "Jakrot" + }, + { + "given": "Hojabr", + "family": "Kakavand" + }, + { + "given": "Richard", + "family": "Kefford" + }, + { + "given": "Kenneth", + "family": "Lee" + }, + { + "given": "Georgina", + "family": "Long" + }, + { + "given": "Graham", + "family": "Mann" + }, + { + "given": "Michael", + "family": "Quinn" + }, + { + "given": "Robyn", + "family": "Saw" + }, + { + "given": "Richard", + "family": "Scolyer" + }, + { + "given": "Kerwin", + "family": "Shannon" + }, + { + "given": "Andrew", + "family": "Spillane" + }, + { + "given": "Jonathan", + "family": "Stretch" + }, + { + "given": "Maria", + "family": "Synott" + }, + { + "given": "John", + "family": "Thompson" + }, + { + "given": "James", + "family": "Wilmott" + }, + { + "given": "Hikmat", + "family": "Al-Ahmadie" + }, + { + "given": "Timothy A.", + "family": "Chan" + }, + { + "given": "Ronald", + "family": "Ghossein" + }, + { + "given": "Anuradha", + "family": "Gopalan" + }, + { + "given": "Douglas A.", + "family": "Levine" + }, + { + "given": "Victor", + "family": "Reuter" + }, + { + "given": "Samuel", + "family": "Singer" + }, + { + "given": "Bhuvanesh", + "family": "Singh" + }, + { + "given": "Nguyen Viet", + "family": "Tien" + }, + { + "given": "Thomas", + "family": "Broudy" + }, + { + "given": "Cyrus", + "family": "Mirsaidi" + }, + { + "given": "Praveen", + "family": "Nair" + }, + { + "given": "Paul", + "family": "Drwiega" + }, + { + "given": "Judy", + "family": "Miller" + }, + { + "given": "Jennifer", + "family": "Smith" + }, + { + "given": "Howard", + "family": "Zaren" + }, + { + "given": "Joong-Won", + "family": "Park" + }, + { + "given": "Nguyen Phi", + "family": "Hung" + }, + { + "given": "Electron", + "family": "Kebebew" + }, + { + "given": "W. Marston", + "family": "Linehan" + }, + { + "given": "Adam R.", + "family": "Metwalli" + }, + { + "given": "Karel", + "family": "Pacak" + }, + { + "given": "Peter A.", + "family": "Pinto" + }, + { + "given": "Mark", + "family": "Schiffman" + }, + { + "given": "Laura S.", + "family": "Schmidt" + }, + { + "given": "Cathy D.", + "family": "Vocke" + }, + { + "given": "Nicolas", + "family": "Wentzensen" + }, + { + "given": "Robert", + "family": "Worrell" + }, + { + "given": "Hannah", + "family": "Yang" + }, + { + "given": "Marc", + "family": "Moncrieff" + }, + { + "given": "Chandra", + "family": "Goparaju" + }, + { + "given": "Jonathan", + "family": "Melamed" + }, + { + "given": "Harvey", + "family": "Pass" + }, + { + "given": "Natalia", + "family": "Botnariuc" + }, + { + "given": "Irina", + "family": "Caraman" + }, + { + "given": "Mircea", + "family": "Cernat" + }, + { + "given": "Inga", + "family": "Chemencedji" + }, + { + "given": "Adrian", + "family": "Clipca" + }, + { + "given": "Serghei", + "family": "Doruc" + }, + { + "given": "Ghenadie", + "family": "Gorincioi" + }, + { + "given": "Sergiu", + "family": "Mura" + }, + { + "given": "Maria", + "family": "Pirtac" + }, + { + "given": "Irina", + "family": "Stancul" + }, + { + "given": "Diana", + "family": "Tcaciuc" + }, + { + "given": "Monique", + "family": "Albert" + }, + { + "given": "Iakovina", + "family": "Alexopoulou" + }, + { + "given": "Angel", + "family": "Arnaout" + }, + { + "given": "John", + "family": "Bartlett" + }, + { + "given": "Jay", + "family": "Engel" + }, + { + "given": "Sebastien", + "family": "Gilbert" + }, + { + "given": "Jeremy", + "family": "Parfitt" + }, + { + "given": "Harman", + "family": "Sekhon" + }, + { + "given": "George", + "family": "Thomas" + }, + { + "given": "Doris M.", + "family": "Rassl" + }, + { + "given": "Robert C.", + "family": "Rintoul" + }, + { + "given": "Carlo", + "family": "Bifulco" + }, + { + "given": "Raina", + "family": "Tamakawa" + }, + { + "given": "Walter", + "family": "Urba" + }, + { + "given": "Nicholas", + "family": "Hayward" + }, + { + "given": "Henri", + "family": "Timmers" + }, + { + "given": "Anna", + "family": "Antenucci" + }, + { + "given": "Francesco", + "family": "Facciolo" + }, + { + "given": "Gianluca", + "family": "Grazi" + }, + { + "given": "Mirella", + "family": "Marino" + }, + { + "given": "Roberta", + "family": "Merola" + }, + { + "given": "Ronald", + "family": "de Krijger" + }, + { + "given": "Anne-Paule", + "family": "Gimenez-Roqueplo" + }, + { + "given": "Alain", + "family": "Piché" + }, + { + "given": "Simone", + "family": "Chevalier" + }, + { + "given": "Ginette", + "family": "McKercher" + }, + { + "given": "Kivanc", + "family": "Birsoy" + }, + { + "given": "Gene", + "family": "Barnett" + }, + { + "given": "Cathy", + "family": "Brewer" + }, + { + "given": "Carol", + "family": "Farver" + }, + { + "given": "Theresa", + "family": "Naska" + }, + { + "given": "Nathan A.", + "family": "Pennell" + }, + { + "given": "Daniel", + "family": "Raymond" + }, + { + "given": "Cathy", + "family": "Schilero" + }, + { + "given": "Kathy", + "family": "Smolenski" + }, + { + "given": "Felicia", + "family": "Williams" + }, + { + "given": "Carl", + "family": "Morrison" + }, + { + "given": "Jeffrey A.", + "family": "Borgia" + }, + { + "given": "Michael J.", + "family": "Liptay" + }, + { + "given": "Mark", + "family": "Pool" + }, + { + "given": "Christopher W.", + "family": "Seder" + }, + { + "given": "Kerstin", + "family": "Junker" + }, + { + "given": "Larsson", + "family": "Omberg" + }, + { + "given": "Mikhail", + "family": "Dinkin" + }, + { + "given": "George", + "family": "Manikhas" + }, + { + "given": "Domenico", + "family": "Alvaro" + }, + { + "given": "Maria Consiglia", + "family": "Bragazzi" + }, + { + "given": "Vincenzo", + "family": "Cardinale" + }, + { + "given": "Guido", + "family": "Carpino" + }, + { + "given": "Eugenio", + "family": "Gaudio" + }, + { + "given": "David", + "family": "Chesla" + }, + { + "given": "Sandra", + "family": "Cottingham" + }, + { + "given": "Michael", + "family": "Dubina" + }, + { + "given": "Fedor", + "family": "Moiseenko" + }, + { + "given": "Renumathy", + "family": "Dhanasekaran" + }, + { + "given": "Karl-Friedrich", + "family": "Becker" + }, + { + "given": "Klaus-Peter", + "family": "Janssen" + }, + { + "given": "Julia", + "family": "Slotta-Huspenina" + }, + { + "given": "Mohamed H.", + "family": "Abdel-Rahman" + }, + { + "given": "Dina", + "family": "Aziz" + }, + { + "given": "Sue", + "family": "Bell" + }, + { + "given": "Colleen M.", + "family": "Cebulla" + }, + { + "given": "Amy", + "family": "Davis" + }, + { + "given": "Rebecca", + "family": "Duell" + }, + { + "given": "J. Bradley", + "family": "Elder" + }, + { + "given": "Joe", + "family": "Hilty" + }, + { + "given": "Bahavna", + "family": "Kumar" + }, + { + "given": "James", + "family": "Lang" + }, + { + "given": "Norman L.", + "family": "Lehman" + }, + { + "given": "Randy", + "family": "Mandt" + }, + { + "given": "Phuong", + "family": "Nguyen" + }, + { + "given": "Robert", + "family": "Pilarski" + }, + { + "given": "Karan", + "family": "Rai" + }, + { + "given": "Lynn", + "family": "Schoenfield" + }, + { + "given": "Kelly", + "family": "Senecal" + }, + { + "given": "Paul", + "family": "Wakely" + }, + { + "given": "Paul", + "family": "Hansen" + }, + { + "given": "Ronald", + "family": "Lechan" + }, + { + "given": "James", + "family": "Powers" + }, + { + "given": "Arthur", + "family": "Tischler" + }, + { + "given": "William E.", + "family": "Grizzle" + }, + { + "given": "Katherine C.", + "family": "Sexton" + }, + { + "given": "Alison", + "family": "Kastl" + }, + { + "given": "Joel", + "family": 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"given": "Robin K.", + "family": "Kelley" + }, + { + "given": "Charles N.", + "family": "Landen" + }, + { + "given": "Joanna", + "family": "Phillips" + }, + { + "given": "Michael", + "family": "Prados" + }, + { + "given": "Jeffry", + "family": "Simko" + }, + { + "given": "Karen", + "family": "Smith-McCune" + }, + { + "given": "Scott", + "family": "VandenBerg" + }, + { + "given": "Kevin", + "family": "Roggin" + }, + { + "given": "Ashley", + "family": "Fehrenbach" + }, + { + "given": "Ady", + "family": "Kendler" + }, + { + "given": "Suzanne", + "family": "Sifri" + }, + { + "given": "Ruth", + "family": "Steele" + }, + { + "given": "Antonio", + "family": "Jimeno" + }, + { + "given": "Francis", + "family": "Carey" + }, + { + "given": "Ian", + "family": "Forgie" + }, + { + "given": "Massimo", + "family": "Mannelli" + }, + { + "given": "Michael", + "family": "Carney" + }, + { + "given": "Brenda", + "family": "Hernandez" + }, + { + "given": "Benito", + "family": "Campos" + }, + { + "given": "Christel", + "family": "Herold-Mende" + }, + { + "given": "Christin", + "family": "Jungk" + }, + { + "given": "Andreas", + "family": "Unterberg" + }, + { + "given": "Andreas", + "family": "von Deimling" + }, + { + "given": "Aaron", + "family": "Bossler" + }, + { + "given": "Joseph", + "family": "Galbraith" + }, + { + "given": "Laura", + "family": "Jacobus" + }, + { + "given": "Michael", + "family": "Knudson" + }, + { + "given": "Tina", + "family": "Knutson" + }, + { + "given": "Deqin", + "family": "Ma" + }, + { + "given": "Mohammed", + "family": "Milhem" + }, + { + "given": "Rita", + "family": "Sigmund" + }, + { + "given": "Andrew K.", + "family": "Godwin" + }, + { + "given": "Rashna", + "family": "Madan" + }, + { + "given": "Howard G.", + "family": "Rosenthal" + }, + { + "given": "Clement", + "family": "Adebamowo" + }, + { + "given": "Sally N.", + "family": "Adebamowo" + }, + { + "given": "Alex", + "family": "Boussioutas" + }, + { + "given": "David", + "family": "Beer" + }, + { + "given": "Thomas", + "family": "Giordano" + }, + { + "given": "Anne-Marie", + "family": "Mes-Masson" + }, + { + "given": "Fred", + "family": "Saad" + }, + { + "given": "Therese", + "family": "Bocklage" + }, + { + "given": "Lisa", + "family": "Landrum" + }, + { + "given": "Robert", + "family": "Mannel" + }, + { + "given": "Kathleen", + "family": "Moore" + }, + { + "given": "Katherine", + "family": "Moxley" + }, + { + "given": "Russel", + "family": "Postier" + }, + { + "given": "Joan", + "family": "Walker" + }, + { + "given": "Rosemary", + "family": "Zuna" + }, + { + "given": "Michael", + "family": "Feldman" + }, + { + "given": "Federico", + "family": "Valdivieso" + }, + { + "given": "Rajiv", + "family": "Dhir" + }, + { + "given": "James", + "family": "Luketich" + }, + { + "given": "Edna M.", + "family": "Mora Pinero" + }, + { + "given": "Mario", + "family": "Quintero-Aguilo" + }, + { + "suffix": "Jr.", + "given": "Carlos Gilberto", + "family": "Carlotti" + }, + { + "given": "Jose Sebastião", + "family": "Dos Santos" + }, + { + "given": "Rafael", + "family": "Kemp" + }, + { + "given": "Ajith", + "family": "Sankarankuty" + }, + { + "given": "Daniela", + "family": "Tirapelli" + }, + { + "given": "James", + "family": "Catto" + }, + { + "given": "Kathy", + "family": "Agnew" + }, + { + "given": "Elizabeth", + "family": "Swisher" + }, + { + "given": "Jenette", + "family": "Creaney" + }, + { + "given": "Bruce", + "family": "Robinson" + }, + { + "given": "Carl Simon", + "family": "Shelley" + }, + { + "given": "Eryn M.", + "family": "Godwin" + }, + { + "given": "Sara", + "family": "Kendall" + }, + { + "given": "Cassaundra", + "family": "Shipman" + }, + { + "given": "Carol", + "family": "Bradford" + }, + { + "given": "Thomas", + "family": "Carey" + }, + { + "given": "Andrea", + "family": "Haddad" + }, + { + "given": "Jeffey", + "family": "Moyer" + }, + { + "given": "Lisa", + "family": "Peterson" + }, + { + "given": "Mark", + "family": "Prince" + }, + { + "given": "Laura", + "family": "Rozek" + }, + { + "given": "Gregory", + "family": "Wolf" + }, + { + "given": "Rayleen", + "family": "Bowman" + }, + { + "given": "Kwun M.", + "family": "Fong" + }, + { + "given": "Ian", + "family": "Yang" + }, + { + "given": "Robert", + "family": "Korst" + }, + { + "given": "W. Kimryn", + "family": "Rathmell" + }, + { + "given": "J. Leigh", + "family": "Fantacone-Campbell" + }, + { + "given": "Jeffrey A.", + "family": "Hooke" + }, + { + "given": "Albert J.", + "family": "Kovatich" + }, + { + "given": "Craig D.", + "family": "Shriver" + }, + { + "given": "John", + "family": "DiPersio" + }, + { + "given": "Bettina", + "family": "Drake" + }, + { + "given": "Ramaswamy", + "family": "Govindan" + }, + { + "given": "Sharon", + "family": "Heath" + }, + { + "given": "Timothy", + "family": "Ley" + }, + { + "given": "Brian", + "family": "Van Tine" + }, + { + "given": "Peter", + "family": "Westervelt" + }, + { + "given": "Mark A.", + "family": "Rubin" + }, + { + "given": "Jung Il", + "family": "Lee" + }, + { + "given": "Natália D.", + "family": "Aredes" + }, + { + "given": "Armaz", + "family": "Mariamidze" + } + ], + "container-title": "Cell Systems", + "language": "en", + "issued": { + "date-parts": [ + [ + 2018, + 3 + ] + ] + }, + "URL": "https://doi.org/gf9twn", + "container-title-short": "Cell Systems", + "PMCID": "PMC6075717", + "PMID": "29596782", + "id": "cDnF3a5Q", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1016/j.cels.2018.03.002" + }, + { + "publisher": "Elsevier BV", + "DOI": "10.1016/s0960-9776(09)70290-5", + "type": "article-journal", + "page": "S141-S145", + "source": "Crossref", + "title": "Prediction of adjuvant chemotherapy benefit in endocrine responsive, early breast cancer using multigene assays", + "volume": "18", + "author": [ + { + "given": "Kathy S.", + "family": "Albain" + }, + { + "given": "Soonmyung", + "family": "Paik" + }, + { + "given": "Laura", + "family": "van't Veer" + } + ], + "container-title": "The Breast", + "language": "en", + "issued": { + "date-parts": [ + [ + 2009, + 10 + ] + ] + }, + "URL": "https://doi.org/bp4rtw", + "container-title-short": "The Breast", + "id": "OW5P00JC", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1016/s0960-9776(09)70290-5" + }, + { + "publisher": "Springer Science and Business Media LLC", + "issue": "10", + "DOI": "10.1038/ng.2764", + "type": "article-journal", + "page": "1113-1120", + "source": "Crossref", + "title": "The Cancer Genome Atlas Pan-Cancer analysis project", + "volume": "45", + "author": [ + { + "given": "John N", + "family": "Weinstein" + }, + {}, + { + "given": "Eric A", + "family": "Collisson" + }, + { + "given": "Gordon B", + "family": "Mills" + }, + { + "given": "Kenna R Mills", + "family": "Shaw" + }, + { + "given": "Brad A", + "family": "Ozenberger" + }, + { + "given": "Kyle", + "family": "Ellrott" + }, + { + "given": "Ilya", + "family": "Shmulevich" + }, + { + "given": "Chris", + "family": "Sander" + }, + { + "given": "Joshua M", + "family": "Stuart" + } + ], + "container-title": "Nature Genetics", + "language": "en", + "issued": { + "date-parts": [ + [ + 2013, + 9, + 26 + ] + ] + }, + "URL": "https://doi.org/f3nt5c", + "container-title-short": "Nat Genet", + "PMCID": "PMC3919969", + "PMID": "24071849", + "id": "AK17eOgD", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1038/ng.2764" + }, + { + "publisher": "Proceedings of the National Academy of Sciences", + "issue": "48", + "abstract": "The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider when a perfect fit to training data in linear regression is compatible with accurate prediction. We give a characterization of linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy. The characterization is in terms of two notions of the effective rank of the data covariance. It shows that overparameterization is essential for benign overfitting in this setting: the number of directions in parameter space that are unimportant for prediction must significantly exceed the sample size. By studying examples of data covariance properties that this characterization shows are required for benign overfitting, we find an important role for finite-dimensional data: the accuracy of the minimum norm interpolating prediction rule approaches the best possible accuracy for a much narrower range of properties of the data distribution when the data lie in an infinite-dimensional space vs. when the data lie in a finite-dimensional space with dimension that grows faster than the sample size.", + "DOI": "10.1073/pnas.1907378117", + "type": "article-journal", + "page": "30063-30070", + "source": "Crossref", + "title": "Benign overfitting in linear regression", + "volume": "117", + "author": [ + { + "given": "Peter L.", + "family": "Bartlett" + }, + { + "given": "Philip M.", + "family": "Long" + }, + { + "given": "Gábor", + "family": "Lugosi" + }, + { + "given": "Alexander", + "family": "Tsigler" + } + ], + "container-title": "Proceedings of the National Academy of Sciences", + "language": "en", + "issued": { + "date-parts": [ + [ + 2020, + 4, + 24 + ] + ] + }, + "URL": "https://doi.org/gjgsxq", + "container-title-short": "Proc. Natl. Acad. Sci. U.S.A.", + "PMCID": "PMC7720150", + "PMID": "32332161", + "id": "jhZXoLtp", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1073/pnas.1907378117" + }, + { + "publisher": "Oxford University Press (OUP)", + "issue": "11", + "abstract": "Abstract\n \n Background\n Assigning every human gene to specific functions, diseases and traits is a grand challenge in modern genetics. Key to addressing this challenge are computational methods, such as supervised learning and label propagation, that can leverage molecular interaction networks to predict gene attributes. In spite of being a popular machine-learning technique across fields, supervised learning has been applied only in a few network-based studies for predicting pathway-, phenotype- or disease-associated genes. It is unknown how supervised learning broadly performs across different networks and diverse gene classification tasks, and how it compares to label propagation, the widely benchmarked canonical approach for this problem.\n \n \n Results\n In this study, we present a comprehensive benchmarking of supervised learning for network-based gene classification, evaluating this approach and a classic label propagation technique on hundreds of diverse prediction tasks and multiple networks using stringent evaluation schemes. We demonstrate that supervised learning on a gene’s full network connectivity outperforms label propagaton and achieves high prediction accuracy by efficiently capturing local network properties, rivaling label propagation’s appeal for naturally using network topology. We further show that supervised learning on the full network is also superior to learning on node embeddings (derived using node2vec), an increasingly popular approach for concisely representing network connectivity. These results show that supervised learning is an accurate approach for prioritizing genes associated with diverse functions, diseases and traits and should be considered a staple of network-based gene classification workflows.\n \n \n Availability and implementation\n The datasets and the code used to reproduce the results and add new gene classification methods have been made freely available.\n \n \n Contact\n arjun@msu.edu\n \n \n Supplementary information\n Supplementary data are available at Bioinformatics online.\n ", + "DOI": "10.1093/bioinformatics/btaa150", + "type": "article-journal", + "page": "3457-3465", + "source": "Crossref", + "title": "Supervised learning is an accurate method for network-based gene classification", + "volume": "36", + "author": [ + { + "given": "Renming", + "family": "Liu" + }, + { + "given": "Christopher A", + "family": "Mancuso" + }, + { + "given": "Anna", + "family": "Yannakopoulos" + }, + { + "given": "Kayla A", + "family": "Johnson" + }, + { + "given": "Arjun", + "family": "Krishnan" + } + ], + "container-title": "Bioinformatics", + "language": "en", + "editor": [ + { + "given": "Zhiyong", + "family": "Lu" + } + ], + "issued": { + "date-parts": [ + [ + 2020, + 4, + 14 + ] + ] + }, + "URL": "https://doi.org/gmvnfc", + "PMCID": "PMC7267831", + "PMID": "32129827", + "id": "bOvwnoRq", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1093/bioinformatics/btaa150" + }, + { + "publisher": "Cold Spring Harbor Laboratory", + "abstract": "AbstractAchieving precision oncology requires accurate identification of targetable cancer vulnerabilities in patients. Generally, genomic features are regarded as the state-of-the-art method for stratifying patients for targeted therapies. In this work, we conduct the first rigorous comparison of DNA- and expression-based predictive models for viability across five datasets encompassing chemical and genetic perturbations. We find that expression consistently outperforms DNA for predicting vulnerabilities, including many currently stratified by canonical DNA markers. Contrary to their perception in the literature, the most accurate expression-based models depend on few features and are amenable to biological interpretation. This work points to the importance of exploring more comprehensive expression profiling in clinical settings.", + "DOI": "10.1101/2020.02.21.959627", + "type": "manuscript", + "source": "Crossref", + "title": "Gene expression has more power for predicting in vitro cancer cell vulnerabilities than genomics", + "author": [ + { + "given": "Joshua M.", + "family": "Dempster" + }, + { + "given": "John M.", + "family": "Krill-Burger" + }, + { + "given": "James M.", + "family": "McFarland" + }, + { + "given": "Allison", + "family": "Warren" + }, + { + "given": "Jesse S.", + "family": "Boehm" + }, + { + "given": "Francisca", + "family": "Vazquez" + }, + { + "given": "William C.", + "family": "Hahn" + }, + { + "given": "Todd R.", + "family": "Golub" + }, + { + "given": "Aviad", + "family": "Tsherniak" + } + ], + "issued": { + "date-parts": [ + [ + 2020, + 2, + 24 + ] + ] + }, + "URL": "https://doi.org/ghczbr", + "id": "1CcaMqQZg", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1101/2020.02.21.959627" + }, + { + "publisher": "Cold Spring Harbor Laboratory", + "abstract": "AbstractPreclinical models like cancer cell lines and patient-derived xenografts (PDXs) are vital for studying disease mechanisms and evaluating treatment options. It is essential that they accurately recapitulate the disease state of interest to generate results that will translate in the clinic. Prior studies have demonstrated that preclinical models do not recapitulate all biological aspects of human tissues, particularly with respect to the tissue of origin gene expression signatures. Therefore, it is critical to assess how well preclinical model gene expression profiles correlate with human cancer tissues to inform preclinical model selection and data analysis decisions. Here we evaluated how well preclinical models recapitulate human cancer and non-diseased tissue gene expression patternsin silicowith respect to the full gene expression profile as well as subsetting by the most variable genes, genes significantly correlated with tumor purity, and tissue-specific genes by using publicly available gene expression profiles across multiple sources. We found that using the full gene set improves correlations between preclinical model and tissue global gene expression profiles, confirmed that GBM PDX global gene expression correlation to GBM tumor global gene expression outperforms GBM cell line to GBM tumor global gene expression correlations, and demonstrated that preclinical models in our study often failed to reproduce tissue-specific expression. While including additional genes for global gene expression comparison between cell lines and tissues decreases the overall correlation, it improves the relative rank between a cell line and its tissue of origin compared to other tissues. Our findings underscore the importance of using the full gene expression set measured when comparing preclinical models and tissues and confirm that tissue-specific patterns are better preserved in GBM PDX models than in GBM cell lines. Future studies can build on these findings to determine the specific pathways and gene sets recapitulated by particular preclinical models to facilitate model selection for a given study design or goal.", + "DOI": "10.1101/2023.04.11.536431", + "type": "manuscript", + "source": "Crossref", + "title": "Evaluating cancer cell line and patient-derived xenograft recapitulation of tumor and non-diseased tissue gene expression profilesin silico", + "author": [ + { + "given": "Avery S.", + "family": "Williams" + }, + { + "given": "Elizabeth J.", + "family": "Wilk" + }, + { + "given": "Jennifer L.", + "family": "Fisher" + }, + { + "given": "Brittany N.", + "family": "Lasseigne" + } + ], + "issued": { + "date-parts": [ + [ + 2023, + 4, + 13 + ] + ] + }, + "URL": "https://doi.org/gr6jr4", + "PMCID": "PMC10120639", + "PMID": "37090499", + "id": "lhYg2Yc3", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1101/2023.04.11.536431" + }, + { + "publisher": "Wiley", + "issue": "1", + "DOI": "10.1111/j.2517-6161.1996.tb02080.x", "type": "article-journal", - "page": "20170387", + "page": "267-288", "source": "Crossref", - "title": "Opportunities and obstacles for deep learning in biology and medicine", - "volume": "15", + "title": "Regression Shrinkage and Selection Via the Lasso", + "volume": "58", + "author": [ + { + "given": "Robert", + "family": "Tibshirani" + } + ], + "container-title": "Journal of the Royal Statistical Society: Series B (Methodological)", + "language": "en", + "issued": { + "date-parts": [ + [ + 1996, + 1 + ] + ] + }, + "URL": "https://doi.org/gfn45m", + "container-title-short": "Journal of the Royal Statistical Society: Series B (Methodological)", + "id": "kX2zf6UE", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1111/j.2517-6161.1996.tb02080.x" + }, + { + "publisher": "American Association for the Advancement of Science (AAAS)", + "issue": "6127", + "DOI": "10.1126/science.1235122", + "type": "article-journal", + "page": "1546-1558", + "source": "Crossref", + "title": "Cancer Genome Landscapes", + "volume": "339", "author": [ { - "given": "Travers", - "family": "Ching" + "given": "B.", + "family": "Vogelstein" }, { - "given": "Daniel S.", - "family": "Himmelstein" + "given": "N.", + "family": "Papadopoulos" }, { - "given": "Brett K.", - "family": "Beaulieu-Jones" + "given": "V. E.", + "family": "Velculescu" }, { - "given": "Alexandr A.", - "family": "Kalinin" + "given": "S.", + "family": "Zhou" }, { - "given": "Brian T.", - "family": "Do" + "given": "L. A.", + "family": "Diaz" }, { - "given": "Gregory P.", - "family": "Way" + "given": "K. W.", + "family": "Kinzler" + } + ], + "container-title": "Science", + "language": "en", + "issued": { + "date-parts": [ + [ + 2013, + 3, + 28 + ] + ] + }, + "URL": "https://doi.org/6rg", + "container-title-short": "Science", + "PMCID": "PMC3749880", + "PMID": "23539594", + "id": "809OyWlC", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1126/science.1235122" + }, + { + "publisher": "Association for Computing Machinery (ACM)", + "issue": "3", + "abstract": "Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small gap between training and test performance. Conventional wisdom attributes small generalization error either to properties of the model family or to the regularization techniques used during training.\n Through extensive systematic experiments, we show how these traditional approaches fail to explain why large neural networks generalize well in practice. Specifically, our experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data. This phenomenon is qualitatively unaffected by explicit regularization and occurs even if we replace the true images by completely unstructured random noise. We corroborate these experimental findings with a theoretical construction showing that simple depth two neural networks already have perfect finite sample expressivity as soon as the number of parameters exceeds the number of data points as it usually does in practice.\n We interpret our experimental findings by comparison with traditional models.\n We supplement this republication with a new section at the end summarizing recent progresses in the field since the original version of this paper.", + "DOI": "10.1145/3446776", + "type": "article-journal", + "page": "107-115", + "source": "Crossref", + "title": "Understanding deep learning (still) requires rethinking generalization", + "volume": "64", + "author": [ + { + "given": "Chiyuan", + "family": "Zhang" }, { - "given": "Enrico", - "family": "Ferrero" + "given": "Samy", + "family": "Bengio" }, { - "given": "Paul-Michael", - "family": "Agapow" + "given": "Moritz", + "family": "Hardt" }, { - "given": "Michael", - "family": "Zietz" + "given": "Benjamin", + "family": "Recht" + }, + { + "given": "Oriol", + "family": "Vinyals" + } + ], + "container-title": "Communications of the ACM", + "language": "en", + "issued": { + "date-parts": [ + [ + 2021, + 2, + 22 + ] + ] + }, + "URL": "https://doi.org/gh57fd", + "container-title-short": "Commun. ACM", + "id": "1HdGWY10w", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1145/3446776" + }, + { + "publisher": "Springer Science and Business Media LLC", + "issue": "4", + "DOI": "10.1186/gb-2011-12-4-r41", + "type": "article-journal", + "source": "Crossref", + "title": "GISTIC2.0 facilitates sensitive and confident localization of the targets of focal somatic copy-number alteration in human cancers", + "volume": "12", + "author": [ + { + "given": "Craig H", + "family": "Mermel" }, { - "given": "Michael M.", - "family": "Hoffman" + "given": "Steven E", + "family": "Schumacher" }, { - "given": "Wei", - "family": "Xie" + "given": "Barbara", + "family": "Hill" }, { - "given": "Gail L.", - "family": "Rosen" + "given": "Matthew L", + "family": "Meyerson" }, { - "given": "Benjamin J.", - "family": "Lengerich" + "given": "Rameen", + "family": "Beroukhim" }, { - "given": "Johnny", - "family": "Israeli" + "given": "Gad", + "family": "Getz" + } + ], + "container-title": "Genome Biology", + "language": "en", + "issued": { + "date-parts": [ + [ + 2011, + 4 + ] + ] + }, + "URL": "https://doi.org/dzhjqh", + "container-title-short": "Genome Biol", + "PMCID": "PMC3218867", + "PMID": "21527027", + "id": "rDV1hhfF", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1186/gb-2011-12-4-r41" + }, + { + "publisher": "Springer Science and Business Media LLC", + "issue": "1", + "abstract": "Abstract\n Background\n In studies of cellular function in cancer, researchers are increasingly able to choose from many -omics assays as functional readouts. Choosing the correct readout for a given study can be difficult, and which layer of cellular function is most suitable to capture the relevant signal remains unclear.\n \n Results\n We consider prediction of cancer mutation status (presence or absence) from functional -omics data as a representative problem that presents an opportunity to quantify and compare the ability of different -omics readouts to capture signals of dysregulation in cancer. From the TCGA Pan-Cancer Atlas that contains genetic alteration data, we focus on RNA sequencing, DNA methylation arrays, reverse phase protein arrays (RPPA), microRNA, and somatic mutational signatures as -omics readouts. Across a collection of genes recurrently mutated in cancer, RNA sequencing tends to be the most effective predictor of mutation state. We find that one or more other data types for many of the genes are approximately equally effective predictors. Performance is more variable between mutations than that between data types for the same mutation, and there is little difference between the top data types. We also find that combining data types into a single multi-omics model provides little or no improvement in predictive ability over the best individual data type.\n \n Conclusions\n Based on our results, for the design of studies focused on the functional outcomes of cancer mutations, there are often multiple -omics types that can serve as effective readouts, although gene expression seems to be a reasonable default option.\n ", + "DOI": "10.1186/s13059-022-02705-y", + "type": "article-journal", + "source": "Crossref", + "title": "Widespread redundancy in -omics profiles of cancer mutation states", + "volume": "23", + "author": [ + { + "given": "Jake", + "family": "Crawford" }, { - "given": "Jack", - "family": "Lanchantin" + "given": "Brock C.", + "family": "Christensen" }, { - "given": "Stephen", - "family": "Woloszynek" + "given": "Maria", + "family": "Chikina" }, { - "given": "Anne E.", - "family": "Carpenter" + "given": "Casey S.", + "family": "Greene" + } + ], + "container-title": "Genome Biology", + "language": "en", + "issued": { + "date-parts": [ + [ + 2022, + 6, + 27 + ] + ] + }, + "URL": "https://doi.org/gqfqnm", + "container-title-short": "Genome Biol", + "PMCID": "PMC9238138", + "PMID": "35761387", + "id": "cAxtCrBP", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1186/s13059-022-02705-y" + }, + { + "publisher": "American Society of Clinical Oncology (ASCO)", + "issue": "8", + "abstract": "Purpose To improve on current standards for breast cancer prognosis and prediction of chemotherapy benefit by developing a risk model that incorporates the gene expression–based “intrinsic” subtypes luminal A, luminal B, HER2-enriched, and basal-like. Methods A 50-gene subtype predictor was developed using microarray and quantitative reverse transcriptase polymerase chain reaction data from 189 prototype samples. Test sets from 761 patients (no systemic therapy) were evaluated for prognosis, and 133 patients were evaluated for prediction of pathologic complete response (pCR) to a taxane and anthracycline regimen. Results The intrinsic subtypes as discrete entities showed prognostic significance (P = 2.26E-12) and remained significant in multivariable analyses that incorporated standard parameters (estrogen receptor status, histologic grade, tumor size, and node status). A prognostic model for node-negative breast cancer was built using intrinsic subtype and clinical information. The C-index estimate for the combined model (subtype and tumor size) was a significant improvement on either the clinicopathologic model or subtype model alone. The intrinsic subtype model predicted neoadjuvant chemotherapy efficacy with a negative predictive value for pCR of 97%. Conclusion Diagnosis by intrinsic subtype adds significant prognostic and predictive information to standard parameters for patients with breast cancer. The prognostic properties of the continuous risk score will be of value for the management of node-negative breast cancers. The subtypes and risk score can also be used to assess the likelihood of efficacy from neoadjuvant chemotherapy. ", + "DOI": "10.1200/jco.2008.18.1370", + "type": "article-journal", + "page": "1160-1167", + "source": "Crossref", + "title": "Supervised Risk Predictor of Breast Cancer Based on Intrinsic Subtypes", + "volume": "27", + "author": [ + { + "given": "Joel S.", + "family": "Parker" }, { - "given": "Avanti", - "family": "Shrikumar" + "given": "Michael", + "family": "Mullins" }, { - "given": "Jinbo", - "family": "Xu" + "given": "Maggie C.U.", + "family": "Cheang" }, { - "given": "Evan M.", - "family": "Cofer" + "given": "Samuel", + "family": "Leung" }, { - "given": "Christopher A.", - "family": "Lavender" + "given": "David", + "family": "Voduc" }, { - "given": "Srinivas C.", - "family": "Turaga" + "given": "Tammi", + "family": "Vickery" }, { - "given": "Amr M.", - "family": "Alexandari" + "given": "Sherri", + "family": "Davies" }, { - "given": "Zhiyong", - "family": "Lu" + "given": "Christiane", + "family": "Fauron" }, { - "given": "David J.", - "family": "Harris" + "given": "Xiaping", + "family": "He" }, { - "given": "Dave", - "family": "DeCaprio" + "given": "Zhiyuan", + "family": "Hu" }, { - "given": "Yanjun", - "family": "Qi" + "given": "John F.", + "family": "Quackenbush" }, { - "given": "Anshul", - "family": "Kundaje" + "given": "Inge J.", + "family": "Stijleman" }, { - "given": "Yifan", - "family": "Peng" + "given": "Juan", + "family": "Palazzo" }, { - "given": "Laura K.", - "family": "Wiley" + "given": "J.S.", + "family": "Marron" }, { - "given": "Marwin H. S.", - "family": "Segler" + "given": "Andrew B.", + "family": "Nobel" }, { - "given": "Simina M.", - "family": "Boca" + "given": "Elaine", + "family": "Mardis" }, { - "given": "S. Joshua", - "family": "Swamidass" + "given": "Torsten O.", + "family": "Nielsen" }, { - "given": "Austin", - "family": "Huang" + "given": "Matthew J.", + "family": "Ellis" }, { - "given": "Anthony", - "family": "Gitter" + "given": "Charles M.", + "family": "Perou" }, { - "given": "Casey S.", - "family": "Greene" + "given": "Philip S.", + "family": "Bernard" } ], - "container-title": "Journal of The Royal Society Interface", + "container-title": "Journal of Clinical Oncology", "language": "en", "issued": { "date-parts": [ [ - 2018, - 4 + 2009, + 3, + 10 ] ] }, - "URL": "https://doi.org/gddkhn", - "container-title-short": "J. R. Soc. Interface.", - "PMCID": "PMC5938574", - "PMID": "29618526", - "id": "PZMP42Ak", - "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1098/rsif.2017.0387" + "URL": "https://doi.org/c2688w", + "container-title-short": "JCO", + "PMCID": "PMC2667820", + "PMID": "19204204", + "id": "lnK82Ey6", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1200/jco.2008.18.1370" }, { "publisher": "Public Library of Science (PLoS)", @@ -236,197 +6797,248 @@ "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1371/journal.pcbi.1007128" }, { - "publisher": "eLife Sciences Publications, Ltd", - "abstract": "The website Sci-Hub enables users to download PDF versions of scholarly articles, including many articles that are paywalled at their journal’s site. Sci-Hub has grown rapidly since its creation in 2011, but the extent of its coverage has been unclear. Here we report that, as of March 2017, Sci-Hub’s database contains 68.9% of the 81.6 million scholarly articles registered with Crossref and 85.1% of articles published in toll access journals. We find that coverage varies by discipline and publisher, and that Sci-Hub preferentially covers popular, paywalled content. For toll access articles, we find that Sci-Hub provides greater coverage than the University of Pennsylvania, a major research university in the United States. Green open access to toll access articles via licit services, on the other hand, remains quite limited. Our interactive browser at https://greenelab.github.io/scihub allows users to explore these findings in more detail. For the first time, nearly all scholarly literature is available gratis to anyone with an Internet connection, suggesting the toll access business model may become unsustainable.", - "DOI": "10.7554/elife.32822", + "publisher": "Public Library of Science (PLoS)", + "issue": "3", + "abstract": "By classifying patients into subgroups, clinicians can provide more effective care than using a uniform approach for all patients. Such subgroups might include patients with a particular disease subtype, patients with a good (or poor) prognosis, or patients most (or least) likely to respond to a particular therapy. Transcriptomic measurements reflect the downstream effects of genomic and epigenomic variations. However, high-throughput technologies generate thousands of measurements per patient, and complex dependencies exist among genes, so it may be infeasible to classify patients using traditional statistical models. Machine-learning classification algorithms can help with this problem. However, hundreds of classification algorithms exist—and most support diverse hyperparameters—so it is difficult for researchers to know which are optimal for gene-expression biomarkers. We performed a benchmark comparison, applying 52 classification algorithms to 50 gene-expression datasets (143 class variables). We evaluated algorithms that represent diverse machine-learning methodologies and have been implemented in general-purpose, open-source, machine-learning libraries. When available, we combined clinical predictors with gene-expression data. Additionally, we evaluated the effects of performing hyperparameter optimization and feature selection using nested cross validation. Kernel- and ensemble-based algorithms consistently outperformed other types of classification algorithms; however, even the top-performing algorithms performed poorly in some cases. Hyperparameter optimization and feature selection typically improved predictive performance, and univariate feature-selection algorithms typically outperformed more sophisticated methods. Together, our findings illustrate that algorithm performance varies considerably when other factors are held constant and thus that algorithm selection is a critical step in biomarker studies.", + "DOI": "10.1371/journal.pcbi.1009926", "type": "article-journal", + "page": "e1009926", "source": "Crossref", - "title": "Sci-Hub provides access to nearly all scholarly literature", - "volume": "7", + "title": "The ability to classify patients based on gene-expression data varies by algorithm and performance metric", + "volume": "18", "author": [ { - "given": "Daniel S", - "family": "Himmelstein" - }, - { - "given": "Ariel Rodriguez", - "family": "Romero" - }, - { - "given": "Jacob G", - "family": "Levernier" + "given": "Stephen R.", + "family": "Piccolo" }, { - "given": "Thomas Anthony", - "family": "Munro" + "given": "Avery", + "family": "Mecham" }, { - "given": "Stephen Reid", - "family": "McLaughlin" + "given": "Nathan P.", + "family": "Golightly" }, { - "given": "Bastian", - "family": "Greshake Tzovaras" + "given": "Jérémie L.", + "family": "Johnson" }, { - "given": "Casey S", - "family": "Greene" + "given": "Dustin B.", + "family": "Miller" } ], - "container-title": "eLife", + "container-title": "PLOS Computational Biology", "language": "en", + "editor": [ + { + "given": "Xing", + "family": "Chen" + } + ], "issued": { "date-parts": [ [ - 2018, + 2022, 3, - 1 + 11 ] ] }, - "URL": "https://doi.org/ckcj", - "PMCID": "PMC5832410", - "PMID": "29424689", - "id": "IhliSZDo", - "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.7554/elife.32822" + "URL": "https://doi.org/gr43qd", + "container-title-short": "PLoS Comput Biol", + "PMCID": "PMC8942277", + "PMID": "35275931", + "id": "1CdDn310M", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.1371/journal.pcbi.1009926" }, { - "id": "zBPP9YKu", - "type": "book", - "call-number": "Z286.O63 S83 2012", - "collection-title": "MIT Press essential knowledge series", - "event-place": "Cambridge, Mass", - "ISBN": "9780262517638", - "note": "OCLC: ocn754518563\nThis CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: isbn:9780262517638", - "number-of-pages": "242", - "publisher": "MIT Press", - "publisher-place": "Cambridge, Mass", - "source": "Library of Congress ISBN", - "title": "Open access", + "publisher": "Foundation for Open Access Statistic", + "issue": "1", + "DOI": "10.18637/jss.v033.i01", + "type": "article-journal", + "source": "Crossref", + "title": "Regularization Paths for Generalized Linear Models via Coordinate Descent", + "volume": "33", "author": [ { - "family": "Suber", - "given": "Peter" + "given": "Jerome", + "family": "Friedman" + }, + { + "given": "Trevor", + "family": "Hastie" + }, + { + "given": "Robert", + "family": "Tibshirani" } ], + "container-title": "Journal of Statistical Software", + "language": "en", "issued": { "date-parts": [ [ - "2012" + 2010 ] ] - } + }, + "URL": "https://doi.org/bb3d", + "container-title-short": "J. Stat. Soft.", + "id": "10aVUDFmA", + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: doi:10.18637/jss.v033.i01" }, { - "source": "PubMed", - "accessed": { + "id": "x24AA6cY", + "type": "webpage", + "URL": "https://wiki.eecs.yorku.ca/course_archive/2012-13/F/6328/_media/bottou-onlinelearning-98.pdf", + "title": "Online Learning and Stochastic Approximations", + "issued": { "date-parts": [ [ - 2023, - 8, - 17 + 1998 ] ] }, - "id": "mSMVRkoc", - "title": "Reproducibility of computational workflows is automated using continuous analysis", "author": [ { - "family": "Beaulieu-Jones", - "given": "Brett K" + "given": "Leon", + "family": "Bottou" + } + ], + "note": "Loaded from an external bibliography file by Manubot.\nsource_bibliography: manual-references.json\nstandard_id: online-learning" + }, + { + "id": "kajx4KkT", + "type": "paper-conference", + "abstract": "There is an increasing realization that algorithmic inductive biases are central in preventing overfitting; empirically, we often see a benign overfitting phenomenon in overparameterized settings for natural learning algorithms, such as stochastic gradient descent (SGD), where little to no explicit regularization has been employed. This work considers this issue in arguably the most basic setting: constant-stepsize SGD (with iterate averaging) for linear regression in the overparameterized regime. Our main result provides a sharp excess risk bound, stated in terms of the full eigenspectrum of the data covariance matrix, that reveals a bias-variance decomposition characterizing when generalization is possible: (i) the variance bound is characterized in terms of an effective dimension and (ii) the bias bound provides a sharp geometric characterization in terms of the location of the initial iterate (and how it aligns with the data covariance matrix). We reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares (minimum-norm interpolation) and ridge regression.", + "container-title": "Proceedings of Thirty Fourth Conference on Learning Theory", + "event-title": "Conference on Learning Theory", + "language": "en", + "page": "4633-4635", + "publisher": "PMLR", + "source": "proceedings.mlr.press", + "title": "Benign Overfitting of Constant-Stepsize SGD for Linear Regression", + "URL": "https://proceedings.mlr.press/v134/zou21a.html", + "author": [ + { + "family": "Zou", + "given": "Difan" }, { - "family": "Greene", - "given": "Casey S" + "family": "Wu", + "given": "Jingfeng" + }, + { + "family": "Braverman", + "given": "Vladimir" + }, + { + "family": "Gu", + "given": "Quanquan" + }, + { + "family": "Kakade", + "given": "Sham" } ], - "container-title-short": "Nat Biotechnol", - "container-title": "Nature biotechnology", - "publisher-place": "United States", - "ISSN": "1087-0156", - "issued": { + "accessed": { "date-parts": [ [ - 2017, - 4 + "2023", + 8, + 28 ] ] }, - "page": "342-346", - "volume": "35", - "issue": "4", - "PMID": "28288103", - "PMCID": "PMC6103790", - "DOI": "10.1038/nbt.3780", - "type": "article-journal", - "URL": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6103790/", - "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: pmc:PMC6103790" - }, - { - "title": "Bitcoin for the biological literature.", - "volume": "566", - "issue": "7742", - "page": "141-142", - "container-title": "Nature", - "container-title-short": "Nature", - "ISSN": "1476-4687", "issued": { "date-parts": [ [ - 2019, - 2 + "2021", + 7, + 21 ] ] }, - "author": [ - { - "given": "Douglas", - "family": "Heaven" - } - ], - "PMID": "30718888", - "DOI": "10.1038/d41586-019-00447-9", - "URL": "https://www.ncbi.nlm.nih.gov/pubmed/30718888", - "type": "article-journal", - "id": "126Wi5Us4", - "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: pubmed:30718888" + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: url:http://proceedings.mlr.press/v134/zou21a.html" }, { - "id": "1GGGHdsew", - "type": "report", - "language": "en-US", - "publisher": "Manubot", - "source": "greenelab.github.io", - "title": "Open collaborative writing with Manubot", - "URL": "https://greenelab.github.io/meta-review/", + "id": "43wsMmMv", + "type": "article-journal", + "abstract": "Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems. This package focuses on bringing machine learning to non-specialists using a general-purpose high-level language. Emphasis is put on ease of use, performance, documentation, and API consistency. It has minimal dependencies and is distributed under the simplified BSD license, encouraging its use in both academic and commercial settings. Source code, binaries, and documentation can be downloaded from http://scikit-learn.sourceforge.net.", + "container-title": "Journal of Machine Learning Research", + "ISSN": "1533-7928", + "issue": "85", + "page": "2825-2830", + "source": "jmlr.org", + "title": "Scikit-learn: Machine Learning in Python", + "title-short": "Scikit-learn", + "URL": "http://jmlr.org/papers/v12/pedregosa11a.html", + "volume": "12", "author": [ { - "family": "Himmelstein", - "given": "Daniel S." + "family": "Pedregosa", + "given": "Fabian" + }, + { + "family": "Varoquaux", + "given": "Gaël" + }, + { + "family": "Gramfort", + "given": "Alexandre" + }, + { + "family": "Michel", + "given": "Vincent" + }, + { + "family": "Thirion", + "given": "Bertrand" + }, + { + "family": "Grisel", + "given": "Olivier" + }, + { + "family": "Blondel", + "given": "Mathieu" + }, + { + "family": "Prettenhofer", + "given": "Peter" + }, + { + "family": "Weiss", + "given": "Ron" }, { - "family": "Rubinetti", + "family": "Dubourg", "given": "Vincent" }, { - "family": "Slochower", - "given": "David R." + "family": "Vanderplas", + "given": "Jake" + }, + { + "family": "Passos", + "given": "Alexandre" }, { - "family": "Hu", - "given": "Dongbo" + "family": "Cournapeau", + "given": "David" }, { - "family": "Malladi", - "given": "Venkat S." + "family": "Brucher", + "given": "Matthieu" }, { - "family": "Greene", - "given": "Casey S." + "family": "Perrot", + "given": "Matthieu" }, { - "family": "Gitter", - "given": "Anthony" + "family": "Duchesnay", + "given": "Édouard" } ], "accessed": { @@ -434,43 +7046,70 @@ [ "2023", 8, - 17 + 28 ] ] }, "issued": { "date-parts": [ [ - "2020", - 5, - 25 + "2011" ] ] }, - "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: url:https://greenelab.github.io/meta-review/" + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: url:https://jmlr.org/papers/v12/pedregosa11a.html" }, { - "id": "QhC8yJ7V", - "type": "document", - "note": "QID: Q56458321\nThis CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: wikidata:Q56458321", - "source": "Wikidata", - "title": "Plan S: Accelerating the transition to full and immediate Open Access to scientific publications", - "title-short": "Plan S", + "id": "Mm8xIDqq", + "type": "article-journal", + "abstract": "LIBLINEAR is an open source library for large-scale linear\nclassification. It supports logistic regression and linear support\nvector machines. We provide easy-to-use command-line tools and\nlibrary calls for users and developers. \nComprehensive documents are available for both beginners and advanced\nusers. Experiments demonstrate that LIBLINEAR is very efficient on\nlarge sparse data sets.", + "container-title": "Journal of Machine Learning Research", + "ISSN": "1533-7928", + "issue": "61", + "page": "1871-1874", + "source": "www.jmlr.org", + "title": "LIBLINEAR: A Library for Large Linear Classification", + "title-short": "LIBLINEAR", + "URL": "http://jmlr.org/papers/v9/fan08a.html", + "volume": "9", "author": [ { - "family": "S", - "given": "cOAlition" + "family": "Fan", + "given": "Rong-En" + }, + { + "family": "Chang", + "given": "Kai-Wei" + }, + { + "family": "Hsieh", + "given": "Cho-Jui" + }, + { + "family": "Wang", + "given": "Xiang-Rui" + }, + { + "family": "Lin", + "given": "Chih-Jen" } ], + "accessed": { + "date-parts": [ + [ + "2023", + 8, + 28 + ] + ] + }, "issued": { "date-parts": [ [ - "2018", - 9, - 4 + "2008" ] ] }, - "URL": "https://www.wikidata.org/wiki/Q56458321" + "note": "This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).\nstandard_id: url:https://www.jmlr.org/papers/v9/fan08a.html" } ] diff --git a/spelling-error-locations.txt b/spelling-error-locations.txt index 913ce1d..587808f 100644 --- a/spelling-error-locations.txt +++ b/spelling-error-locations.txt @@ -1,51 +1,195 @@ -content/02.delete-me.md:44:adipiscing -content/02.delete-me.md:44:aliqua -content/02.delete-me.md:44:amet -content/02.delete-me.md:44:consectetur -content/02.delete-me.md:44:dolore -content/02.delete-me.md:44:eiusmod -content/02.delete-me.md:44:elit -content/02.delete-me.md:44:incididunt -content/02.delete-me.md:44:ipsum -content/02.delete-me.md:44:labore -content/02.delete-me.md:44:Lorem -content/02.delete-me.md:44:magna -content/02.delete-me.md:44:sed -content/02.delete-me.md:44:tempor -content/02.delete-me.md:45:aliquip -content/02.delete-me.md:45:commodo -content/02.delete-me.md:45:consequat -content/02.delete-me.md:45:enim -content/02.delete-me.md:45:exercitation -content/02.delete-me.md:45:laboris 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-content/02.delete-me.md:47:sunt -content/02.delete-me.md:237:Pandoc's -content/02.delete-me.md:247:Pandoc's +content/02.introduction.md:5:transcriptomics +content/20.header.md:1:transcriptomic +content/20.header.md:3:Bioinformatics +content/20.header.md:3:biorxiv +content/20.header.md:3:bioRxiv +content/20.header.md:3:Optimizer’s +content/20.header.md:3:preprint +content/20.header.md:3:transcriptomic +content/20.header.md:5:Chikina +content/21.abstract.md:6:optimizers +content/21.abstract.md:7:scikit +content/21.abstract.md:8:optimizers +content/21.abstract.md:12:SGD +content/21.abstract.md:13:sparsities +content/21.abstract.md:14:SGD +content/21.abstract.md:14:sparsities +content/21.abstract.md:15:optimizers +content/21.abstract.md:15:tradeoffs +content/21.abstract.md:19:dataset +content/21.abstract.md:19:figshare +content/21.abstract.md:19:Vogelstein +content/22.introduction.md:3:bioinformatics +content/22.introduction.md:3:preclinically +content/22.introduction.md:4:datasets 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