Covariate-Dependent Graphical Model Estimation via Neural Networks

This is the official repo for the paper titled "Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees", by Jiahe Lin, Yikai Zhang and George Michailidis, published in Transactions on Machine Learning Research (TMLR), 2025. [Link to paper]

Setup

The following installs the necessary packages and their dependencies into the venv:

pip install -e .

Repo Outline

• bin/: shell scripts for running synthetic data experiments with multiple data replicas; see also Synthetic Data Experiments section
• configs/:
  • _synthetic_.yaml: config file for the parameters used in synthetic data generation;
  • *.yaml: config file that stores the hyperparameters used for running the end-to-end training
• generator/: scripts used for generating synthetic data
  • simulator/: various simulator objects for synthetic data generation;
  • generated data are automatically saved to data_sim/${data_str}_seed${data_seed}/.
• models/: main implementation of the models
• notebook/: demo for running the model on the S&P 100 stock data (Appendix C of the paper)
• utils/:
  • datasets/: torch.utils.data.dataset.Dataset objects used for loading the data, depending on their storing format;
  • utils_train.py: functions for facilitating each step required for training the neural network;
• ./:
  • run_sim.py: script for running synthetic data experiments with nn-based covariate-dependent graphical model estimation
  • run_complete.R: script for running synthetic data experiments using glasso or neighborhood selection (mb).

Synthetic Data Experiments

Valid DATA_STR: GGM1, GGM2, NPN1, NPN2, DAG1, DAG2.

• Generate data

  ## for Gaussian data
  python -u generator/generate_GGM.py --data_str=$DATA_STR --data_seed=$DATA_SEED
  ## for DAG-based DGP
  python -u generator/generate_DAG.py --data_str=$DATA_STR --data_seed=$DATA_SEED
  ## for non-paranormal based DGP
  python -u generator/generate_NPN.py --data_str=$DATA_STR --data_seed=$DATA_SEED

  See configs/_synthetic_.yaml

  To generate multiple data replicas all at one

  cd bin
  bash generate.sh $DATA_STR

• Run experiments

  To run a specific synthetic dataset

  ## VERSION is either empty (default, neural network based method) or `reggmm` (linear method)
  python -u run_sim.py --data_str=$DATA_STR --train_size=$TRAIN_SIZE --gpu=$GPU_ID --data_seed=$DATA_SEED --version=$VERSION

  To run multiple synthetic data replicas in one go:

  cd bin
  bash run.sh $DATA_STR $GPU_ID $VERSION

  To run competitor models that leverage R packages (glasso or neighborhood selection aka mb) can be run through bin/run-r.sh.

Finally, to run the entire pipeline for any specific data setting (as specified through $DATA_STR) encompassing generating data, running proposed DNN model and competitors, refer to bin/run-all.sh

Real Data Experiments

See Appendix E of the manuscript for the accessibility of the raw data.

The resting-state fMRI Dataset

• Raw data is stored in the format of .RData. We first leverage the reticulate package to convert the data so that it can be read in through Python. See data/fmri-data-convert.R, which outputs the corresponding .npz files.
• See notebooks/demo-run-fmri-data.ipynb for the end-to-end model run and results visualization.

S&P 100 Constituents Dataset

• In this repo, we provide a copy of the processed daily data (see folder data/stock/*). Here, $x$ (node values) correspond to the $\beta$-adjusted residual returns (relative to SPX) of the constituent stocks, with the $\beta$ calculated based on a 252-day lookback window; $z$ (covariates) correspond to the returns of SPX, Nasdaq and the level of VIX.
• See notebooks/demo-run-stock-data.ipynb for the end-to-end model run and results visualization.

Citation and Contact

To cite this work:

@article{lin2025covariate,
    title = {Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees},
    author = {Lin, Jiahe and Zhang, Yikai and Michailidis, George},
    year = {2025},
    journal = {Transactions on Machine Learning Research},
    issn={2835-8856},
    url = {https://openreview.net/pdf?id=beqSqPgE33}
}

For questions on the code implementation, contact Jiahe Lin.