diff --git a/lectures/live-coding/lecture07-in-lecture.ipynb b/lectures/live-coding/lecture07-in-lecture.ipynb new file mode 100644 index 0000000..e912716 --- /dev/null +++ b/lectures/live-coding/lecture07-in-lecture.ipynb @@ -0,0 +1,2902 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6050eb56-ab4c-4d68-ac6d-fc8ced6c162b", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Regularization with LASSO\n", + "**Computational Packages and Some Practical Issues**" + ] + }, + { + "cell_type": "markdown", + "id": "7a3b4b57-8423-48fa-a63d-8651e72df203", + "metadata": {}, + "source": [ + "## Learning Objectives:\n", + "\n", + "At the end of this lecture, you should be able to:\n", + "\n", + "- Describe the Lasso method and its advantages over the least squares;\n", + "\n", + "- Apply Lasso to a dataset using R;\n", + "\n", + "- Recognize the impact the Lasso method has on the inference of the regression coefficients;\n", + "\n", + "- Identify the problem of applying Lasso with categorical variables;\n", + "\n", + "\n", + "## 1. Quick Review of Linear Regression\n", + "\n", + "### 1.1 Linear Regression\n", + "\n", + "The linear regression equation is given by:\n", + "\n", + "$$\n", + "Y_i = \\beta_0 + \\beta_1X_{1i} + \\beta_2X_{2i} + \\ldots + \\beta_pX_{pi} + \\varepsilon_i,\\quad i=1,\\ldots,n\n", + "$$ where $\\varepsilon$ is a random error.\n", + "\n", + "
\n", + "\n", + "### 1.2 Fitting Linear Regression model\n", + "\n", + "Minimize the *residual sum of squares* (RSS):\n", + "\n", + "$$\n", + " RSS(\\beta_0, ..., \\beta_p) = \\sum_{i=1}^n \\left(y_i - \\beta_0 - \\beta_1X_{i1} - \\ldots - \\beta_p X_{ip}\\right)^2\n", + "$$\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "29a12c19-6b4f-4f61-95a5-0d5fc384dc5e", + "metadata": {}, + "source": [ + "## 2. Application\n" + ] + }, + { + "cell_type": "markdown", + "id": "d8b032b9-e183-4f45-a182-c43cba482fa3", + "metadata": { + "tags": [] + }, + "source": [ + "### 2.1 Loading some packages\n", + "\n", + "Let's start by loading some packages we will need." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "162fb8df-47b8-4881-85cc-69dfc660053d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "Attaching package: ‘gridExtra’\n", + "\n", + "\n", + "The following object is masked from ‘package:dplyr’:\n", + "\n", + " combine\n", + "\n", + "\n", + "Updating HTML index of packages in '.Library'\n", + "\n", + "Making 'packages.html' ...\n", + " done\n", + "\n" + ] + } + ], + "source": [ + "# Loading some libraries\n", + "library(tidyverse) \n", + "library(tidymodels)\n", + "library(knitr)\n", + "library(broom)\n", + "library(leaps)\n", + "library(glmnet)\n", + "library(gridExtra)\n", + "\n", + "install.packages('Brq')\n", + "library(Brq) # This package contains the data we will use" + ] + }, + { + "cell_type": "markdown", + "id": "a901e33e-5a3e-438f-aa21-0b1ffe008f9b", + "metadata": {}, + "source": [ + "### 2.2 Prostate Cancer data\n", + "\n", + "Data on 97 prostate cancer patients.\n", + "\n", + "- **lcavol**: log(cancer volume)\n", + "- **lweight**: log(prostate weight)\n", + "- **age**: age of the patient\n", + "- **lbph**: log(amount of benign prostatic hyperplasia)\n", + "- **svi**: Seminal vesicle invasion. (True or False)\n", + "- **lcp**: log(capsular penetration)\n", + "- **gleason**: Gleason score. The Gleason score measures how abnormal the tissue looks. The lower the score is, the more the cells look like regular prostate tissue. You can learn more about the [Gleason Score here](https://www.pcf.org/about-prostate-cancer/diagnosis-staging-prostate-cancer/gleason-score-isup-grade/)\n", + "- **pgg45**: Percentage Gleason scores 4 or 5. Scores 4 and 5 are considered very high; the cells barely look like normal prostate tissue.\n", + "- **lpsa**: log(prostate-specific antigen)\n", + "\n", + "We want to model `lpsa`, using the remaining variables as explanatory variables. Let's take a look at our data." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "ece666a3-9faf-4859-87c1-77058574f72f", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Loading the data\n", + "data(\"Prostate\")\n", + "cancer_prostate <- tibble(Prostate)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2d753648-aa9c-4b5a-9291-f6d7de8d040b", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 6 × 9
lcavollweightagelbphsvilcpgleasonpgg45lpsa
<dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl>
-0.57981852.76945950-1.3862940-1.3862946 0-0.4307829
-0.99425233.31962658-1.3862940-1.3862946 0-0.1625189
-0.51082562.69124374-1.3862940-1.386294720-0.1625189
-1.20397283.28278958-1.3862940-1.3862946 0-0.1625189
0.75141613.43237362-1.3862940-1.3862946 0 0.3715636
-1.04982213.22882650-1.3862940-1.3862946 0 0.7654678
\n" + ], + "text/latex": [ + "A tibble: 6 × 9\n", + "\\begin{tabular}{lllllllll}\n", + " lcavol & lweight & age & lbph & svi & lcp & gleason & pgg45 & lpsa\\\\\n", + " & & & & & & & & \\\\\n", + "\\hline\n", + "\t -0.5798185 & 2.769459 & 50 & -1.386294 & 0 & -1.386294 & 6 & 0 & -0.4307829\\\\\n", + "\t -0.9942523 & 3.319626 & 58 & -1.386294 & 0 & -1.386294 & 6 & 0 & -0.1625189\\\\\n", + "\t -0.5108256 & 2.691243 & 74 & -1.386294 & 0 & -1.386294 & 7 & 20 & -0.1625189\\\\\n", + "\t -1.2039728 & 3.282789 & 58 & -1.386294 & 0 & -1.386294 & 6 & 0 & -0.1625189\\\\\n", + "\t 0.7514161 & 3.432373 & 62 & -1.386294 & 0 & -1.386294 & 6 & 0 & 0.3715636\\\\\n", + "\t -1.0498221 & 3.228826 & 50 & -1.386294 & 0 & -1.386294 & 6 & 0 & 0.7654678\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 6 × 9\n", + "\n", + "| lcavol <dbl> | lweight <dbl> | age <dbl> | lbph <dbl> | svi <dbl> | lcp <dbl> | gleason <dbl> | pgg45 <dbl> | lpsa <dbl> |\n", + "|---|---|---|---|---|---|---|---|---|\n", + "| -0.5798185 | 2.769459 | 50 | -1.386294 | 0 | -1.386294 | 6 | 0 | -0.4307829 |\n", + "| -0.9942523 | 3.319626 | 58 | -1.386294 | 0 | -1.386294 | 6 | 0 | -0.1625189 |\n", + "| -0.5108256 | 2.691243 | 74 | -1.386294 | 0 | -1.386294 | 7 | 20 | -0.1625189 |\n", + "| -1.2039728 | 3.282789 | 58 | -1.386294 | 0 | -1.386294 | 6 | 0 | -0.1625189 |\n", + "| 0.7514161 | 3.432373 | 62 | -1.386294 | 0 | -1.386294 | 6 | 0 | 0.3715636 |\n", + "| -1.0498221 | 3.228826 | 50 | -1.386294 | 0 | -1.386294 | 6 | 0 | 0.7654678 |\n", + "\n" + ], + "text/plain": [ + " lcavol lweight age lbph svi lcp gleason pgg45 lpsa \n", + "1 -0.5798185 2.769459 50 -1.386294 0 -1.386294 6 0 -0.4307829\n", + "2 -0.9942523 3.319626 58 -1.386294 0 -1.386294 6 0 -0.1625189\n", + "3 -0.5108256 2.691243 74 -1.386294 0 -1.386294 7 20 -0.1625189\n", + "4 -1.2039728 3.282789 58 -1.386294 0 -1.386294 6 0 -0.1625189\n", + "5 0.7514161 3.432373 62 -1.386294 0 -1.386294 6 0 0.3715636\n", + "6 -1.0498221 3.228826 50 -1.386294 0 -1.386294 6 0 0.7654678" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Printing the data\n", + "cancer_prostate %>% head()" + ] + }, + { + "cell_type": "markdown", + "id": "8bf2cf60-c589-4e5d-aa7d-e6d631c9a3ae", + "metadata": {}, + "source": [ + "### 2.3 Data splitting\n", + "\n", + "The first thing we need to do is to split the data into a training and a test set." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "941bf635-3c23-4907-a157-cb134a3c3b85", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "set.seed(1) # Let's set the seed for reproducibility\n", + "\n", + "cancer_split <- initial_split(cancer_prostate, prop = 0.7)\n", + "cancer_train <- training(cancer_split)\n", + "cancer_test <- testing(cancer_split)" + ] + }, + { + "cell_type": "markdown", + "id": "483ebad0-a5f5-4469-a1fa-1f09c8473030", + "metadata": {}, + "source": [ + "### 2.4 Data Summary\n", + "\n", + "- Let's look at some summary statistics from our training set." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "154aac6f-881e-430f-891b-2ab2a62fa884", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + " lcavol lweight age lbph \n", + " Min. :-1.0498 Min. :2.375 Min. :44.00 Min. :-1.3863 \n", + " 1st Qu.: 0.6597 1st Qu.:3.395 1st Qu.:60.00 1st Qu.:-1.3863 \n", + " Median : 1.4586 Median :3.683 Median :64.00 Median : 0.4383 \n", + " Mean : 1.3839 Mean :3.684 Mean :63.88 Mean : 0.1861 \n", + " 3rd Qu.: 2.0417 3rd Qu.:3.893 3rd Qu.:68.00 3rd Qu.: 1.6292 \n", + " Max. : 3.8210 Max. :6.108 Max. :77.00 Max. : 2.3263 \n", + " lcp gleason pgg45 lpsa \n", + " Min. :-1.3863 Min. :6.000 Min. : 0.00 Min. :-0.4308 \n", + " 1st Qu.:-1.3863 1st Qu.:6.000 1st Qu.: 0.00 1st Qu.: 1.9283 \n", + " Median :-0.5978 Median :7.000 Median :15.00 Median : 2.6776 \n", + " Mean :-0.1920 Mean :6.731 Mean :22.99 Mean : 2.5994 \n", + " 3rd Qu.: 0.8109 3rd Qu.:7.000 3rd Qu.:40.00 3rd Qu.: 3.0469 \n", + " Max. : 2.9042 Max. :9.000 Max. :90.00 Max. : 5.5829 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "summary(cancer_train |> select(-svi))" + ] + }, + { + "cell_type": "markdown", + "id": "76f658bf-9256-45c9-86f8-b7862ec39a1d", + "metadata": {}, + "source": [ + "- Note the difference in units! This will be important." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "63c86f67-af52-4750-beb9-3822f853ff34", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "0.209" + ], + "text/latex": [ + "0.209" + ], + "text/markdown": [ + "0.209" + ], + "text/plain": [ + "[1] 0.209" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The proportion of true for `svi`\n", + "round(mean(cancer_train$svi), 3)" + ] + }, + { + "cell_type": "markdown", + "id": "427290bc-26a4-46ac-b12a-b010cc0bac40", + "metadata": {}, + "source": [ + "### 2.5 Fitting Linear Regression in R" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "d9022f55-90cd-4e1d-9c6c-38fb9c455348", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 9 × 5
termestimatestd.errorstatisticp.value
<chr><dbl><dbl><dbl><dbl>
(Intercept) 0.4451641411.756911004 0.25337898.008714e-01
lcavol 0.5657474130.110406555 5.12421943.576901e-06
lweight 0.3996320240.204722013 1.95207165.576296e-02
age -0.0105312620.014990277-0.70253954.851529e-01
lbph 0.0641624350.074144784 0.86536683.904029e-01
svi 0.9312335680.309218287 3.01157343.845797e-03
lcp -0.0677922970.116703587-0.58089305.635631e-01
gleason 0.0426665970.218193059 0.19554528.456496e-01
pgg45 0.0028365820.005302523 0.53494955.947299e-01
\n" + ], + "text/latex": [ + "A tibble: 9 × 5\n", + "\\begin{tabular}{lllll}\n", + " term & estimate & std.error & statistic & p.value\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\t (Intercept) & 0.445164141 & 1.756911004 & 0.2533789 & 8.008714e-01\\\\\n", + "\t lcavol & 0.565747413 & 0.110406555 & 5.1242194 & 3.576901e-06\\\\\n", + "\t lweight & 0.399632024 & 0.204722013 & 1.9520716 & 5.576296e-02\\\\\n", + "\t age & -0.010531262 & 0.014990277 & -0.7025395 & 4.851529e-01\\\\\n", + "\t lbph & 0.064162435 & 0.074144784 & 0.8653668 & 3.904029e-01\\\\\n", + "\t svi & 0.931233568 & 0.309218287 & 3.0115734 & 3.845797e-03\\\\\n", + "\t lcp & -0.067792297 & 0.116703587 & -0.5808930 & 5.635631e-01\\\\\n", + "\t gleason & 0.042666597 & 0.218193059 & 0.1955452 & 8.456496e-01\\\\\n", + "\t pgg45 & 0.002836582 & 0.005302523 & 0.5349495 & 5.947299e-01\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 9 × 5\n", + "\n", + "| term <chr> | estimate <dbl> | std.error <dbl> | statistic <dbl> | p.value <dbl> |\n", + "|---|---|---|---|---|\n", + "| (Intercept) | 0.445164141 | 1.756911004 | 0.2533789 | 8.008714e-01 |\n", + "| lcavol | 0.565747413 | 0.110406555 | 5.1242194 | 3.576901e-06 |\n", + "| lweight | 0.399632024 | 0.204722013 | 1.9520716 | 5.576296e-02 |\n", + "| age | -0.010531262 | 0.014990277 | -0.7025395 | 4.851529e-01 |\n", + "| lbph | 0.064162435 | 0.074144784 | 0.8653668 | 3.904029e-01 |\n", + "| svi | 0.931233568 | 0.309218287 | 3.0115734 | 3.845797e-03 |\n", + "| lcp | -0.067792297 | 0.116703587 | -0.5808930 | 5.635631e-01 |\n", + "| gleason | 0.042666597 | 0.218193059 | 0.1955452 | 8.456496e-01 |\n", + "| pgg45 | 0.002836582 | 0.005302523 | 0.5349495 | 5.947299e-01 |\n", + "\n" + ], + "text/plain": [ + " term estimate std.error statistic p.value \n", + "1 (Intercept) 0.445164141 1.756911004 0.2533789 8.008714e-01\n", + "2 lcavol 0.565747413 0.110406555 5.1242194 3.576901e-06\n", + "3 lweight 0.399632024 0.204722013 1.9520716 5.576296e-02\n", + "4 age -0.010531262 0.014990277 -0.7025395 4.851529e-01\n", + "5 lbph 0.064162435 0.074144784 0.8653668 3.904029e-01\n", + "6 svi 0.931233568 0.309218287 3.0115734 3.845797e-03\n", + "7 lcp -0.067792297 0.116703587 -0.5808930 5.635631e-01\n", + "8 gleason 0.042666597 0.218193059 0.1955452 8.456496e-01\n", + "9 pgg45 0.002836582 0.005302523 0.5349495 5.947299e-01" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Fitting the linear regression model\n", + "cancer_lm <- lm(lpsa ~ ., data = cancer_train)\n", + "\n", + "# Printing the coefficients' information\n", + "tidy(cancer_lm)" + ] + }, + { + "cell_type": "markdown", + "id": "f73d414c-1f83-44a3-9d32-5870fba962d8", + "metadata": {}, + "source": [ + "## 3. Improving OLS\n", + "\n", + "\n", + "### 3.1 Goals of linear regression\n", + "\n", + "There are mainly two reasons to fit a linear regression model:\n", + "\n", + "- **Prediction**: We want to predict the response based on the values of the predictors the best we can. So, we want our model to generalize well to unseen data.\n", + "\n", + "- **Inference**: We are interested in interpreting the association between our response and the predictors and checking their significance.\n", + "\n", + "### 3.2 Variable selection\n", + "\n", + "- Inference: use the simplest model possible (fewest predictors).\n", + " - easier to interpret\n", + " - the principle of parsimony (Occam's razor).\n", + "\n", + "
\n", + "\n", + "- Variable selection: select a subset of the most important predictors\n", + "\n", + "- Relevant to inference and prediction\n", + "\n", + "### 3.3 Regularization\n", + "\n", + "- Helps with the overfitting problem.\n", + "\n", + "- Overfitting: your model does very well in the training data but poorly in unseen data.\n", + "\n", + "- Regularization: restrict (or penalize) our optimization." + ] + }, + { + "cell_type": "markdown", + "id": "86764a76-1e5c-434e-86d0-cab138d2b1d4", + "metadata": {}, + "source": [ + "### 3.3.1 Lasso\n", + "\n", + "\n", + "#### **Example**\n", + "\n", + "- To be able to visualize what the LASSO method is doing, let's restrict our attention to a small case of two covariates.\n", + "\n", + "- Let us consider only two covariates of the Prostate Cancer dataset: `lcavol` and `lweight`.\n", + "\n", + "- We will consider all the covariates later." + ] + }, + { + "cell_type": "markdown", + "id": "41fc5f36-e199-4f1c-811f-0355f9bf490f", + "metadata": {}, + "source": [ + "**Step 1: Standardize the covariates**\n", + "\n", + "- Remember, in LASSO, we are penalyzing large $\\beta$s. \n", + " - Units matter!! \n", + "\n", + "
\n", + "\n", + "- To use LASSO, we **must** standardize the covariates.\n", + "\n", + "- In this case, we will also center the response (this is not required in general)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "f7677787-ddb2-4557-adeb-a296b3d456d5", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# Standardizing the predictors and centring the response\n", + "cancer_train_std <- \n", + " cancer_train |>\n", + " select(lcavol, lweight, lpsa) |>\n", + " mutate(lcavol = (lcavol - mean(lcavol)) / sd(lcavol),\n", + " lweight = (lweight - mean(lweight)) / sd(lweight),\n", + " lpsa = (lpsa - mean(lpsa)))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "8e88a9bc-7e52-45d0-940c-ee0e8f16c7a8", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 3 × 3
variablemeansd
<chr><dbl><dbl>
lcavol -3.388820e-171.000000
lweight-8.566815e-171.000000
lpsa 1.657332e-161.129692
\n" + ], + "text/latex": [ + "A tibble: 3 × 3\n", + "\\begin{tabular}{lll}\n", + " variable & mean & sd\\\\\n", + " & & \\\\\n", + "\\hline\n", + "\t lcavol & -3.388820e-17 & 1.000000\\\\\n", + "\t lweight & -8.566815e-17 & 1.000000\\\\\n", + "\t lpsa & 1.657332e-16 & 1.129692\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 3 × 3\n", + "\n", + "| variable <chr> | mean <dbl> | sd <dbl> |\n", + "|---|---|---|\n", + "| lcavol | -3.388820e-17 | 1.000000 |\n", + "| lweight | -8.566815e-17 | 1.000000 |\n", + "| lpsa | 1.657332e-16 | 1.129692 |\n", + "\n" + ], + "text/plain": [ + " variable mean sd \n", + "1 lcavol -3.388820e-17 1.000000\n", + "2 lweight -8.566815e-17 1.000000\n", + "3 lpsa 1.657332e-16 1.129692" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Let's double-check that everything is in order (for our mental sanity).\n", + "cancer_train_std |>\n", + " summarise(across(everything(), list(mean = mean, sd = sd))) |>\n", + " pivot_longer(cols = everything(), names_to = c(\"variable\", '.value'), names_sep = \"_\")" + ] + }, + { + "cell_type": "markdown", + "id": "b2937383-d345-49c5-be6b-7be06048ed5b", + "metadata": {}, + "source": [ + "- Ok, everything looks good. All variables are centred (i.e., have 0 mean), and only the predictors are scaled (i.e., have std. deviation of 1)." + ] + }, + { + "cell_type": "markdown", + "id": "a5527be7-5c04-404c-b091-489e712a80e3", + "metadata": {}, + "source": [ + "**The model**\n", + "\n", + "Our regression model is:\n", + "\n", + "$$\n", + "lpsa_i = \\beta_1\\times lcavol_i + \\beta_2\\times lweight_i + \\varepsilon_i\n", + "$$ \n", + "\n", + "Note that there's no intercept (we already removed it by centring all the variables)." + ] + }, + { + "cell_type": "markdown", + "id": "5b6defc1-1045-48ba-ab63-ea8a5bcdcd05", + "metadata": {}, + "source": [ + "**OLS**\n", + "\n", + "To fit our regression model using the least square, we need to minimize our RSS:\n", + "\n", + "$$\n", + " RSS(\\beta_1, \\beta_2) = \\sum_{i=1}^n \\left(lpsa_i - \\beta_1\\times lcavol_{i} - \\beta_2 \\times lweight_{i}\\right)^2\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "27ee1d3d-0308-4728-ab01-70d0b53881b3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 2 × 5
termestimatestd.errorstatisticp.value
<chr><dbl><dbl><dbl><dbl>
lcavol 0.78466880.094878588.2702429.668369e-12
lweight0.20459370.094878582.1563743.475968e-02
\n" + ], + "text/latex": [ + "A tibble: 2 × 5\n", + "\\begin{tabular}{lllll}\n", + " term & estimate & std.error & statistic & p.value\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\t lcavol & 0.7846688 & 0.09487858 & 8.270242 & 9.668369e-12\\\\\n", + "\t lweight & 0.2045937 & 0.09487858 & 2.156374 & 3.475968e-02\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 2 × 5\n", + "\n", + "| term <chr> | estimate <dbl> | std.error <dbl> | statistic <dbl> | p.value <dbl> |\n", + "|---|---|---|---|---|\n", + "| lcavol | 0.7846688 | 0.09487858 | 8.270242 | 9.668369e-12 |\n", + "| lweight | 0.2045937 | 0.09487858 | 2.156374 | 3.475968e-02 |\n", + "\n" + ], + "text/plain": [ + " term estimate std.error statistic p.value \n", + "1 lcavol 0.7846688 0.09487858 8.270242 9.668369e-12\n", + "2 lweight 0.2045937 0.09487858 2.156374 3.475968e-02" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Fit the model using OLS\n", + "\n", + "ols_lm <- lm(lpsa ~ 0 + lcavol + lweight, data = cancer_train_std)\n", + "\n", + "coef_ols_two_vars <- \n", + " ols_lm |>\n", + " coef() |>\n", + " as.numeric()\n", + "\n", + "tidy(ols_lm)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "25ddf2bf-bf77-44df-81a3-67b8716da0ac", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "37.8591578735627" + ], + "text/latex": [ + "37.8591578735627" + ], + "text/markdown": [ + "37.8591578735627" + ], + "text/plain": [ + "[1] 37.85916" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The RSS is: \n", + "rss_two_vars <- sum(ols_lm$residuals**2)\n", + "rss_two_vars" + ] + }, + { + "cell_type": "markdown", + "id": "3ff7dc94-90a3-4135-b08e-5ca6fb79724c", + "metadata": {}, + "source": [ + "#### Question\n", + "\n", + "Do you think LASSO will be able to beat OLS and get a smaller RSS? Why or why not?" + ] + }, + { + "cell_type": "markdown", + "id": "639184d2-9a8c-4c2d-9c05-d35c4ff2a769", + "metadata": { + "tags": [] + }, + "source": [ + "**LASSO**\n", + "\n", + "- Now let's apply LASSO.\n", + "\n", + "- We need to define the constraint. Let's use $\\left|\\beta_1\\right| + \\left|\\beta_2\\right| \\leq 0.5$\n", + " - this is equivalent to using $\\lambda = 0.311$;\n", + "\n", + "
\n", + "\n", + "- the OLS solution would not be a valid solution because $0.7847+ 0.2046 = 0.9893 \\geq 0.5$.\n", + "\n", + "- The only solutions that would be acceptable would be the ones that lie within the square shown in the figure below." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "5f3ed477-b5ef-48ef-a2cd-3391067fbc06", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "application/pdf": 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jw8IC9UeXBlIC9Gb250CiAgIC9TdWJ0eXBlIC9UcnVlVHlwZQogICAvQmFzZUZv\nbnQgL05TRkRNWStMaWJlcmF0aW9uU2FucwogICAvRmlyc3RDaGFyIDMyCiAgIC9MYXN0Q2hh\nciAxMTcKICAgL0ZvbnREZXNjcmlwdG9yIDE2IDAgUgogICAvRW5jb2RpbmcgL1dpbkFuc2lF\nbmNvZGluZwogICAvV2lkdGhzIFsgMjc3LjgzMjAzMSAwIDAgMCAwIDAgMCAwIDAgMCAwIDAg\nMCAzMzMuMDA3ODEyIDI3Ny44MzIwMzEgMCA1NTYuMTUyMzQ0IDU1Ni4xNTIzNDQgNTU2LjE1\nMjM0NCAwIDAgNTU2LjE1MjM0NCAwIDAgMCAwIDAgMCAwIDAgMCAwIDAgMCAwIDAgMCAwIDAg\nMCAwIDAgMCAwIDU1Ni4xNTIzNDQgMCAwIDc3Ny44MzIwMzEgMCAwIDAgNjY2Ljk5MjE4OCAw\nIDAgMCAwIDAgMCAwIDAgMCAwIDAgMCAwIDAgMCAwIDAgMCAwIDAgMCAyMjIuMTY3OTY5IDAg\nMCAyMjIuMTY3OTY5IDAgNTU2LjE1MjM0NCA1NTYuMTUyMzQ0IDAgMCAwIDUwMCAyNzcuODMy\nMDMxIDU1Ni4xNTIzNDQgXQogICAgL1RvVW5pY29kZSAxNCAwIFIKPj4KZW5kb2JqCjE3IDAg\nb2JqCjw8IC9MZW5ndGggMTggMCBSCiAgIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlCiAgIC9MZW5n\ndGgxIDM4MTIKPj4Kc3RyZWFtCnicrVZvcBPHFX+7J1kCgyU5tuOgwJ045JjKRsJ/iE2FddjS\nIUchtmyrSCYYCWxjaIJN5FDiNEUkTULEHwMhTBrSwod0EidQr0yo5U4T3D8fmk4y0HYymba0\nOJR+aeNxm4bMpAlW355sgpmmn7pzu/fe77332923u3cLBADmQQIEMG/d3S81fL/hbwA0irWo\nu2/bw/HfyQxAtwfAoN/20GPdR1fN24IRLwOQX/Z0xTo/eXVoGUBuArFVPQjkBXL0qKdRX9bz\ncP8ewzPwW9Qvo258qHdrDK5CGerXUM95OLanT7fN8BvUP0Jd6nukq2/gVx2fAixYgP2/DxS8\n+O7Uh3B0BliRIuB0jxh0xsmKVI7+sntEoChCSuCwnsMjhpx5X7hHCMcrLTaL3Waxeak0vYy8\nON2jD/37Da/uPeyJwuHpDbpG/bsgQR2MKd4XCshLZvK44YCBDriTbrpDGBCSgtAt7hbpfRXt\nFTsqhEJqp130Ufo01T9fSAoL7YX0bted/iqXS3HRqIu40plxZXXBnX5XlasqD/yKy6E4TjuE\n0w7mGHcIDiVhW6hCnjnPlScY8+52Na9cWVLbnA8LrbaS5nn6IvBUTlZ4PJP5tc7JWuLs2DRZ\nsch8edOuRYjUOp2OTbvMk5bala5NvABWgk9BHpWXltwjLyGFFtlStaqyYgktRNCwRCBLhMqK\nOlpdtYLK1XVEey/No4W6xures3u6T9fkCMKb165ufbG7Wl4TXFH7yMaaLz67e11wg8O/s7Gk\nJJiI7N1lrd3gVnu8S8kLkZf66++9p/bB6ukP9GcmLzvbn2xp7G2pyc+9d9Nz03+4Y+ldecvv\n31G/dmew/LD1wEDZ+lpJXj8QxlTr38UsP6HfB4XwmNbOKbrVUADfAsjw9b+lnd4A/9dizL7e\nhLdgGE7PMe2H72B7Zg52AX4Bb2jSSTj0P2jH4PUZ6Th8D579Sr8d8BTyvIL9f1miiD4GL2LP\naXgVT9NSUom9fnPG+kd4579TkQ/JO3AMXkPPYzCK7Unczo/Tj+EYbYGd9ANhHzwJz+EcT5Ht\nMIj+UXiFbIQORLOlA7qg9zbSJByBH8IAfgVuFv2+zL9g4Rev4sifQ54TsB123RLxGvmMvwQR\nx/4jOK9h+2aNBr+wg/6Y0hvPo3IUtmGNkd/jOA8Ja8Grt5AhAMUXCYfaWluCzU0PrL8/cF+j\nf53q8zbUr1U8dWvcX19dW3PvquqVLueK8rLSe0rsy+SlNrG4wGI25S3MnT/PaMjR6wRKoMwn\nq1GJlUSZrkT2+8u5LscQiN0CRJmEkDrXh0lRzU2a66mgZ/dtnkrWU7npScySG9zlZZJPlth7\nXllKk/ZgGOVDXjkisUlNXq/JuhJNWYiKzYYRkq+4xysxEpV8TN3dk/RFvciXyp3fIDd0zS8v\ng9T8XBRzUWKlcl+KlNYRTaClvtUpCsaFvFsm2H2xTtYcDPu8VpstUl7WyPJkr2aCBo2S5TQw\ng0YpbedDhwNSqmw8eTBthi1Rx4JOuTP2YJgJMYxNCr5k8llmcbDlspctH7hWjDPvYmWy18cc\nnDXQcrOfwJddEqa3m2UpeR1wOvLkR3OR2AySYzdfBy6qmN5kUpUlNRlNxtKZxBZZMsvJ1IIF\nyT4fZhiawxiVzvzkgJWpByPMHO0hq2cmq7YE2B3BjWFG7arUE0MEH49sq7HaLJFZn+avMgMm\nAtOBObXZ+MQPpBXYggpLBMNZXYIt1hFQnI4Io1FuGZ+1FIa4JTFruRkelXE1A63hJNPZGztl\nH+b4QIwltuB+2sGXQjazvE+tNjmZb5FqnRHNV8JRNXZul5i+BNOCUbcG4E7hIUmzpuR9mn1N\nWrGDEku+VCsjDefxyb7ozLO7pxgJpPIy5ndkl74tzBQvCkpsZo18KZcTI2JRXKLtXm35mFPu\nYwVy/c315MPybW8NayEzYayggUF060wUc/q8vGfJl4x6s0PgXHIwPAaVmYlUlWQ9VwlVEPFy\n56IG3FclvmS4s5uJUWsnnrRuKWy1MSWCCxyRw10RvtEwQ8snsDub1iOjDW3hQKscCLaHa2YG\nkjVwOp3ddxuNHLZmaXDLMaPdKIWpVYigoxkBSUVBrndjywx2I1YzJlxD+Vatd0thYoVZbxwG\nWy75urwzflyfQ6rn26nBP8uWw1XkafBbbRFbtpSXUTRLMx1jhJEn1T9rEuz4JUCMIo0G8VwW\n8z0vheUuOSL3SExpDvO58fRoWZ5JhpbzmbVqm6PdkixME9jQPKvwZDLVYb01uWydpt9U/beZ\nG2fNUtIoB1qTnFyeIQQceSMDvoWVGotVO/38PMtqDA8xnmjtPCdTisLPcg8/tkm5sTMpt4bd\nmjd+QZ6wDvC+8iFAAm315WX4MatPyWR/MKWQ/a3t4TEzXgH3t4VHKKEN0fpIahnawmMS/is0\nlHKUg1yRuMKZWlAxav7WMQUgoVl1GqDpW9MENMw4ixHYmqZZzDyLUcR0WUzRMF5wlYp7MMf4\n/fZJnXx9vh3pSUYjfI9DEWYEH8KIXIfZketShOYsYPPlrnqWK9dz3MNxTxbP4bgBdwYpIuVl\nA0mzT75eXK790Hm1/P0bfbt8m03u6yBm7yoXFmW0v/HFY+s/nI7eeN64zeAHfpGhsxcB/M/W\nTT8ADcbx6ej0J8ZtGtOthdKPwKt7CQ6jXIb37mxflLRAGxwEPTKZwQnt+Bf/gX4cb9g0NU95\nmxjQS9TaU0SnHCbjN8jwDQI3yPymz4n0ObneXCp+rJaK/1S/Jv5DdYibp/ZOUdNU09TmqcGp\n4Sl97l+vLRH/clUVTVeJclUtEj+cUMWLE1cmpiYEZaJylTqhFot/WnMl9Oc1QugKEUKXhYxo\nel98n2qN8utiq3rx5+Stcbf4s+YS8advl4qZMdKc7ksn0gK/Y2fS+RWqOOoZbRrtHd07emp0\neNTQN3J6hI0IphFy5Dxh54npPDGaznnOTZ0TEuwIo4yNs0tMcA57hunps+wsHT976Sx1nvGc\noafeIOOvX3qdNg0NDlHnUO/QhaHMkO7lk8vE5pOk9wS5cIKcUBeLLxy/U9x7fPB45rjgOqoc\npYmjpG8wMUiPDJLxwUuDtOng5oO9B4Vn1Ix46mny3adWiv1xjxjHGfTudIs71WpxESkO3VVZ\nHDJUCqEcnHMUbZuxPqiuFDe2+8V2fN9RkR/SY050FUKoVyAmwSPQqWAmSJVgdY2qBO2l6kWl\nrZk0qpLoR851WIdVckWdUmlCJUUVhSELMYXMFaYQXo5CBIgomjymzaa9Jp3J5DQ1mXpNg6Yr\npozJ4EFsyiT0AkkUET1JkyOptlaHI5A2ZPBna2jeyMh+Zm/lrRJsZzn7GYTaN4ZThByOPH3o\nENQvDrCK1jCLLo4EWCcKChcSKJgXp4qgPtIf73/UwQvJCtDvcMTjXCJcc2RtmkQccTSjW7w/\njkr/oxB3xPtJPN4P8X7E46QD5Xicw3GCEVjjjiw9MiBxBxJg05+ljsfRP47x8eIO3PL/AYrZ\n5gEKZW5kc3RyZWFtCmVuZG9iagoxOCAwIG9iagogICAyNjI5CmVuZG9iagoxOSAwIG9iago8\nPCAvTGVuZ3RoIDIwIDAgUgogICAvRmlsdGVyIC9GbGF0ZURlY29kZQo+PgpzdHJlYW0KeJxd\nkEFqxDAMRfc+hZYzi8FJug2BMt1k0U5p2gM4tpwaGtkoziK3r+IJU6jABun/Z76lr/1LTyGD\nfudoB8zgAznGJa5sEUacAqm6ARdsPrpy29kkpQUetiXj3JOPqm1Bf4i4ZN7g9OziiGcFAPrG\nDjnQBKev63AfDWtKPzgjZahU14FDL8+9mvRmZgRd4EvvRA95uwj25/jcEkJT+voeyUaHSzIW\n2dCEqq2kOmi9VKeQ3D/9oEZvvw0Xdy3u6mlsivuY79z+yUcouzJLnrKJEmSPEAgfy0ox7VQ5\nv0QdcJYKZW5kc3RyZWFtCmVuZG9iagoyMCAwIG9iagogICAyMjQKZW5kb2JqCjIxIDAgb2Jq\nCjw8IC9UeXBlIC9Gb250RGVzY3JpcHRvcgogICAvRm9udE5hbWU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6n/AH2v+NH9k3P91P8Avtf8aAKdFXP7Juf7qf8Afa/4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FSpUqNGjZydnfM36u7du/ft29evXz9XV9eX+MMBAwYUKlQofyMpCcUOQL5JSkry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\nrJnoOQCqHMIOgFMKCgpKSUkJDg62/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yend = y4)) +\n", + " labs(x = 'β1', y = 'β2') +\n", + " xlim(-1, 1) +\n", + " ylim(-1, 1) +\n", + " geom_point(aes(x,y), color = \"darkgreen\", size = 3, data = tibble(x = coef_ols_two_vars[1], y = coef_ols_two_vars[2])) + \n", + " annotate(\"text\", x = coef_ols_two_vars[1]-0.02, y = coef_ols_two_vars[2] + 0.06, label = \"OLS solution\")" + ] + }, + { + "cell_type": "markdown", + "id": "4f125102-79e3-4706-ab8c-096f5860c5bb", + "metadata": {}, + "source": [ + "- The LASSO method then needs to **shrink** the coefficients until they are in the square.\n", + " - The LASSO solution is the best solution in the feasible region (the square)." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "30692221-bc92-464b-879b-fadcf354cb36", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3 x 1 sparse Matrix of class \"dgCMatrix\"\n", + " s0\n", + "(Intercept) 1.938557e-16\n", + "lcavol 5.000075e-01\n", + "lweight . " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fit <- glmnet(cancer_train_std |> select(lcavol, lweight), cancer_train_std$lpsa, lambda = 0.311)\n", + "coef(fit)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "352331f9-151a-4dfb-b4d9-b9d96c9b3853", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "application/pdf": 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VhyXuY882viS+5HUj+SvSR5yZpxnR9+eyGNgHZ1n62+xpjGmhea50mTdB7vOw9T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\n0T+O8fHiDtzy/wGK2eYBCmVuZHN0cmVhbQplbmRvYmoKMTggMCB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6n/AH2v+NH9k3P91P8Avtf8aAKdFXP7Juf7qf8Afa/4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u3m5nb9+vURI0ZMmzatX79+CxcuTEhI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x2, y = y2, xend = x3, yend = y3)) +\n", + " geom_segment(aes(x = x3, y = y3, xend = x4, yend = y4)) +\n", + " geom_segment(aes(x = x1, y = y1, xend = x4, yend = y4)) +\n", + " labs(x = 'β1', y = 'β2') +\n", + " xlim(-1, 1) +\n", + " ylim(-1, 1) +\n", + " geom_point(aes(x,y), color = \"darkgreen\", size = 3, data = tibble(x = coef_ols_two_vars[1], y = coef_ols_two_vars[2])) + \n", + " annotate(\"text\", x = coef_ols_two_vars[1]-0.02, y = coef_ols_two_vars[2] + 0.06, label = \"OLS solution\") + \n", + " geom_point(aes(x,y), color = \"red\", size = 3, data = tibble(x=lasso_coef[2], y=lasso_coef[3])) + \n", + " annotate(\"text\", x = lasso_coef[2], y = lasso_coef[3] - 0.06, label = \"LASSO solution\")" + ] + }, + { + "cell_type": "markdown", + "id": "a9b1fa68-be3a-41a4-84a9-3469f4012ad9", + "metadata": { + "tags": [] + }, + "source": [ + "- The LASSO solution is in a vertice of the square, where one of the coefficients is zero.\n", + "\n", + "- This is not unusual. The LASSO solution will generally be in a vertice, where one or more of the coefficients are zero.\n", + "\n", + "- LASSO is also considered a variable selection method. The LASSO coefficients, in this case, were $\\beta_1 = 0.5$ and $\\beta_2=0$.\n", + "\n", + "## Open questions for our lecture\n", + "\n", + "- How do we pick $\\lambda$?\n", + "\n", + "- How does this `glmnet` package work?\n", + "\n", + "- What happens when we have categorical variables?\n", + "\n", + "- What happens when we have correlated variables?\n", + "\n", + "- How does the inference work with a LASSO solution?" + ] + }, + { + "cell_type": "markdown", + "id": "cb937ee7-f673-4da1-87b2-883ed9f958db", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Review Questions" + ] + }, + { + "cell_type": "markdown", + "id": "227d2d2c-7caf-4cab-9448-de6031081004", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "**True or False:**\n", + "\n", + "We must standardize the predictors before applying LASSO. " + ] + }, + { + "cell_type": "markdown", + "id": "552fcaa9-f931-4ae7-aa3b-da4876c47427", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Why? " + ] + }, + { + "cell_type": "markdown", + "id": "521f92c5-e465-4a91-993c-bda8d04566c7", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "**True or False:**\n", + "\n", + "The penalty term compromises LASSO's ability to fit the intercept term properly. For this reason, we should always center the response." + ] + }, + { + "cell_type": "markdown", + "id": "17305496-86ac-4036-9c7a-67fa5c429021", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "**True or False:**\n", + "\n", + "When we increase the $\\lambda$ value of the penalty term, the absolute value of each coefficient will be reduced by LASSO. " + ] + }, + { + "cell_type": "markdown", + "id": "f4da2d5b", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "- Imagine you have a restriction that $|\\beta_1|$ and $|\\beta_2|$ must be less than 1. \n", + " - You could have $|\\beta_1| = 0.6$ and $|\\beta_2| = 0.4$.\n", + " \n", + "
\n", + " \n", + "- Now, if we reduce our budget to 0.7. Possible results are:\n", + " - $|\\beta_1| = 0.7$ and $|\\beta_2| = 0$.\n", + " - $|\\beta_1| = 0$ and $|\\beta_2| = 0.7$." + ] + }, + { + "cell_type": "markdown", + "id": "b1c66e98", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "- The main idea is that the set of variables selected in a model with 4 variables might have different variables than in a model with 3 variables, or with 2 variables, and so on. " + ] + }, + { + "cell_type": "markdown", + "id": "e72471cd-7252-42fe-8460-ac02ad2212ae", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "**True or False:**\n", + "\n", + "When we increase the $\\lambda$ value of the penalty term, the sum of the absolute values of the coefficients will be reduced by LASSO. " + ] + }, + { + "cell_type": "markdown", + "id": "ef11eabb-0b63-4bf4-a2a5-bb3d555f8a48", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "**True or False:**\n", + "\n", + "LASSO's solution improves the Residual Sum of Squares in comparison to OLS, which is one of the reasons LASSO is superior to OLS. " + ] + }, + { + "cell_type": "markdown", + "id": "b864ec24-c7a6-497a-977b-19fd4d6e8af0", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Review the LASSO method" + ] + }, + { + "cell_type": "markdown", + "id": "27d02673-b50c-47bc-bdb1-2f5b688142a8", + "metadata": {}, + "source": [ + "In LASSO, change the OLS objective function by adding a penalty term to it:\n", + "\n", + "$$\n", + "LASSO(\\beta) = \\sum_{i=1}^n \\left(y_i - \\beta_0 - \\beta_1X_{i1} - \\ldots - \\beta_p X_{ip}\\right)^2 + {\\color{red}{\\lambda\\sum_{i=1}^p \\left|\\beta_i\\right|}}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "90a22354", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "- LASSO regularizes **and** selects features simultaneously;" + ] + }, + { + "cell_type": "markdown", + "id": "2346189f-3568-4b58-935a-b3dc733be49d", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "- The penalty term keeps the coefficients in check;\n", + " 1. Large values of $\\lambda$ will...?\n", + " 2. Small values of $\\lambda$ will...?\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "1433a0b2", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "- LASSO has no closed-form solution. We need to use algorithms; " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "8fd850f0", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "options(repr.plot.width = 20, repr.plot.height = 10)\n", + "\n", + "\n", + "lasso_large_lambda <- ggplot(tibble(x1 = -0.5, x2 = 0, x3 = 0.5, x4 = 0,\n", + " y1 = 0, y2 = 0.5, y3 = 0, y4 = -0.5)) + \n", + " geom_segment(aes(x = x1, y = y1, xend = x2, yend = y2)) +\n", + " geom_segment(aes(x = x2, y = y2, xend = x3, yend = y3)) +\n", + " geom_segment(aes(x = x3, y = y3, xend = x4, yend = y4)) +\n", + " geom_segment(aes(x = x1, y = y1, xend = x4, yend = y4)) +\n", + " labs(x = 'β1', y = 'β2', title = 'Large Lambda') +\n", + " xlim(-1, 1) +\n", + " ylim(-1, 1) +\n", + " geom_point(aes(x,y), color = \"darkgreen\", data = tibble(x=c(0.78), y=c(0.25)), size = 5) + \n", + " annotate(\"text\", x = 0.78-0.025, y = 0.18, label = \"OLS solution\", size = 8) + \n", + " theme(text = element_text(size = 30))\n", + "\n", + "\n", + "lasso_small_lambda <- ggplot(tibble(x1 = -2, x2 = 0, x3 = 2, x4 = 0,\n", + " y1 = 0, y2 = 2, y3 = 0, y4 = -2)) + \n", + " geom_segment(aes(x = x1, y = y1, xend = x2, yend = y2)) +\n", + " geom_segment(aes(x = x2, y = y2, xend = x3, yend = y3)) +\n", + " geom_segment(aes(x = x3, y = y3, xend = x4, yend = y4)) +\n", + " geom_segment(aes(x = x1, y = y1, xend = x4, yend = y4)) +\n", + " labs(x = 'β1', y = 'β2', title = 'Small Lambda') +\n", + " xlim(-3, 3) +\n", + " ylim(-3, 3) +\n", + " geom_point(aes(x,y), color = \"darkgreen\", data = tibble(x=c(0.78), y=c(0.25)), size = 5) + \n", + " annotate(\"text\", x = 0.78-0.02, y = 0.025 + 0.06, label = \"OLS solution\", size = 8) + \n", + " theme(text = element_text(size = 30))" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "1aa81f4b", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + 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U2FolVVij1s6OSwOJ4zOXJkwkQ2tLkiO6SO9nWNCteObUe4qpGRBxWzS8mSKpWs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\nICAvVyBbMSAyIDJdCiA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AaolIJCa6rEDqcXd+ar/8Ei7NfFNv8W/iHqQW58SaxrCRT3b8uAwaeTB6gM8oJ9di+lAH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\nFtZWUKwwwRqMK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Ccnp1v/8saNG7duwtnZefz48dOmTbOysoh/cwDAg0lP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title" + ] + }, + "metadata": { + "application/pdf": { + "height": 600, + "width": 1200 + }, + "image/jpeg": { + "height": 600, + "width": 1200 + }, + "image/png": { + "height": 600, + "width": 1200 + }, + "image/svg+xml": { + "height": 600, + "isolated": true, + "width": 1200 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "grid.arrange(lasso_large_lambda, lasso_small_lambda, ncol=2)" + ] + }, + { + "cell_type": "markdown", + "id": "b003daca", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Fitting LASSO \n", + "\n", + "### Prostate Cancer Data Problem" + ] + }, + { + "cell_type": "markdown", + "id": "bed4217d", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "- Do you want to learn how to fit LASSO to a dataset? " + ] + }, + { + "cell_type": "markdown", + "id": "58a9168e", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Let's start by loading the data" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "15ca1e83", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "# Loading the data\n", + "data(\"Prostate\")\n", + "\n", + "cancer_prostate <- \n", + " tibble(Prostate) \n", + "\n", + "# Printing the first 10 rows\n", + "head(cancer_prostate, 10)" + ] + }, + { + "cell_type": "markdown", + "id": "f396473b", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Data Dictionary\n", + "- **lcavol**: log(cancer volume) \n", + "- **lweight**: log(prostate weight)\n", + "- **age**: age of the patient\n", + "- **lbph**: log(amount of benign prostatic hyperplasia)\n", + "- **svi**: Seminal vesicle invasion. (True or False)\n", + "- **lcp**: log(capsular penetration)\n", + "- **gleason**: Gleason score. The Gleason score measures how abnormal the tissue looks. The lower the score is, the more the cells look like regular prostate tissue. You can learn more about the [Gleason Score here](https://www.pcf.org/about-prostate-cancer/diagnosis-staging-prostate-cancer/gleason-score-isup-grade/)\n", + "- **pgg45**: Percentage Gleason scores 4 or 5. Scores 4 and 5 are considered very high; the cells barely look like normal prostate tissue.\n", + "- **lpsa**: log(prostate-specific antigen)" + ] + }, + { + "cell_type": "markdown", + "id": "06064626", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "- Unfortunately, the units for the variables are not readily available and are unknown. \n", + "\n", + "- However, remember that the units are fundamental to interpreting the model. \n", + "\n", + "- So always make sure you know what the units are (even though I'm not sure what the units are in this case 😉). \n" + ] + }, + { + "cell_type": "markdown", + "id": "a6b77f3d", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Step 1: Data splitting\n", + "\n", + "Even though we will be fitting the LASSO method and not comparing it with other models (such as., k-nn regression), there's still plenty we still need to learn. For example, we still need to figure out the following:\n", + "\n", + "1. which covariates are relevant? \n", + "2. how much regularization should we use?\n", + "\n", + "We will use the data to make these decisions. But once we've selected the model, we need to be able to assess our model. We must use different data to do this. \n", + "\n", + "### Exercise 1\n", + "\n", + "So let's start by splitting the dataset into two sets: (1) train set, with 70% of the rows; and (2) test set, with the remaining 30%. \n", + "\n", + "_Save the train set in an object called `cancer_train` and test set in `cancer_test`._\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bfa0affe", + "metadata": {}, + "outputs": [], + "source": [ + "set.seed(20230530) # Do not change this\n", + "\n", + "cancer_prostate_split <- initial_split(..., prop = ...)\n", + "\n", + "cancer_train <- training(...)\n", + "cancer_test <- testing(...) " + ] + }, + { + "cell_type": "markdown", + "id": "8fa48902", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Exercise 2 \n", + "\n", + "Let's take a look at some summary quantities of our data. First, remove the `svi` variable (we don't want to calculate the summary of a binary variable). " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "faa8f6cf", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "... |> \n", + " ...(...) |>\n", + " summary()" + ] + }, + { + "cell_type": "markdown", + "id": "70226e16", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Step 2: Data Standardization\n", + "\n", + "- DO NOT FORGET: we need to standardize the data before applying LASSO!\n", + "\n", + "- Luckily for us, `glmnet` automatically standardizes the data for us! \n" + ] + }, + { + "cell_type": "markdown", + "id": "256eb98e", + "metadata": {}, + "source": [ + "## Step 3: Calling the `glmnet` function\n", + "\n", + "- `glmnet` is much more flexible than we need here. \n", + "\n", + "- So, let's focus only on the arguments that matter to us;\n", + "\n", + "- You can learn more with [`glmnet`'s vignette](https://glmnet.stanford.edu/articles/glmnet.html) or calling help `?glmnet`\n", + "\n", + "\n", + "\n", + "### Exercise 3\n", + "\n", + "To train a regression using LASSO, we can use the package `glmnet` in R. A few points to keep in mind:\n", + "\n", + "- `glmnet` actually uses a penalty function that generalizes LASSO. So, to reduce that generalization to LASSO, we set alpha = 1, which is the default. \n", + "\n", + "\n", + "- we can define a grid of values to evaluate by providing `lambda`, or we can just say how many lambdas we want to try out, and the function will define the values on its own. \n", + "\n", + "Now, fill in the code below to run LASSO with our `cancer_train` dataset. We want to try out 200 values for `lambda`. Store the model in an object named `lasso_cancer_fitted`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "34005f9e", + "metadata": {}, + "outputs": [], + "source": [ + "set.seed(20230530)\n", + "\n", + "# Fill in the code\n", + "\n", + "lasso_cancer_fitted <- # The variable to store the fitted model\n", + " glmnet(\n", + " x = ... |> select(-...), # First argument is the covariates (note that we need at least two columns)\n", + " y = cancer_train$..., # Second argument is the response\n", + " alpha = 1, # This is the default and is equivalent to LASSO \n", + " nlambda = ..., # the number of lambda values to try (default is 100)\n", + " #lambda = ..., # alternatively, the values of lambda you want try\n", + " standardize = TRUE, # Default value is TRUE\n", + " )\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "a7a11a12", + "metadata": {}, + "source": [ + "## Step 4: Extracting information from fitted model\n", + "\n", + "- The fitted model is a complex R object. \n", + "\n", + "- We will use some functions to extract the main parts of our model" + ] + }, + { + "cell_type": "markdown", + "id": "b60b73c5", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Exercise 4: the solution Path\n", + "\n", + "If we call the `plot` function directly on the fitted model and it will show the value of the coefficients for different values of lambda. We need to specify `xvar = 'lambda'`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e1ca7c2f", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "...(..., xvar = 'lambda')" + ] + }, + { + "cell_type": "markdown", + "id": "f34da8f6", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Exercise 5: grabbing the coefficients\n", + "\n", + "To see what the coefficients are, we call the `coef` function. Naturally, the values of coefficients depend on lambda. We can specify one or more values of lambda using the `s` argument. \n", + "- If you don't specify an `s` value, coefficients for all fitted $\\lambda$ will be returned;\n", + "- If you pick a $\\lambda$ not fitted by the model, it returns an \"approximation\" of the coefficients via interpolation; usually, this approximation is quite accurate. \n", + "\n", + "Obtain the coefficients for the model with $\\lambda=0.4$ and $\\lambda=0.1$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f020689b", + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "coef(..., s = c(...)) # here lambda is called `s` (as in \"size\" of the model, but lower s --> larger models)" + ] + }, + { + "cell_type": "markdown", + "id": "e3c29cf8", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Example 6: \n", + "\n", + "You can specify `exact = TRUE` to fit the model for a given $\\lambda$ and obtain the exact coefficients.\n", + " - In this case, we need to provide $x$ and $y$ again;" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3282ba8b", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "coef(lasso_cancer_fitted, \n", + " s = 0.4, \n", + " exact = TRUE, \n", + " x = cancer_train |> select(-lpsa),\n", + " y = cancer_train$lpsa)" + ] + }, + { + "cell_type": "markdown", + "id": "6d9d1882", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Step 5: making predictions\n", + "\n", + "### Exercise 6\n", + "\n", + "For prediction, the flow is very similar. We call the `predict` function and specify one or more lambda values we want in the `s` argument, but we also need to provide the `newx` matrix containing the data to be used for prediction. \n", + "\n", + "Unfortunately, `glmnet` doesn't play well with data frames and requires a matrix for `newx`.\n", + "\n", + "Use `cancer_train` data to obtain the predictions for the model `lasso_cancer_fitted` using $\\lambda=0.4$ and $\\lambda=0.1$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "28de91ff", + "metadata": { + "scrolled": true, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + " \n", + "predict(lasso_cancer_fitted, # Fitted model\n", + " newx = ... |> select(-...) |> as.matrix(), # A matrix (yes, tibble don't work) containing the data for prediction,\n", + " s = c(..., ...) # one or more values of lambda\n", + " ) " + ] + }, + { + "cell_type": "markdown", + "id": "0aff4e3d-2e40-4e65-8935-8f63c8b62a24", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Tuning: the process of selecting $\\lambda$: \n", + "\n", + "- We saw that `glmnet` fits LASSO for many different values of $\\lambda$. Which $\\lambda$ should we use? \n", + "\n", + "- This is called hyper-parameter tuning, and we usually do this using cross-validation. \n", + "\n", + "- We decide on a metric, such as MSE, and pick $\\lambda$ with the best performance in the cross-validation set. \n", + "\n", + "### Exercise 7\n", + "\n", + "Luckily for us, we don't need to do this ourselves. Instead, we can call `cv.glmnet`, which will do this entire process for us. The function is very similar to `glmnet`. Fill in the code below to run `cv.glmnet`. \n", + "\n", + "_Save the fitted model in an object called `cancer_cv_lasso`._" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7286570a", + "metadata": { + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "cancer_cv_lasso <- \n", + " cv.glmnet(\n", + " x = ... |> ... |> as.matrix(), # Covariates\n", + " y = ..., # Response\n", + " lambda = NULL, # A sequence of lambdas. Default lets the function choose its own sequence. \n", + " nfolds = 10, # number of folds to be used in the cross validation\n", + " standardize = TRUE\n", + " )\n", + "\n", + "print(cancer_cv_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "21c0dfc7-bf7d-4356-acaf-1e9c8529851e", + "metadata": {}, + "source": [ + "You can also select the measure you want to use to select $\\lambda$ (e.g., MSE, MAE) using `type.measure`. \n", + "\n", + "Check the documentation for more info: `?cv.glmnet`." + ] + }, + { + "cell_type": "markdown", + "id": "54a0dde2", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## `plot` functions for `cv.glmnet`\n", + "\n", + "The `coef` and `predict` functions work exactly the same as for the `glmnet`. But the plot function is a little different. Let's check! \n", + "\n", + "### Exercise 8\n", + "\n", + "Call the `plot` function directly on the fitted `cv.glmnet` model. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dde6b53d", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [], + "source": [ + "plot(...)" + ] + }, + { + "cell_type": "markdown", + "id": "e8d092e5", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "- The plot shows the estimated MSE for different value of lambdas; \n", + "\n", + "- The numbers at the top show how many variables are included in the model for each lambda; \n", + "\n", + "- The error bars represent the variation of MSE over the different folds of the cross-validation;\n", + "\n", + "- First vertical dotted line (on the left), the best CV $\\lambda$ value; \n", + "\n", + "- Second vertical dotted line (on the right), the most regularized model (highest $\\lambda$) that the CV performance is 1 std. dev. from the best one. " + ] + }, + { + "cell_type": "markdown", + "id": "50faa166", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## `coef`, and `predict` functions for `cv.glmnet`\n", + "\n", + "- They work pretty much the same way;\n", + "\n", + "- Except now we can use two string for `s` argument:\n", + " - \"lambda.1se\"\n", + " - \"lambda.min\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b3a7143e", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [], + "source": [ + "coef(cancer_cv_lasso, \n", + " s = 'lambda.1se') # two new possible values: \"lambda.min\" or \"lambda.1se\" (default)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "81887bcb", + "metadata": {}, + "outputs": [], + "source": [ + "coef(cancer_cv_lasso, \n", + " s = 'lambda.min')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "66aed716", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [], + "source": [ + "predict(\n", + " cancer_cv_lasso, \n", + " newx = cancer_train |> select(-lpsa) |> as.matrix(),\n", + " s = 'lambda.1se') " + ] + }, + { + "cell_type": "markdown", + "id": "28f1b3c2", + "metadata": {}, + "source": [ + "# Some \"caveats\"\n" + ] + }, + { + "cell_type": "markdown", + "id": "b312718e", + "metadata": {}, + "source": [ + "## LASSO and categorical variable\n", + "\n", + "- When we fit categorical data, we use dummy variables (one-hot-encoding); \n", + "\n", + "\n", + "- What happens if LASSO removes one of the dummy variables but leaves the others? Does it make sense? \n", + "\n", + "\n", + "- There are some LASSO extensions, such as Group LASSO, that deal with this. " + ] + }, + { + "cell_type": "markdown", + "id": "1179d4fa-8601-41c7-b766-33087bb05c36", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### LASSO Inference\n", + "\n", + "- The LASSO method gives biased estimates for the parameters; (you will see this in the worksheet)\n", + " - Biased estimates are not the end of the world, but can make inference trickier; \n", + "\n", + "
\n", + "\n", + "- Confidence intervals are not immediately available for LASSO\n", + " - There are a few proposals for confidence intervals available for coefficients and hypothesis testing for LASSO models; " + ] + }, + { + "cell_type": "markdown", + "id": "ead2e9eb", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "- The trickier part is that inference for LASSO triggers the post-selection inference problem;\n", + " - I have prepared an activity to walk you through this problem and illustrate the bias in the LASSO estimate. \n", + " \n", + "
\n", + " \n", + "- An approach to deal with this is to use data split. \n", + " - In the first split, we run LASSO to select the variables; \n", + " - In the second split, we fit OLS and use that inference; " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.2.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/lectures/live-coding/lecture07-more-on-regularized-regression-methods.ipynb b/lectures/live-coding/lecture07-more-on-regularized-regression-methods.ipynb new file mode 100644 index 0000000..4b314b9 --- /dev/null +++ b/lectures/live-coding/lecture07-more-on-regularized-regression-methods.ipynb @@ -0,0 +1,2419 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nbgrader": { + "grade": false, + "grade_id": "cell-3410823c297a225b", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + }, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Introduction to Regularized Regression Methods" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nbgrader": { + "grade": false, + "grade_id": "cell-b77ba84637c0d579", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "# Last class:\n", + "\n", + "## Part I: Post-Inference Problem\n", + " \n", + " - Simulation study to show that the type-I error rate inflates when the same data is used to select a model and make inference\n", + " \n", + " - Proposed a solution: split the data\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Today:\n", + "\n", + "## Part II: how to select and train models at once\n", + " \n", + " - Regularized methods\n", + " \n", + " - Predictive models" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nbgrader": { + "grade": false, + "grade_id": "cell-6f048d81f2cffe21", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "In previous worksheets we learned how to select a model using *stepwise* algorithms\n", + "\n", + "- these are *greedy* algorithms \n", + "\n", + "- results depend on the order in which variables are selected \n", + "\n", + "- variables are either *in* or *out*\n", + "\n", + "#### If we can think *out* as the estimated coefficient being $0$, can we *smoothly* shrink the estimator instead of selecting between a value and $0$?\n", + "\n", + "Let's illustrate idea this with data:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nbgrader": { + "grade": false, + "grade_id": "cell-aa844e3860a3dcbe", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "## Dataset\n", + "\n", + "In this section we will work with a richer real estate dataset, the [Ames `Housing` dataset](https://www.kaggle.com/c/home-data-for-ml-course/), compiled by Dean De Cock. It has 79 input variables on different characteristics of residential houses in Ames, Iowa, USA that can be used to predict the property's final price, `SalePrice`. We will use a subset of 21 continuous input variables:\n", + "\n", + "- `LotFrontage`: Linear $\\text{ft}$ of street connected to the house.\n", + "- `LotArea`: Lot size in $\\text{ft}^2$.\n", + "- `MasVnrArea`: Masonry veneer area in $\\text{ft}^2$.\n", + "- `TotalBsmtSF`: Total $\\text{ft}^2$ of basement area.\n", + "- `GrLivArea`: Above grade (ground) living area in $\\text{ft}^2$.\n", + "- `BsmtFullBath`: Number of full bathrooms in basement.\n", + "- `BsmtHalfBath`: Number of half bathrooms in basement.\n", + "- `FullBath`: Number of full bathrooms above grade.\n", + "- `HalfBath`: Number of half bathroom above grade.\n", + "- `BedroomAbvGr`: Number of bedrooms above grade (it does not include basement bedrooms).\n", + "- `KitchenAbvGr`: Number of kitchens above grade.\n", + "- `Fireplaces`: Number of fireplaces.\n", + "- `GarageArea`: Garage's area in $\\text{ft}^2$.\n", + "- `WoodDeckSF`: Wood deck area in $\\text{ft}^2$.\n", + "- `OpenPorchSF`: Open porch area in $\\text{ft}^2$.\n", + "- `EnclosedPorch`: Enclosed porch area in $\\text{ft}^2$.\n", + "- `ScreenPorch`: Screen porch area in $\\text{ft}^2$.\n", + "- `PoolArea`: Pool area in $\\text{ft}^2$.\n", + "\n", + "The following variables will be used to construct a variable `ageSold`\n", + "- `YearBuilt`: Original construction date.\n", + "- `YrSold`: Year sold." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nbgrader": { + "grade": false, + "grade_id": "cell-0e57653584382931", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "Run this code to prepare a working dataset" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n", + "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.3 \u001b[32m✔\u001b[39m 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‘package:yardstick’:\n", + "\n", + " mcc, rmse\n", + "\n", + "\n", + "The following object is masked from ‘package:tidyr’:\n", + "\n", + " replace_na\n", + "\n", + "\n", + "Loading required package: Matrix\n", + "\n", + "\n", + "Attaching package: ‘Matrix’\n", + "\n", + "\n", + "The following objects are masked from ‘package:tidyr’:\n", + "\n", + " expand, pack, unpack\n", + "\n", + "\n", + "Loaded glmnet 4.1-8\n", + "\n", + "\n", + "Attaching package: ‘cowplot’\n", + "\n", + "\n", + "The following object is masked from ‘package:lubridate’:\n", + "\n", + " stamp\n", + "\n", + "\n" + ] + } + ], + "source": [ + "library(broom)\n", + "library(latex2exp)\n", + "library(tidyverse)\n", + "library(tidymodels)\n", + "library(repr)\n", + "library(gridExtra)\n", + "library(faraway)\n", + "library(mltools)\n", + "library(leaps)\n", + "library(glmnet)\n", + "library(cowplot)\n", + "\n", + "options(repr.plot.width=7, repr.plot.height=6)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "nbgrader": { + "grade": false, + "grade_id": "cell-95e16218a5e51a83", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[1mRows: \u001b[22m\u001b[34m1460\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m81\u001b[39m\n", + "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n", + "\u001b[1mDelimiter:\u001b[22m \",\"\n", + "\u001b[31mchr\u001b[39m (43): MSZoning, Street, Alley, LotShape, LandContour, Utilities, LotConf...\n", + "\u001b[32mdbl\u001b[39m (38): Id, MSSubClass, LotFrontage, LotArea, OverallQual, OverallCond, Ye...\n", + "\n", + "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n", + "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n" + ] + } + ], + "source": [ + "Housing <- read_csv(\"data/Housing.csv\")\n", + "\n", + "# Use `YearBuilt` and `YrSold` to create a variable `ageSold`\n", + "Housing$ageSold <- Housing$YrSold - Housing$YearBuilt\n", + "\n", + "\n", + "# Select subset of input variables\n", + "Housing <- Housing %>%\n", + " select(LotFrontage, LotArea, MasVnrArea, TotalBsmtSF, \n", + " GrLivArea, BsmtFullBath, BsmtHalfBath, FullBath, HalfBath, BedroomAbvGr, KitchenAbvGr, Fireplaces,\n", + " GarageArea, WoodDeckSF, OpenPorchSF, EnclosedPorch, ScreenPorch, PoolArea, ageSold, SalePrice\n", + " )\n", + "\n", + "# Remove those rows containing `NA`s and some outliers\n", + "Housing <- drop_na(Housing) %>% \n", + " filter(LotArea < 20000)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "nbgrader": { + "grade": false, + "grade_id": "cell-96b5268b39205b8e", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "#run this cell\n", + "set.seed(1234)\n", + "\n", + "Housing_split <- initial_split(Housing, prop = 0.6, strata = SalePrice)\n", + "training_Housing <- training(Housing_split)\n", + "testing_Housing <- testing(Housing_split)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### In the following example, I use only the first 5 covariates to simplify the presentation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Run these cells to fit the \"forward\" selection algorithm on this (smaller) training set:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "Housing_forward_sel <- regsubsets(\n", + " x = SalePrice ~ ., nvmax = 19,\n", + " data = training_Housing[,c(1:5,20)],\n", + " method = \"forward\",\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "nbgrader": { + "grade": false, + "grade_id": "cell-c5c4ca7fca323e94", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 5 × 6 of type lgl
(Intercept)LotFrontageLotAreaMasVnrAreaTotalBsmtSFGrLivArea
1TRUEFALSEFALSEFALSEFALSETRUE
2TRUEFALSEFALSEFALSE TRUETRUE
3TRUEFALSEFALSE TRUE TRUETRUE
4TRUEFALSE TRUE TRUE TRUETRUE
5TRUE TRUE TRUE TRUE TRUETRUE
\n" + ], + "text/latex": [ + "A matrix: 5 × 6 of type lgl\n", + "\\begin{tabular}{r|llllll}\n", + " & (Intercept) & LotFrontage & LotArea & MasVnrArea & TotalBsmtSF & GrLivArea\\\\\n", + "\\hline\n", + "\t1 & TRUE & FALSE & FALSE & FALSE & FALSE & TRUE\\\\\n", + "\t2 & TRUE & FALSE & FALSE & FALSE & TRUE & TRUE\\\\\n", + "\t3 & TRUE & FALSE & FALSE & TRUE & TRUE & TRUE\\\\\n", + "\t4 & TRUE & FALSE & TRUE & TRUE & TRUE & TRUE\\\\\n", + "\t5 & TRUE & TRUE & TRUE & TRUE & TRUE & TRUE\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 5 × 6 of type lgl\n", + "\n", + "| | (Intercept) | LotFrontage | LotArea | MasVnrArea | TotalBsmtSF | GrLivArea |\n", + "|---|---|---|---|---|---|---|\n", + "| 1 | TRUE | FALSE | FALSE | FALSE | FALSE | TRUE |\n", + "| 2 | TRUE | FALSE | FALSE | FALSE | TRUE | TRUE |\n", + "| 3 | TRUE | FALSE | FALSE | TRUE | TRUE | TRUE |\n", + "| 4 | TRUE | FALSE | TRUE | TRUE | TRUE | TRUE |\n", + "| 5 | TRUE | TRUE | TRUE | TRUE | TRUE | TRUE |\n", + "\n" + ], + "text/plain": [ + " (Intercept) LotFrontage LotArea MasVnrArea TotalBsmtSF GrLivArea\n", + "1 TRUE FALSE FALSE FALSE FALSE TRUE \n", + "2 TRUE FALSE FALSE FALSE TRUE TRUE \n", + "3 TRUE FALSE FALSE TRUE TRUE TRUE \n", + "4 TRUE FALSE TRUE TRUE TRUE TRUE \n", + "5 TRUE TRUE TRUE TRUE TRUE TRUE " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
(Intercept)
816.389268745144
GrLivArea
119.093847084307
\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[(Intercept)] 816.389268745144\n", + "\\item[GrLivArea] 119.093847084307\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "(Intercept)\n", + ": 816.389268745144GrLivArea\n", + ": 119.093847084307\n", + "\n" + ], + "text/plain": [ + "(Intercept) GrLivArea \n", + " 816.3893 119.0938 " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
(Intercept)
-40522.4417957512
TotalBsmtSF
83.8826321740436
GrLivArea
88.1288102843254
\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[(Intercept)] -40522.4417957512\n", + "\\item[TotalBsmtSF] 83.8826321740436\n", + "\\item[GrLivArea] 88.1288102843254\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "(Intercept)\n", + ": -40522.4417957512TotalBsmtSF\n", + ": 83.8826321740436GrLivArea\n", + ": 88.1288102843254\n", + "\n" + ], + "text/plain": [ + " (Intercept) TotalBsmtSF GrLivArea \n", + "-40522.44180 83.88263 88.12881 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "summary(Housing_forward_sel)[[1]]\n", + "\n", + "coef(Housing_forward_sel,1)\n", + "coef(Housing_forward_sel,2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The estimated coefficient for `TotalBsmtSF` \"jumps\" from 0 to 83.88. Similarly for other coefficients in other steps. \n", + "\n", + "### Can the selection be done more \"smoothly\"??" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Shrinkage (aka regularization) methods!!\n", + "\n", + "They shrink coefficients in a continuous way by adding a bound to their size!! We'll focus on 2 methods (there are many other penalty functions one can use!):\n", + "\n", + "\n", + "- **Ridge** uses an $L_2-$norm to measure the size of the coefficients $$\\lVert \\beta \\rVert_2^2 = \\sum_{j = 1}^{p} \\beta_j^2.$$\n", + "\n", + "\n", + "- **Lasso** uses an $L_1-$norm to measure the size of the coefficients $$\\lVert \\beta \\rVert_1 = \\sum_{j = 1}^{p} |\\beta_j|.$$\n", + "\n", + "\n", + "This \"shrinkage\" process biases the estimated coefficients!\n", + "\n", + "- we sacrifice bias for a lower variance to gain prediction performance!!\n", + "\n", + "> **Important:** since the method depend on the *size* of the coefficients, we need to standardize the input variables (default option)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "#### Geometrically:\n", + "\n", + "![](img/shrink.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Ridge\n", + "\n", + "- Proposed in 1970 by Hoerl, A.E. and Kennard, R. in \\emph{Technometrics}\n", + "\n", + "\n", + "- It does not shrink parameters to $0$, so it does *not* select variables \n", + "\n", + "\n", + "- It has been proposed as a method to address multicollinearity problems (we'll skip the math)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### LASSO: least absolute shrinkage and selection operator\n", + "\n", + "- Proposed in 1996 by Tibshirani in \\emph{JRSS}\n", + "\n", + "\n", + "- **Lasso** uses an $L_1-$norm to measure the size of the coefficients $$\\lVert \\beta \\rVert_1 = \\sum_{j = 1}^{p} |\\beta_j|.$$\n", + "\n", + "\n", + "- it *does* shrink coefficients to $0$, thus it can be used to *simultaneously select and train (estimate)* a model!!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Mathematically:\n", + "\n", + "**Example**: Ridge estimators \n", + "\n", + "$$\n", + "\\ \\min_{\\beta_0, \\boldsymbol{\\beta}} \\ \\sum_{i=1}^n \\left(Y_i - \\beta_0 - \\boldsymbol{X}_i \\boldsymbol{\\beta} \\right)^2\n", + "$$\n", + "#### subject to\n", + "$$\n", + "\\sum_{j=1}^p \\, \\beta_j^2 \\ \\le \\ C \\; \\text{ for some } C > 0.\n", + "$$\n", + "\n", + "\n", + "This is mathematically equivalent to minimizing a *penalized* RSS:\n", + "\n", + "$$\n", + "\\sum_{i=1}^n \\left(Y_i - \\beta_0 - \\boldsymbol{X}_i \\boldsymbol{\\beta} \\right)^2 + \\ \\lambda \\ \\sum_{j=1}^p \\, \\beta_j^2 \\\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### How much to shrink?? the penalty parameter\n", + "\n", + "- The additional term $\\lambda \\sum_{j = 1}^{p} \\beta_j^2$ is the *penalty* term, and $\\lambda$ is called the *penalty parameter*. \n", + "\n", + "\n", + "- If $\\lambda = 0$, the objective function of the shrinkage methods is the same as that of LS!! Same estimators!! \n", + "\n", + "\n", + "\n", + "- As $\\lambda$ grows, coefficients are shrunk. \n", + "\n", + " - LASSO eventually shrinks them all to zero \n", + " - Ridge will never reach a value of zero \n", + " \n", + " \n", + "- The penalty parameter $\\lambda$ can be selected using the data. This process is called \"tuning\".\n", + "\n", + " - an option is to select the value that yields the smallest $\\text{MSE}_{\\text{test}}$. \n", + " - this tuning is done using an internal cross-validation or a validation set so that the model does not use *test* data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### In R:\n", + "\n", + "To build a regularized regression we can use the package `glmnet` in `R`\n", + "\n", + "1. the `glmnet()` function requires: a **matrix** with input variables and a vector of responses\n", + "\n", + "2. the argument `alpha = 1` corresponds to a LASSO penalty and `alpha = 0` for a Ridge penalty \n", + "\n", + "> There are infinite other options in between known as *Elastic Net* \n", + "\n", + "3. `glmnet()` selects a grid of $\\lambda$ values by default or you can specify one\n", + "\n", + "4. it is recommended to use given extraction fuctions to obtain the objects, e.g., estimated coefficients \n", + "\n", + "5. the function `cv.glmnet()` can be used to find an \"optimal\" value of $\\lambda$ by cross-validation\n", + "\n", + "> CV creates many *test sets* from the training set (we'll see CV later)\n", + "\n", + "6. we can visualize how the estimated test MSE changes for different values of $\\lambda$\n", + "\n", + "Run the code below to perform these steps" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": true, + "tags": [] + }, + "outputs": [], + "source": [ + "# step 1: using matrices\n", + "\n", + "Housing_X_train <- as.matrix(training_Housing[,-20])\n", + "Housing_Y_train <- as.matrix(training_Housing[,20])\n", + "\n", + "Housing_X_test <- as.matrix(testing_Housing[,-20])\n", + "Housing_Y_test <- as.matrix(testing_Housing[,20])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Warning message in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):\n", + "“collapsing to unique 'x' values”\n" + ] + }, + { + "data": { + "application/pdf": 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ggBm1kTiA5nfuYilkIPuPEQ+0o9yyRVZVwUFpFaFpZS5il2yAhnVx3EiVU7A4Mn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\nIPugzWWNG+ye7HzGBwUA2Vu0GEd/gd3XqZdUfw3hByf0K+SqbcG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stIsx/wAt76dYk+gLEZPtVRi5PlirsuEJTkowV2+xq0V5x/wuNtfG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plRYyjDrY8lP46lNsTMmDm0INfgKbyu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B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\ne6T6SiX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"image/jpeg": { + "height": 360, + "width": 420 + }, + "image/png": { + "height": 360, + "width": 420 + }, + "image/svg+xml": { + "height": 360, + "isolated": true, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# step 2 and 3: fitting LASSO on a given grid (try using the default as well)\n", + "\n", + "Housing_LASSO <- glmnet(\n", + " x = Housing_X_train, y = Housing_Y_train,\n", + " alpha = 1,\n", + " lambda = exp(seq(5, 12, 0.1))\n", + ")\n", + "\n", + "plot(Housing_LASSO)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Call: glmnet(x = Housing_X_train, y = Housing_Y_train, alpha = 1, lambda = exp(seq(5, 12, 0.1))) \n", + "\n", + " Df %Dev Lambda\n", + "1 0 0.00 162800\n", + "2 0 0.00 147300\n", + "3 0 0.00 133300\n", + "4 0 0.00 120600\n", + "5 0 0.00 109100\n", + "6 0 0.00 98720\n", + "7 0 0.00 89320\n", + "8 0 0.00 80820\n", + "9 0 0.00 73130\n", + "10 0 0.00 66170\n", + "11 0 0.00 59870\n", + "12 1 8.61 54180\n", + "13 2 17.17 49020\n", + "14 2 26.39 44360\n", + "15 3 34.92 40130\n", + "16 3 41.94 36320\n", + "17 4 48.49 32860\n", + "18 4 53.88 29730\n", + "19 4 58.28 26900\n", + "20 4 61.89 24340\n", + "21 4 64.85 22030\n", + "22 4 67.27 19930\n", + "23 4 69.25 18030\n", + "24 4 70.87 16320\n", + "25 4 72.20 14760\n", + "26 4 73.28 13360\n", + "27 6 74.25 12090\n", + "28 6 75.11 10940\n", + "29 6 75.82 9897\n", + "30 6 76.40 8955\n", + "31 8 77.04 8103\n", + "32 9 77.66 7332\n", + "33 9 78.22 6634\n", + "34 10 78.73 6003\n", + "35 11 79.37 5432\n", + "36 11 79.91 4915\n", + "37 11 80.35 4447\n", + "38 12 80.75 4024\n", + "39 12 81.07 3641\n", + "40 13 81.34 3294\n", + "41 13 81.57 2981\n", + "42 14 81.75 2697\n", + "43 14 81.91 2441\n", + "44 14 82.04 2208\n", + "45 14 82.15 1998\n", + "46 14 82.24 1808\n", + "47 14 82.31 1636\n", + "48 14 82.37 1480\n", + "49 14 82.42 1339\n", + "50 14 82.46 1212\n", + "51 14 82.49 1097\n", + "52 14 82.52 992\n", + "53 15 82.54 898\n", + "54 15 82.56 812\n", + "55 15 82.57 735\n", + "56 15 82.58 665\n", + "57 15 82.59 602\n", + "58 17 82.61 545\n", + "59 17 82.62 493\n", + "60 17 82.62 446\n", + "61 17 82.63 403\n", + "62 17 82.64 365\n", + "63 17 82.64 330\n", + "64 18 82.64 299\n", + "65 18 82.65 270\n", + "66 18 82.65 245\n", + "67 18 82.65 221\n", + "68 18 82.65 200\n", + "69 18 82.66 181\n", + "70 18 82.66 164\n", + "71 18 82.66 148\n" + ] + } + ], + "source": [ + "print(Housing_LASSO)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "20 x 1 sparse Matrix of class \"dgCMatrix\"\n", + " s1\n", + "(Intercept) 1.116881e+05\n", + "LotFrontage . \n", + "LotArea . \n", + "MasVnrArea . \n", + "TotalBsmtSF 1.447926e+01\n", + "GrLivArea 3.126415e+01\n", + "BsmtFullBath . \n", + "BsmtHalfBath . \n", + "FullBath . \n", + "HalfBath . \n", + "BedroomAbvGr . \n", + "KitchenAbvGr . \n", + "Fireplaces . \n", + "GarageArea 9.785771e+00\n", + "WoodDeckSF . \n", + "OpenPorchSF . \n", + "EnclosedPorch . \n", + "ScreenPorch . \n", + "PoolArea . \n", + "ageSold . " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#step 4: extracting estimated coefficients for a given level of regularization\n", + "coef(Housing_LASSO, s = 40000)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "application/pdf": 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S4Xvm65ekEdVXNMy7efyx5SXFRDS4udjPAUFKxHukyfwTBfULT2i4o3lo9//cEH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Yvsf2Tzhnz/Nz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\n4zl9sr8ruj6jI+Jcz4d9t/Z1Tl9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z//nKsA9DASQkhZWdnFixf9/PxkMtnKlSu5DkdrpFKpsbHx8+fPNdpNTU3lcrku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\nxZGRkRKJpFu3buPHj8/JyXF/yA4ipB3AVzQ0NBBCJk+e3LVrV/b4kCFDKCW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"height": 360, + "isolated": true, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# step 5: selecting best lambda by CV\n", + "\n", + "Housing_cv_LASSO <- cv.glmnet(\n", + " x = Housing_X_train, y = Housing_Y_train,\n", + " alpha = 1,\n", + " lambda = exp(seq(5, 12, 0.1))\n", + ")\n", + "\n", + "plot(Housing_cv_LASSO, main = \"Lambda selection by CV with LASSO\\n\\n\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot shows the *estimated* test $\\text{MSE}$ ($y$-axis) for a grid of values of $\\lambda$ ($x$-axis) on the natural log-scale. \n", + "\n", + "> the numbers at the top $x$-axis indicate the number of inputs whose estimated coefficients are different from zero for different values of $\\lambda$. \n", + "\n", + "> the error bars represent the variation across the different test sets of the CV (folds)\n", + "\n", + "The two vertical dotted lines correspond to two values of $\\lambda$:\n", + "\n", + "- $\\hat{\\lambda}_{\\text{min}}$ which provides the minimum MSE in the grid.\n", + "\n", + "\n", + "- $\\hat{\\lambda}_{\\text{1SE}}$ largest value of lambda such that the corresponding MSE is within 1 standard error of that of the minimum (more penalization at a low cost)\n", + "\n", + "Run the code below to obtain $\\hat{\\lambda}_{\\text{min}}$ and call it `Housing_lambda_min_MSE_LASSO`" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "1096.63" + ], + "text/latex": [ + "1096.63" + ], + "text/markdown": [ + "1096.63" + ], + "text/plain": [ + "[1] 1096.63" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "7" + ], + "text/latex": [ + "7" + ], + "text/markdown": [ + "7" + ], + "text/plain": [ + "[1] 7" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Housing_lambda_min_LASSO <- round(Housing_cv_LASSO$lambda.min, 4)\n", + "\n", + "round(Housing_lambda_min_LASSO,2)\n", + "round(log(Housing_lambda_min_LASSO),2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### LASSO \"smoothly\" selects variables and trains the corresponding model !\n", + "\n", + "> for values of lambda in the grid\n", + "\n", + "Run the code below to visualize the estimated regression coefficients over the $\\lambda$-grid" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "application/pdf": 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eOQjVqHehqSOxVvTkLKmcxxnJ/tx1X5\n+Cld+TLrGV07s6uDqYVdqVLRwVG/Xic9/3T9C9cCJxgvaqTKieOfvr3+cv0YkrFCT9hjODzO\n0V/zml9d6yT9p09dO/b8KfwP8qiAWAplbmRzdHJlYW0KZW5kb2JqCjUgMCBvYmoKICAgMzY3\nNAplbmRvYmoKMyAwIG9iago8PAogICAvRXh0R1N0YXRlIDw8CiAgICAgIC9hMCA8PCAvQ0Eg\nMSAvY2EgMSA+PgogICA+PgogICAvRm9udCA8PAogICAgICAvZi0wLTAgNiAwIFIKICAgPj4K\nPj4KZW5kb2JqCjIgMCBvYmoKPDwgL1R5cGUgL1BhZ2UgJSAxCiAgIC9QYXJlbnQgMSAwIFIK\nICAgL01lZGlhQm94IFsgMCAwIDUwNCA0MzIgXQogICAvQ29udGVudHMgNCAwIFIKICAgL0dy\nb3VwIDw8CiAgICAgIC9UeXBlIC9Hcm91cAogICAgICAvUyAvVHJhbnNwYXJlbmN5CiAgICAg\nIC9JIHRydWUKICAgICAgL0NTIC9EZXZpY2VSR0IKICAgPj4KICAgL1Jlc291cmNlcyAzIDAg\nUgo+PgplbmRvYmoKNyAwIG9iago8PCAvTGVuZ3RoIDggMCBSCiAgIC9GaWx0ZXIgL0ZsYXRl\nRGVjb2RlCiAgIC9MZW5ndGgxIDExNTEyCj4+CnN0cmVhbQp4nOV6e1xTV7roWmvvvIEkhARI\nCNlhE14BgkTUACEbISGISlCiPIqA8lZ5GLCKVukoVtEW+hhbR091pvahtWOwtuq0HZk5c3o6\nnemtZ/rrudM7PaPz/P3OaTl6e9reO9MR7rd2go92Zn73j/vf3bL2Xuv71vrWWt97rYgwQkiJ\nxhCDuE1b2wd/9e1nHQiZdyNEmjZtH+Yq/qHiPxCy/BLahq7B7q2hD/gwQtZbCMkk3Vt2dv30\njxXZQOEcQinXejrbOz5/8Uw6Qln/G2BLegAQVyO1IJRdAO30nq3DO7ZNKj6Hdj20B7cMbGrv\nm9r0W2j/BNrFW9t3DLIPy/4FoRxoIm5wW+fg6DsbvoQ2B/N/iAiqhG+HJAirlaH8aYwcpRdk\nrHy2cFoq+bj0AkOgiqYZCpZQ8AWZVPGX0guYwp1aq9Zm1VorCTeXjp+Z65EE//xyJfsezITR\nmvlPWbPkYZSLXhNS1sV2xR6IZYKkk5Ampo8hQXunnQRzOnNIxuX5XwqNcVq/Xo6lSpycfiyd\nHEr/KJ0wlVYs5TnA8CrUL1j02KE/qSdTeqzPH0u32PqtHKfqv6bEHiVWGkNZWZr0YatUEwqp\n9qlItwobVFglSUYeZ0tLy6xnNt7lmMWOlqFZp8M5W1ho1HzcMrTNOKt12RcVtA61Dm1DLbgF\n2ekrUhLiCJ+WTzKXpjLOwjJStDgf2nFExuuseitThp2FqYQ1C3ve2DXw/LaKuNdVWd5Ov29b\nXW7O6iF/3sryosSwg7He3mcqmNrU+9J2Af+sL7zXt7h51KfPqinh7fWjteVba3M1KbYE8uWx\nuXJbkTDyPSolgnqAd8mSoygdLUPnhYIjejxqmDCQRlmvTGTfKMPUkw5C6vkOfphn6tM60obT\nmKJUbyoZL8SFl+dvCXnKWP9+I7YZi4xe44iRNRixfiAhARjpsJ20kSkbthWPOcz9GiWnJMrL\n8zNCUmqGX2nOGeG4xUmhZP0xPdGrZYtDlIWzwESRgYXYYW+ZjTDPOFvomF1UANy1A7uAZ/Td\nssA3DAyLjzApUZaPKef0kaYsykh9QiqhjGWTS0JnB3ZdHnV7v/XGdv+e7tWJ51J21a3YUZ+3\n6EKo7cSA+1K6v8+3qKPOmVXTt7y825+B3+ub3lu1YRrj02/ilB+2pVb0ByzNdb7DvzjS3Fo2\n8uJg9fa1eebyvpWrH+kozguOUn3sRYiNAX2MQ5VC3qhqQkV6VVjSL5WiQAzWxHAxJEbVCv0Q\nhwTUBuYrQShmOFYqSUIeD914y5ATCuUC3TToKtHzi41kqbXIysb0XRirejNw8GLnbRXzHHvz\ne3Mfzv3L3I8unsFe7ML5Tx6jcmVQI8jVCHLNRm5Uh64K+0eyxrPIiHXcSkbM42YykjKeQkaS\nxpPIaOJEIhnVTejIaAwelU/IyahsQkZGmQmGjJBxQoLeTi8J1nTWkKbyvnKyuF+f029Rp1tq\nwTwseosSBK0us5QRS5mj7GQZM1WGy9aO+am5KNPVFSMu1yrHiFG2aiQiXlG4Lhd2DM3eNQyX\nwwHbdWlmNRExR6V857tgIUWLy8jSonyGfqmA9QCX6VMZ5muC1n1d8EbXyOu7d7/2oMtR27mk\npMVjdQ2+sDV0ZmCJ1dPidveszP21qayjumqjJ8VQ3BUIdi/V8imVoXW1A16OA0NbM1hpxoea\nnu4vK9v6dOOqHeuLFGxc2fq+khX7NrmKN+1fUdy33h3DKovW7yArixo8PO9pKMpp8Ofn+xtu\nP+dsrc7LW9G+uHzzqpycVVtFu2sD+cRH7e6HQu+ZTPycCn875vkYclaLj2nxML+fJ8Pcfu4p\njhm1TFi+Y2FGTROm75iYXcbDxuNGpimrL4s0kl5CNElggEvk2Ib6HTqPjtTqruoI0nG6Ap2g\nC+skMl2xakCpdPRzZmym5mfiMvxm3eJQa9JAEklKkuSE0mRxocQ7TgyEpHU5WqIm6HTMaj7e\nAIKadYJs7C2i07prhhiEQ+Jw1H9hyu2lccyCsJyF8d8wwviq/W9tr/tWl99wLuXB5uqdwQKi\nr27ZsrTt+JYSz47zA5989hNb9WZfeY8/k/f1eAu71xaRf3tz7g9vbrD6BmtNzUHvxLUjjhVO\nk3f3+c1bw7uWz50+v3qiqyQ/OFpTNdroTPNtRmJcOAF2qAY7VKINAscpxhREoZD3kykWsw48\niQnGrJRBREOIjEioJzNqDP5KSb2kQ8JIWEYDLZaRSuV4GIFlzhZ6nE67w9lix44NLYlgoY4W\nDTimlkUFziKrVlJkgyClP4G7536MV72A1x9jS3939g9fJR0T5R0AefMgbx3KRINCoNHWayM+\n6zprl5VZZ+oykcbE3kRgDd6uPaAlO2MPxRJVDFbJ8U7ZIRnZzhxgCEuwDExtKuFUAknIHkvt\np8EoOaSW8VHHSWOOaFNGMKINLfc8CxK66ynxN8XCrxq/2NV9YV9Nzf6LfZ3T+1deyoLosnK4\nNiu7dlt11bZaO/nRz+Y+eXnFirNY//MPceILFRUvzP37hy9dH1+6bPz6i9/79SMlJY/8Gvje\nLfq/oygLfVdYNcLiEeO4kYxqJjSk04bX2XC2tdHaa2V6eZzC42Q9HjGNm4jUhDPN/YJcyMjx\nC3I8KcfynLH4ft1wxv4MosvQgLMkiGqvBYIHkmc8Fo8fiN8SvzueUcYb40l8bChJhjMiknJ5\nZmkojndRBXY6WxwRV2OHOELdSyR4RL7OojLJnXibWcZEvYpUZtV3O5/83smx2vTK1uIlrSsc\nssuK5cPPbe49PVTqDA6O7t66Lolc3zvy6uO7dx9cV9pcZkktbSzRrjzQWVy4cWpD1djwlu7O\nrl7XsYguNuNrpJYMgme2CgmICGSQMAShN07i9zFxYAzZECQM2EHVSVdk1Tfjz/G1U6fEsauj\nMboE/VL49l2/PFI8XkxGnONOMuIYd5CR2PFYMmqbsJFm7WYtMWZjSHO25x/IJxAUqzNxRv+S\n5EWtyQPJJDM5M1mp4/oXLaLJjs6hO6ljpnRY5x5T9d+MJDlLkoeNRs2jGfiBjC0ZuzMYZYYx\ng2TwoVyZJvSwCq9VbVKFVEwChLV7Uh/qOCJ8Bw8vJkB3o7c2njr5FvjMDi0qiErgrpe/PwVa\nQiVix0WRZCiDT5PeIxrR4bPJnp2vhva9Olys+IHcvmLLioPHvd07nV0bnf3NJeP7Hnwy5jVV\nYNezjdvPbnGm+QdWB/esycbj7c/0Li3ffKhau+yB5ekH9q9uLYo/oV+6oXpo3+hAXMtEc15J\n58FVZVvWlWlYRUnDIOX9S6DLDvAhErRMyNKwBSxBrIblWIFtY8fYU+wtVs4yTQhpIJQzMoQZ\nphXFU2ukTmIWeADeQUsdw0tXyTuSh78ynYjkXetozsquhhwhDQ0LJTu5QxwZTtmfQrYbDhjI\nzvhD8eRozAsxhI1JiCEqhUlBVBKTBJxAAngrVCVMqbE6fawgHadTm0hI5f3X03FylQXMJiGg\n1KQGGMMdn9BiH/qmW8CaSETVWP9aomT+838OXdhVjv+w59LIsrcya7ZUegdWZ+eu6i3zDq7O\nIalzv5/7j8ojH0ySAt+RXxzZc3pjZvam07v2PL8xK3PjC+L+5tYzN9katAh50UeCf3TRxCKy\nXXZARjrLcDCmM4Y0FfcVkwxmCUMy4sEjYEVicuLOxEOJrNRsMG83HzCzCodPKEwriMN7467H\nkbiqMalPQjdbl5jil0hKq9RGSMa5KqGKvF+FURVXNVUVrmID16vwTBWurcJjVaeqiLrKUUWu\nVd2iNSzPVqctDVg06vKA3qAIFElxhhRLkQl5CkXlLaR/GHg0NLRt2zb6pUJ0OuwRRYZUHliI\n7nGt+J6o58b8vXHPkOikyYozjtFrE6RfT0hIestUlxD3WvyuDneHL4MklAQH/d1Pttjt7ccH\nQmfyCcOw5GVMCL6euyjQvcS7qdxiETZWLuleUzi3PqNqY6mxpi6tZse672fXFPPeifce+da1\nx1f1tieXLc1iFPbS6sy//NPv/sC8PfTdroKC7u8OjpzcmJPf8WxE99aD7oVA9wpROXjowp3u\nQ26yM+ZQDCFZili/UmKUEHuSQuuXpOhTiM2W6hPyFQPL9i6bXMYsqxhLqNKLKqdP8ev1nioL\ng5mCipkKcqoCV1AEB7porcsyuOoUCqOzNQE7EiYhYiWoA0ZNvjOADGIonaUZrpZ6CtBROzD6\nLp8pmwsdYq5hBw8hScugHPXg+920AdhqAFexVB9NPoD7maIYZMDyBAN+9rnTdfteWv9fKcXr\nSxbXl2VI31Qu6z7e//P/llOiTo1Lq8hwVucnMVKz94ERft3DwZx/Wv5gU1Frwrmjmw+thuNW\nScWGYpM6s8KpFTavtr8xPZcfqGOZQbnctLRuyeL6Eu4Rz8bhokYWawubqhvaqK84iJCUB76W\nkB9fQTnzN16Vq/zc5fkbwjxU0kp8CMXm+z5y/MlBXnfgbEej45CDkTrwC47XHf/q+KODPeTA\n2x240YGlDoPD52BkjuQY39uxWBpriF0S+8fYL2Ml8tiv3Pin7o/c/+5m3nDjY2582I173Tvd\npNmNq93Y7i5xkz+58Sdu/JEb/8yN37rbCUOXbLfLTUxurHDjdz9xf+UmvSD8Y+4r7p+6JYBe\ndbdHhAidityZ6CE3hhlq3M3uzW7W4sYsneITNznvvuomgN/rvg+tcuPvzFMywjy+7sZA5jwl\nc9xN9tLFbHaTWjcuceN0sSvMdqfTcUpr0k063LjGjT2ULFa7LW4S6bTLfdj9svsNNzsgjo9M\n1feGmy6GEefA4gwY6MNWvqKDbtJ9/IyuFXe4n6JbpEtlYAuf0wEvu3/lZmDQZjdeLA5Su7Hr\nDQB+5WZOufEwHRLZGxOZjs4FuNO0MwXvcrNA6Jobkzb3lPuUe8bNwuwFbuxwYyTo3FieVhTI\n0iRLwf/o1I5YpAevU+iJOB0c8Smt1PNQ1xPxPuIzFHm2/VXoPZivo1vvQ9+XDt4ZCt5tCExt\nwx1o5HAGPs5ut2oXXJaWp9VMZyqjd4qWl+iMBuMIJtKJQQmOlUtdD5Tzr1K3dRZDfsMkLatp\nF3ZNpjBJpYEOYc2DK9MvLPQi36/tKzflBR+qu/0oszatpqJAJsl1lQC6yLxxM33nPvB4x21H\npJ+9fs/a24+C79ov3vX8HFmQEz0hKHoX7VxEdvLYQs0sSab0H0g9mkqqTY0mUs02suQAPgp5\nPkV6AAlx8xSHuaKxHInOh+I18QXxt+JZeXy4CHuK8GDRVBGxFOH5IjxTdKOIJNsCZk08itFL\nHAES8Vri8TwSHmhkiNzt0KBgbxEvJyCqWtMyMnmapfBlTBFE/gSpTCpz0qQ7/uunVNY8t23X\nc07w9Qz+PmXaRcgDMVv4/Oh7P3orpazNW7W1OiOjeotveZtgIWm3323cZFxWkMaCf/dnsrNz\njalL9cmGnqa5T+d+O3iquyC/64Udw89usud3PbeQYzA3o7zaJawPpnWmkabCvkLiwtWYLFH6\nlETBJrM72UMsK5UZZDQ+szqfkIMm429CSl00xlVZIEB+gzH6eKRyBOQaZIukGWLc9IiMiR5B\noqEyom826qGJFjINGhTz8WKRL6kkkYeTPI4yY8G7M0Xi/vFju04XwgntIuXLOWARuf0/7rBk\nxWaRJd/vacIJOIksadqotDtyFPi5r3SZ/lK7QmkrKDLiQZEn3S/sCJ3cGOUJpvddkp2QS2ei\nV4TanXGH4iJ58y7bYRvpy8C704+kk7503JeCgzLcxOAcc5+ZHEjEOYl9iUQi18uJhOgJkTQH\njG1Gct541Ug4I4ZUxJimodEvRxbr12iyuWxcy2OeR60WFqk1alKgFtSD6jH1jPqaWqpWK1v1\nOhQJguIbt2gh/EEFeBi9Arn/DgTfozdLE2mikZ5BT3NL0p2FbKIsn2GSdlx5SPA+/MbImke2\nrrOeyBh8+ur2l+fmX1nXfB6j07/B+VWvJVR2HWL/HHjq2t69HzxTb1+9uXx17cEO19Z/xDEn\nn8fKNzrDr5QWNvtyojlCEsSyFGRDm4X8Jr6PJ02pfakkyHQyRF6tUJiqBIsZT5mxOXPMhqos\nWqwtyJzJvJbJZFJG6CANkMslKGCzSbiAQSMJxBnu3P9oXQ5sp7py//0e3am4xyWRLRJt9J7H\njDMjF3synMBXbwuMPJr8rNbddWzLra9W7g93HLw04PiBeuqRvE31xSz+X8HJbtcGf15ec7UD\np2LjMx/sL2k4/ovRpImX/8G8Yu9GUQ/MYCClknch9/uuoGKUOqVTWaFkY5XUVfTJY/xGtQbH\naZI12CdBBMcTi9lhrjW3mveaJ80nzTK12QPV8+ar5uvmm2ZZSSvUSATHmIV1HX6zkJnr58wF\n5jYzc17sxAhmrAYqRBeIQYgJJEvVGGKAx0nNhwp6yG4fAkdNvTK9NqYf6ok3tGDws3yRcyGv\n1EdYYcZOPe69+MwzhpKuOs5r1ObFZznNqg+YS3+pZi7tGy3prLFLpYcYiSG7NLN9H8j0EGzc\nDf6A3r+HhFhGBhkJS880jJwVdVef5GdZuWJegW8o8HUFDitmFOSkAg/SuxOLAiMFviUiFLS7\nNs3mr1VggEvUrB6txYjKF9zAkP1uVKIpnl3cED3XOvUMmP6hixcvSrhz5/58gy3+6u3I+Rj0\njXkX9C0TjQh1OzV4ZyLeZMObGMz5LBa57xTMqcgGLYNjKh8wWri93CR3nWM5zqjh5IPyMfk1\n+Q3QNrlG3iY2ZwAgA/0DrbNkw0kzamtOemdDz0Ra50OOoSR6uRWxtvv0Tszh2XsvlLHOJPSu\nantY/bqitPup9r0XBgrTyxu6txU3P9YtxF6J29a7qlswkbSWE0NlPVtiKnZvcK17+r0dW198\nKOhMLFy/vTKuqc/ZfSKyV8gTmf+EvdrQ1isoDRQuXaby23xCAOGTaB4ElTmGREu6kcnOZGJ1\nJh7LxKJRcbpEP+SEM7EYxWpiC2JvxN6iOWE0qYjkFJErZDGy22mkiloYxKi/HdJpLGdciYuD\nHqG7Ouvi3QBuLFvT52v6Vn3m3wvXkUAd2Ztl/hbJkeRClg8RJysO98ZRJ8tkxeLeWHqtxRxm\nMcvBMWMLu5s9wZ5jWWjF+AcMew3EEBNrYDQ+hXxSgpFEI+EkgoSVScaSsFoaiKHXEgq1Lnqw\nfY+qFG6h+3Q6ZxPFazj6kwrE4KGWITHiFFGjWerUO/V89KhAcrKDy3750P6iHe+84/QYF5nl\nqtgvyC/2ffbZvtvB1R65NLIHF+ji63B2XYreEoLD+fvzyYB+r35Sz2w2YNsSnGPC+sVYDAOq\nVFMqSa8GP+8X6H0rmdKd0oV1jM41pqpWCsmpfqUy10/9BqGXr22uGRcZc2GXaG2ZOX6PC2tc\nWJcryQ5wKB1Ppd9KJ+npnCYuIGlTDarImAqrVBLYMFVezWz0E+9yYZptDEV+Y7LP3v8jycL9\n7L2XKnghxGbSy/Ml1I1AzODTpDSmJKZKmNdLBp/r3fD0tlXxJxOnxorbfZn5a0Z85WPdwgfv\nvvpByvcUBZXB/NFh+6ot5famYM0yK7avfLDObhZ6V1rW12kyywsWeXIsOm2Ot2vVU8f3HE7I\ncfHqFTW5rkyzRpXMO5Y3RM6eoCbsUvFONhEsPfAdNT4mxQeleFzzbQ3ZrsFJBkxvQI4aGINE\niNH7Jc3KzcpdSkYpxwOJUgvBg+QGIfTStoAEoCqRE8SG5AYDVkmlmP6A4gSP44yawDYn9aQt\nEFnpRUz0qgmU31qEnVpwn3GMjBYrM3T2dg8Zf+vtuSmiSdDL556W6BISpPgz7Jn7EfYcYV7/\ny8rHmAcl5nRbzO1P5UaTUSZqCkN/xUExiCWr4ZuKNACJQ3vRPF6L2/EOvAc/Qd4mH3MZXAFX\nzJ2zps3P099G0Sm8BrcB/qEoXgd41x38334wzPEx/g4+gZ+Ff6ei/96Gf+/gdwAf9zdHKsS3\nDEmRHHhvAkoE1srSn56+8ei+AVH93VXd+6iRFiQbjxLAF8VC2xCFa1AS8CnyGFHy/zW9/y8f\nyc8hSj8EVqJHO8X3fQ9bDNx9EKH5T2nr7ntu/f/bVcgjn4voLXQenboPdRDtQeL/G7jnuYr+\nEb0s1o6jR/8O2SvobLT2FDqGHvmb/frQPqBzGua/+7QBdCd6Bma+jF4Ec0jDTph1cxT7K/TT\nv04K/wb/FD2BXoKeT6BL8D4OrmgX+Qw9QdagfvLfmYfRtyA7OoVO4l40Cf3b0GncjDYANPJs\nQJ1o4GtEJ9AUeh6NorG7IMnD8/+FYv/yIqz8ENA5inrR0D0jXsJ/oh/GAmv/PnpNhD28gJT5\nmT7yOiG3n4TG46gbSjv+CNb5KFOOKiVafAYhwdvYEKxfu6YuULt61cqaFdX+Kp+3smJ5ueAp\nc5eWFLuWLV1StKjAkZ+Xm5WZYUvn06yWpAStRh0Xq1Iq5DKphGUIRrle3tfGhTPawmwG7/fn\n0TbfDoD2ewBtYQ5Avvv7hLk2sRt3f08BenZ9racQ6Snc6Yk1XCkqzcvlvDwXfq+S5y7jproG\nqD9ayTdy4VmxvkqssxliIxYaViuM4LxJPZVcGLdx3rBve8+Et60S6E2rlBV8RacyLxdNK1VQ\nVUEtnMUPTuOsMixWSJa3eJogeSydNszYvO0d4UBdg7fSZLU25uVWh+P4ShGFKkSSYWlFWCaS\n5Hrp0tFhbjp3ZuLIZQ3a2GaP6eA72h9oCDPtMHaC8U5MPBLW2sPZfGU4e/T3SbDzznAuX+kN\n2ynVmjV35qm5OyUOS2wanpv4AsF2+NlP74e0RyFSm+YLRKs+YO/EhI/nfBNtE+2X58c28pyG\nn5iOiZkY9AKHUaABRl2e/8FhU9h3pDGsaevBxdHN+tbUhHV1zQ1hYvNxPe0AgT8Pb11msmob\nF/oE/hYaASOAHcBTq5Vu/PBlAW2ERnisriHS5tBG0wUkOOyNYdJGMTMLGH2QYsYWMHeGt/Eg\nzZq1DRNh1lbdwXuBx4fbw2MbQZ/6qCh4TTjuS5OVn4jXci5Ho9i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pvPSOPTXJTrvV4/7HZy9dW9tjSjmUqsGb8vyPh9QXCzr3VlY/NT1TW373FMT3Zd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MAFqdlmK+v2iY/7BaIRZwnQUA4EHxpthh\npBgA2MM36QZPqWBKR3wmBABXwJtih5FiANDqyozMxkuGj4Z4SYRYrgMAV8CbK4UxUgwAWt3X\naboIT9GEaCzXAYCL4E2xw0gxAGhd+Tp66zXT/Ic9sVoHAC6DN8UOI8UAoHX93xldZz/x0EgZ\n10EAAFoNb4odRooBQCu6UWXbnWl662FPrNYBgCvhzc0TGCkGbiQtjfj5kagornO4shWndQPD\nZP1Csbc5ALgU3hQ7jBQDdxEfT5KSiEhEtm4lkyZxncY1nSy0HMkz73jCj+sgAACtjDfFjmCk\nGLgDhiFr1xJCCE2TtWtR7OyBZsnyVO2UTh6d/SRcZwEAaGV8KnZ1MFIMXBlNE6v19nFDl5PC\ng9t02VCkpzdO8OE6CABA6+NTscNIMQB4QDUU81Wafl4flY+CN7eOAQA0H2+KHUaKAcCD+/KM\nzk8hfPYhJddBAADsgjfFDiPFAOAB3ayy/XjV+N1YHzFW6wDARfHm7Q0jxQDgAS1P1Q6NkA8O\nx47EAOCyeFPsMFIMAB7Evlvm00WWhf3UXAcBALAj3hQ7jBQDgPtmtrGfnNS+1F3ZRsOb608A\nAO4Db4odRooBwH37NsNgtrGv9FRxHQQAwL548+HVTiPFaJreu3ev2Wxu5DXnzp17sOwAwKUS\nA/2vdP2ywV4qKQbDAoCL402xs9NIsfz8/FmzZlnvbAnbkLo1QpZl7y85AHDr45O6tt7ix2Ow\nySUAuD7eFDtin5FiUVFRTd5vkZSUFB8fLxDgsz4A/5wvsezNMm2d5CfEbzAAuAE+Fbs6GCkG\nAM3EsGRZinZSe0WPAIyFBQC3wKdih5FiANAiW64ab9XY/jUWY2EBwF3wpthhpBgAtEiNmfni\nrO7V3qoAD97c/g8A8IB4U+wwUgzcglBIhELCMIQQ0sI7gaCeZSlaP4XwxW4YCwsAboQ3H2Qx\nUgzcgkhEhg69fTxiBKdR+O1QrvmXLNOnj2okuGkCANwJb1bsmjlSLDk52TF5AOwlOZls3kwC\nAkhcHNdR+EpLMYuPaeN7qLrhngkAcDO8KXYYKQbuQq0ms2dzHYLf3k/RqqWCub0xZwIA3A5v\nTsVipBgANMfvudTuTNPnQzUyEU7CAoDb4c2KnZ1GigGAK9FZ2MXHav/WHSdhAcBN8abY2Wmk\nGAC4kvdP1Colgtf64CQsALgp3hQ7Yp+RYgDgMo7kUbtumv7zuC9OwgKA2+JTsbtDLpfHxMT8\n9fHq6ura2tqoqCiHJwIAjuks7KJjtbN6qHoH4WMeALgv3tw8QQi5ePHi+PHjo6KiBg0alJiY\nePfZ2DqffvppmzZtOMkGANxanqpViAWv405YAHBvvFmxS0lJGT58OEVRHh4eRUVFJ06c2LJl\nS3JyMgaIAUBKAZV83bj5cV+5GCdhAcCt8WbF7uOPP2YYJjk5Wa/X63S6L7/8MjU1dfTo0QaD\ngetoAMAlvYV9+0jtzG7KPjgJCwBujzfF7uLFi1OnTo2LixMIBDKZLCEhYf/+/RkZGU899dRf\nz8kCgPv4MFUrFwn+HqvmOggAAPd4U+xKSkratm179yPDhg377rvv9u7d+8Ybb3CVCsAu0tJI\nTg7XIfjhUK5523Xjp0O9cBIWAIDwqNgFBgZeuHCh3oMzZsx45513Vq1a9fnnn3OSCqD1xceT\n2FgSHU0w+LgpJQb67cO18b1wJywAwG28KXaTJ0/evXv36tWrrVbr3Y9/+OGHzz///FtvvZWQ\nkGA0GrmKB9A6GIasXUsIITR9+wDugWbIvIM10d7ieb1xEhYA4Dbe3BX73nvv7dix47XXXtu5\nc+fBgwfvPC4QCNatW+fl5bVy5UoO4wG0Dpomdz66NDQWGe5Ymaa7WW3b/aSfiDefTwEA7I43\n74i+vr7nzp2bM2dOly5d6j0lEAi++uqrbdu2tWvXjpNsAOBgpwotSen6z4Z6haoxRRAA4E+8\nWbEjhPj5+a1Zs+Zez06ePHny5MmOzAMAnKg0MQmHql/oqhwRJec6CwCAc+HNih0AACGEYckb\nh2oClaIF/XBpHQBAffwuditWrBg4cCDXKQDAcb45r88os3w90lsixP4mAAD18elU7F9lZmam\npKRwnQIAHORsseWrc7oVQzXhnri0DgCgAfxesQMA91FLMW/+XvN0J4+JMQquswAAOCkUOwDg\nAZaQtw7XKiWCdx/x5DoLAIDz4vepWABwE99nGFILqOQn/DA6DACgEfxesfvkk0/y8/O5TgEA\n9pVeal1xWrdssFe0Nz6LAgA0ht/vkhqNRqPRcJ0CAOyoSE+/cqBqcgfFpPa4tA4AoAn8XrED\nANdmsrFzDlRHeoqXDsSldQAATeP3ih0AuDCGJX//rabGzGyf7CcV4dI6AICmodgBgJNacUZ3\nqojaGufno8C5BQCAZsHbJYAzEQqJ8L+/lSK33oM3+Ybpuwv6lcO92/vg8ycAQHOh2AE4E5GI\nDB16+3jECE6jcOlcieXdo7WLBngOjZRxnQUAgE/wURjAySQnk82bSUAAiYvjOgo3CnT0Kweq\n42IUz3VRcp0FAIBnUOwAnIxaTWbP5joEZwxW9m/7qtppxMsG4zZYAIAWQ7EDAGfBsCThtxqj\njd000VsixG2wAAAthmIHAM7i45PatBLLtkm+3nJc/gsAcD9Q7ADAKWy6bNxwybBuvE8bDd6X\nAADuEz4WAwD3km+Y3j9R+9EQTf9Q3AYLAHD/UOwAgGMHss0Lj9S8N9DriQ6YBgsA8EBQ7ACA\nS8fyqb//VvNGrPrZhzy4zgIAwHsodgDAmdRCKn5/9Zxeqtk9VVxnAQBwBSh2AMCN9FLL7P3V\nzzzk8VpvtDoAgNaBYgcAHLhSYX1pb/WTHTwW9cdGxAAArQbFDsD5pKWRnByuQ9jRtUrrjF+q\nRkTJFg9AqwMAaE0odgBOJj6exMaS6GiSnMx1FLvIrrG9sKfqkRDpx49qMF0CAKB1odgBOBOG\nIWvXEkIITd8+cC15Wnr67qqegdKvRniL0OoAAFobih2AM6FpYrXePqYoTqO0vsxq29M7Kzv5\nileN1Ijw3gMAYAd4cwUAR7hUbp22q7KrvyRxtLcEp2ABAOwDxQ4A7O50kWX67soh4bLEUd4y\nnIIFALAbFDsAsK/fc6mZe6smt/f4bCjOwAIA2JeY6wAA4Mp23TQtOFzzUnfVWw+ruc4CAOD6\nUOwAwF5+uGxcdqL2nUc8X+ym5DoLAIBbQLEDALtIStd/cVb30RCvJzt6cJ0FAMBdoNgBQCtj\nCfnkpHbDJePXI71Ht5FzHQcAwI2g2AFAa7IxZOGRmoM55vXjfR4OkXIdBwDAvaDYAUCr0VLM\n3F9rMqutmx7z7eIv4ToOAIDbQbEDgNaRr6Nn7a0SCMjPk/xC1SKu4wAAuCNsKgUArSCjzPrk\n9opApWhrHFodAABnUOwA4EH9mm2evqtyaKR87TgftRSDJQAAOINTsQDwQNb/YfgoVTu3t2pe\nH2xBDADAMRQ7AGciFBKhkDAMIYSInP2EJs2SD1Jqf7pqWjFMMzFGwXUcAADAqVgApyISkaFD\nbx+PGMFplCYYrWz8/qrdmeYNE3zQ6gAAnARW7ACcTHIy2byZBASQuDiuo9xTTq1t7q81FppN\nnuwX4ensK4sAAO4DxQ7AyajVZPZsrkM0Zk+W6d2jtb2DpF8O12hkWPUHAHAiKHYA0FwWmv3k\nlO6Hy4a5vVSv9VYLcf8rAICTQbEDgGYp1NGvH6zO19HrxvkMCJNxHQcAABqA0ygA0LTfcsyP\n/Vwhlwj2TPFHqwMAcFpYsQOAxtAM+eKs7tsL+pd7qN7sqxbh9CsAgBNDsQOAeyrW068drMnV\n2taO8xkUjoU6AABnh1OxANCwPVnm8Vsr5GKyd4o/Wh0AAC/wb8WOZdns7Oxbt27pdDpCiJeX\nV0xMTHh4ONe5AFyH3sIuPVG7K9M0r7c6vpcKp18BAPiCT8Wuurr6ww8/3LhxY1lZWb2nIiIi\nZs2aNX/+fIUCO+ADPJALZdY3DtUwDPufib69g6RcxwEAgBbgTbErLi4eMGBAdnZ2TEzMuHHj\nIiMjlUolIUSr1WZlZR09evS9997btm3b4cOHvb29uQ4LwEs0Q77L0H95VvdYtGLZIC8PCVbq\nAAB4hjfFbvHixQUFBVu2bJkyZcpfn6VpOikp6dVXX33//fdXrlzp+HgArSktjfj5kagoR/7M\nAh39xqGam9W2L4ZpJkRj5RsAgJd4c/PEnj17ZsyY0WCrI4SIRKI5c+Y89dRT27dvd3AwgFYW\nH09iY0l0NElOdtjPTL5hGrulXC4W7H/KD60OAIC/eFPsKisr27Vr1/hrOnXqVFpa6pg8AHbB\nMGTtWkIIoenbB3ZWaWJeOVD9j6O1b/ZV/3uCT6BS5IAfCgAAdsKbU7EhISEZGRmNvyY9PT0k\nJMQxeQDsgqaJ1Xr7mKLs+qNYQpKvmz5M1YaoRTue8Gvvw5t3AwAAuBferNjFxcVt3bp1xYoV\nVEP/2hkMhiVLluzcuXPq1KmOzwbAO/k6+sU9VYuO1T7X1WP7ZF+0OgAA18Cbd/OlS5ceP358\nwYIFy5Yt69u3b3h4uEqlYllWr9fn5uaeOXPGaDQOGjRo0aJFXCcFcGo0QzZeNnxxRveQn2T3\nFL92Gt68CQAAQJN4856u0WhOnjy5Zs2aDRs2HDlyhKbpO09JJJLevXvPnDlz5syZIhGuEAK4\np2uV1neO1ubU0m/2VT/XRSnEfiYAAK6FN8WOECKVShMSEhISEsxmc35+ft3kCU9Pz4iICKkU\n26gCNMZsY5Mu6L85bxgULv1mtHcQbpIAAHBFfCp2dViWLSoqys3NvTNSTCaTYaQYQCOO5VNL\nT2jNNnb1KM2IKDnXcQAAwF74VOwwUgygpXJqbR+mao/mUyCEyZMAACAASURBVNM7K9/sq1ZJ\ncfIVAMCV8abYYaQYQIsYbey3F/T/TDf0CpLsesKvo6+E60QAAGB3vCl2GCkG0EwsITtumD49\npRULBR8N8ZrUHsvYAADugjf72GGkGEBzXCyzTkmuXHysdlpnj0PT/NHqAADcCm+KHUaKATSu\nSE8nHKp5Irkiykt0aJr/vD5qmQhX1AEAuBfenIrFSDGAe6k0MYnn9ZuvGDv5irfE+fUMxOV0\nAABuijcrdhgpBvBXRiublK4f9p+y4/nUF8M02yaj1QEAuDXerNhhpBjA3Uw29qerxsTzeplI\n8E4/zykdPUS8+ZgGAAD2wptih5Fi4BaEQiIUEoYhhJB7/J/ZxpCfrxlXndNbGXZWN+UL3ZS4\nlg4AAOrwptgRjBQDdyASkaFDyaFDhBAyYkS9J60Mm3zDtOacXm9h/9ZD+VxXpUKMSgcAAH/i\nU7Grg5Fi4OKSk8nmzSQggMTF3XnMaGN/umL8LsNgsDLPdVW+3F2lxgwJAAD4Cz4VO4wUA7eg\nVpPZs+98pbewP183/jNdT7Pk2Yc8Xuiq9JLhYjoAAGgYb4odRoqBu6k0MT9cNqz/w6iWCuJ7\nqqZ28sCJVwAAaBxvih1GioH7yNPS317Q/3zdFOEpWtzfc2KMQoxFOgAAaAbeFLvmjBQ7duzY\n9u3bUeyAp2iWHMkzb7psPJ5PdfGXrByhGRklF2KRDgAAmo03xa6ZI8WSk5MdkwegFVWYmG3X\njJuvGMuMzIgo2frxPgPCZFyHAgAA/uFNscNIMXBJl8qt6/8w7M40hahEz3T2mNLRw0eB064A\nAHCfeFPs4uLiVq1aFRsb+9prr8lk9RczDAbDZ599tnPnzrfffpuTeAAtorOw268bN18xZtfY\nhkbKvx3rMzBMhrOuAADwgAQsy3KdoVlqamqGDx9+/vx5tVrdyEixvXv3qlSq5n/b3Nzc/v37\nm0ymRl5DUZTRaNTpdC36zgANulJh3XTZuOumSSUVPNXJ4+lOHsEqjEsBAOATi8Uik8lSUlL6\n9+/PdZb6eFPsCCEWi6VupNgff/zRWiPFbDbbL7/8YrVaG3nN1atXlyxZQlEU5lvAfbMy7MFs\n6serxpQCqou/5IWuyseica8rAAAvodi1MgePFEtNTR0wYACKHdyfUgP941XjD5eNlI19LEYx\n4yGPjr4SrkMBAMD9c+Zix5tr7O7ASDHgBZ2FPZRj/iXLdDSPivEWJ8Sq42IUHpLmXUaXlkb8\n/EhUlH0jAgCAy+FTscNIMXB+NRRzKIfad8uUUmBRiAUjomSbJ/rGBrdkrTc+niQlEZGIbN1K\nJk2yW1IAAHBBvCl2GCkGzqyGYg7nUnuzTMfzLUqJYGikbPUozeBwmaSld7oyDFm7lhBCaJqs\nXYtiBwAALcKbYoeRYuCEyozMwWzzgWzzqUJKIxeOaiP/fpx3vxCZ6L7viqBpcudWHopqpZgA\nAOAueFPsMFIMnEe+jj5wy/xrtjm91OLvIRrdRj63l6pPsFSEjegAAIBTvCl2GCkGnMvX0ody\nzXuzzOdLLKFq0fAo+Vv91L0CpdhYGAAAnARvih1GigEnbAw5V2I5nGs+lEvdqrF18BGPbit/\nf5BnJ2xZAgAAzoc3xQ4jxcCRKk3M0TzqcJ75eD5ltLK9gqRTOipGtZFHefHmVwYAANwQb/6V\nWrp06fHjxxcsWLBs2bJGRootWrSI66TAVywhl8qtR/Kow7nmP8qtXjLhkAjZ8sFeA8NlGhlm\nRAAAAA/wpthpNJqTJ0/WjRQ7cuRIa40UA8jX0akFVEqB5WQRVW1iOvlJhkbIFg/w7BaAmyEA\nAIBneFPsCCFSqTQhISEhIcHBI8XA9VSbmdRCS2ohlVJA5WvpAA/hgDDZO/08B4RJA5X4bAAA\nAHzFp2J3h1wuj4mJqTumafrGjRsGg6FLly5yuZzbYODMTDY2rdiSUkilFFiuVVo9JIJ+IbIX\nuyoHhMmivXn5iwAAAFAPn/49S01NXbly5Y0bN9q0abN48eJevXplZmZOmjTp0qVLhBC1Wv3J\nJ5/MmTOH65jgRGiWXCq3phRQKYXU+RIry5JeQZLRbeTLBnl285fe/zbCAAAATok3xe706dOP\nPvqo1WqVSCQZGRm///57enr6Cy+8kJ2dPX36dJPJ9Ouvv86dOzc8PPyxxx7jOixwiSXkVo3t\nVKElpYA6VWTRUkwHX8mAUOnfuqtiQ6QeYlw3BwAALos3xW758uWEkO3bt0+cOLGkpGTs2LFL\nliw5derUkSNHBg4cSAi5ceNGr169Vq1ahWLnhqpMTEaZ9UKZJaPMmlFm1VJMiEo0IEz2/iDP\nR0JlfgoszQEAgFvgTbE7efLk1KlTJ02aRAgJDQ1duXLl8OHDBw8eXNfqCCHt27efMmXKzp07\nOY0JDmK2sVcrrRll1gul1gtllnwtrRALHvKTdA+QTOno0TNQEqLCPRAAAOB2eFPstFrt3SPF\nHn74YUJI586d735NSEhI3a2y4HpsDLleZb1YZv2j3PpHufV6lZVlSVuNuFuA5OXuqh6Bko4+\nElwzBwAAbo43xS4sLCw7O/vOl0ql0svLS6PR3P2arKwsX19fh0cDu7Ax5Ga19UqF7Y9yyx9l\n1quVNopmQ9Wibv6SCe3k7z7i2cVfopa63AVzQiERCgnDEEIINmUEAIAW4k2xGzZs2A8//PDy\nyy/fOfdaU1Nz9wtOnTpVdwUeF+mgFegs7NVK69UK65VK25UK680qm5VhA5WiLn6SRyPlr/eR\ndPWX+Lj81XIiERk6lBw6RAghI0ZwnQYAAHiGN8Vu4cKF27dvHzx48MKFCz/66KN6z86YMeOn\nn35iWRazYvnCxpDsGtuNatuNKuvNKtuVSmu+lhYJSBuNuJOv5LFoeSdfSWc/ia/LN7m/Sk4m\nmzeTgAASF8d1FAAA4BneFLvo6OiUlJTXX3+9waFhGRkZQUFBq1evjo2NdXw2aBLNkgKt7XqV\n7Wa17XqlLbPaequGtjKsl0zY3kcc4y2O76Hq6Cfp4CNWYDsStZrMns11CAAA4CXeFDtCSKdO\nnQ4ePNjgU/v37w8JCXFwHrgXLcVk19K3amx3/pdTS1toVikRRHuLO/hInujo0cFHHOMtxvwu\nAACAVsSnYtcItDquVJmYPB2dr7Xla+l8LZ2rtWVV2ypMDCEkUClqqxG11Yhjgz3aasRtNeJQ\ntcjtl+MAAADsiN/FbsWKFTt27Dhx4gTXQVwcRbNlBqbMSJcZmTIDXaSn87R0vpbO09oMVpYQ\n4qMQRqhF4Z7iPsHSpzt5tNGI22rESglaHAAAgEPxu9hlZmampKRwncIV1JiZChNTYWRKjXSl\niSkz0hVGptTAlBnpciNTSzF1L/OWC/09hMEqUYSnqE+wNEItCvMURXiiwwEAADgFfhc7aA4L\nzVabmUoTU2FiKk3MneMqE11hYsoMTKWJsTIsIUQkJL5yoZ+HKMBD6KsQ9gyS+ClkQUqRn0IY\npBL5KYRSnEoFAABwYih2PGa0sbVmpoZias1sNcVUmZgaM1NNMTVmpsp8+7/VZkZvYeteLxUJ\nfORCX4XQz0PoIxe28RL3DRH5KYR+CmGAUuSrEPoqhChuAAAA/IVi51y0FKO1sFqK0d35r4XR\nUqzWwtRSTK2ZraGYWoqppZgaM1u3zEYIERCikQu95UKNXOgtE3orhO29xd5yobdC6CMX+siF\nPgqhv4cIJ0wBAABcG7+L3SeffLJo0SKuU7TM+RLLrzlmnYXVUYzOwuqtrM7C6C2s3sLo/ru0\nVkctFXjKhJ5SoadMoJYKPWWCCC9RN5nESybUyAVeMqGXTKiRCbxkQi85VtoAAACA58VOo9HU\nGxfr/PK09M0qm0oqVMuEYZ5ClUSgkgrU0roDoadMUNfkPGXoagAAANAy/C52fBTXXhHXXsF1\nCnBuaWnEz49ERXGdAwAAeMb9BnECOLn4eBIbS6KjSXIy11EAAIBnUOwAnAnDkLVrCSGEpm8f\nAAAANBuKHYAzoWlitd4+pihOowAAAP+g2AEAAAC4CBQ7AAAAABeBYgcAAADgIlDsAAAAAFwE\nih0AAACAi0CxAwAAAHARKHYAAAAALgLFDgAAAMBFoNgBAAAAuAgUOwAAAAAXgWIHAAAA4CJQ\n7P6/vXuPiuI8/D/+LKwLS5aLKMilhIt6EK1aLlVEjAhNPWAOSqINNTFGJKm3BFKjxqTWpGp6\n0jRGipBGjRq1MZy05qbVNFTBKOoqGE0EEiJCvECsF0RckNv+/pjT/e4PE0m97LPMvl9/7Twz\nzHxmxN0PO7OzAAAAKkGxAwAAUAmt7AA9gE6nE0K4uLjIDgL1cxYi/7+PKz79dJVGIzMNAOCH\nKfXA3mjMZrPsDD3AsWPH2tvb78iqfve735lMpieeeOKOrE0FampqlixZsmbNGr1eLzuLvVi2\nbNnw4cNTU1NlB7EXBw8e3Lx5c15enuwgdmTu3LnTpk2LjY2VHcRefPTRR8eOHVuyZInsIPai\nubn5ySefXLZsWUhIiOws9mLt2rVubm7Lly+/I2vTarXDhw+/I6u6syh2tjZjxgwhxIYNG2QH\nsRdlZWXR0dFXrlzx8PCQncVexMfHJycnv/DCC7KD2IuCgoKsrKz6+nrZQeyIn59fTk7Oww8/\nLDuIvVixYsXOnTv37dsnO4i9aGxs9PT0LC0tjYqKkp3FXjjI6y/X2AEAAKgExQ4AAEAlKHYA\nAAAqQbEDAABQCYodAACASlDsAAAAVIJiBwAAoBIUOwAAAJWg2AEAAKgE3xVra/b51XIS6XQ6\nJycnrZZfxf+j0+n4PbHGAbkRx6QLDkgXWq3WycmJY2LNQY4GX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] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "20 x 2 sparse Matrix of class \"dgCMatrix\"\n", + " Full_OLS s1\n", + "(Intercept) 45822.7774 44109.5208\n", + "LotFrontage 27.2866 . \n", + "LotArea 1.9631 1.7403\n", + "MasVnrArea 36.6718 32.5969\n", + "TotalBsmtSF 36.9469 37.9546\n", + "GrLivArea 82.9417 80.9013\n", + "BsmtFullBath 11144.9818 9407.9130\n", + "BsmtHalfBath 3482.7632 . \n", + "FullBath 9165.1128 7159.1181\n", + "HalfBath 290.2871 . \n", + "BedroomAbvGr -15968.2776 -12964.7247\n", + "KitchenAbvGr -33430.6905 -29590.9030\n", + "Fireplaces 2092.4632 2414.9024\n", + "GarageArea 44.8185 46.5876\n", + "WoodDeckSF 14.5117 10.5983\n", + "OpenPorchSF 34.9419 20.0826\n", + "EnclosedPorch 7.4118 . \n", + "ScreenPorch -15.0181 . \n", + "PoolArea 100.2163 73.2391\n", + "ageSold -481.2720 -489.9599" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "set.seed(1234)\n", + "\n", + "# Full LS\n", + "Housing_full_OLS <- lm(SalePrice ~ .,\n", + "data = training_Housing\n", + ")\n", + "\n", + "# LASSO\n", + "Housing_LASSO_min <- coef(Housing_cv_LASSO, s = \"lambda.min\")\n", + "\n", + "Housing_reg_coef <- round(cbind(\n", + " Full_OLS = coef(Housing_full_OLS),\n", + " LASSO_min = Housing_LASSO_min), 4)\n", + "\n", + "Housing_reg_coef" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can use the trained LASSO model to predict the response of the test set!!\n", + "\n", + "Run the code below to compare the prediction performance of LS with those of LASSO in the test set" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# Full LS predictions\n", + "\n", + "Housing_test_pred_full_OLS <- predict(Housing_full_OLS, newdata = testing_Housing)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# LASSO predictions with lambda.min\n", + "\n", + "Housing_test_pred_LASSO_min <- predict(Housing_cv_LASSO, \n", + " newx = Housing_X_test, \n", + " s = \"lambda.min\")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 2 × 2
ModelR_MSE
<chr><dbl>
OLS Full Regression 31397.47
LASSO Regression with minimum MSE31340.37
\n" + ], + "text/latex": [ + "A tibble: 2 × 2\n", + "\\begin{tabular}{ll}\n", + " Model & R\\_MSE\\\\\n", + " & \\\\\n", + "\\hline\n", + "\t OLS Full Regression & 31397.47\\\\\n", + "\t LASSO Regression with minimum MSE & 31340.37\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 2 × 2\n", + "\n", + "| Model <chr> | R_MSE <dbl> |\n", + "|---|---|\n", + "| OLS Full Regression | 31397.47 |\n", + "| LASSO Regression with minimum MSE | 31340.37 |\n", + "\n" + ], + "text/plain": [ + " Model R_MSE \n", + "1 OLS Full Regression 31397.47\n", + "2 LASSO Regression with minimum MSE 31340.37" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Comparison\n", + "\n", + "Housing_R_MSE_models <- rbind(tibble(\n", + " Model = \"OLS Full Regression\",\n", + " R_MSE = rmse(\n", + " preds = Housing_test_pred_full_OLS,\n", + " actuals = testing_Housing$SalePrice\n", + " )\n", + "),\n", + " tibble(\n", + " Model = \"LASSO Regression with minimum MSE\",\n", + " R_MSE = rmse(\n", + " preds = Housing_test_pred_LASSO_min,\n", + " actuals = testing_Housing$SalePrice\n", + " )\n", + " )\n", + ")\n", + "\n", + "Housing_R_MSE_models" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "#### In this example the full LS model has slightly worse prediction performance than LASSO\n", + "\n", + "> results may depend on the split of the data. We need to make several splits to assess these models" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Can we use LASSO for inference??\n", + "\n", + "In the second part of worksheet 10 you will examine this question." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.2.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}