Identifying Latent Stochastic Differential Equations

This repo provides code for learning latent stochastic differential equations with variational autoencoders. The main idea is given a time series, uncover the latent differential equation that governs the time series.

To get started, check out some of the examples in the notebook to get an idea of how the code works.

For synthetic data, the code uses a yaml file that details the necessary components of the experiment to generate data and train the network.

For real data, you must specify a subclass of the SDEDataset to define the aspects of your data.

Main functions

• To run the code with a particular yaml file, simply run python3 train.py -f experiment.yaml.
• To compute some statistics regarding how well the learned drift recovered the SDE, run python3 comp_crlb.py -f experiment.yaml.
• To test the autoencoder reconstruction capabilities on new data, run python3 test.py -f experiment.yaml.
• To analyze all the results run python3 analyze.py -f experiment.yaml

These are the four main functions that are used to compute properties of an experiment. However, usually the most interesting one is simply train.py to see what kind of SDE may be generating your data.

The code is written in PyTorch and uses mainly dependencies of PyTorch.

DNA Dataset

The data used for the DNA experiment is available here: https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/OJHYZA Download the relevant files and load them into another folder called data/DNA/. From there, the existing code should work to load the files (unfortunately cannot upload due to file size).

Questions/Feedback

Feel free to send the author an email on any issues or suggestions. We will continue to try to make the code more user-friendly and optimized.

Reference

To read the paper via open access, check the paper on arxiv Identifying Latent Stochastic Differential Equations The full paper is published in IEEE Transactions on Signal Processing Identifying Latent Stochastic Differential Equations

If the code was helpful, please consider citing the publication here:

@article{hasan2021identifying,
  title={Identifying Latent Stochastic Differential Equations},
  author={Hasan, Ali and Pereira, Jo{\~a}o M and Farsiu, Sina and Tarokh, Vahid},
  journal={IEEE Transactions on Signal Processing},
  volume={70},
  pages={89--104},
  year={2021},
  publisher={IEEE}
}