This repository contains the research code for

Vaidotas Simkus, Benjamin Rhodes, Michael U. Gutmann. Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data. Journal of Machine Learning Research, 2023.

The paper can be found here: https://jmlr.org/papers/v24/21-1373.html.

The code is shared for reproducibility purposes and is not intended for production use. It should also serve as a reference implementation for anyone wanting to use VGI for model estimation from incomplete data.

Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are typically controlled by free parameters that are estimated from data by maximum-likelihood estimation. However, when faced with real-world datasets many of the models run into a critical issue: they are formulated in terms of fully-observed data, whereas in practice the datasets are plagued with missing data. The theory of statistical model estimation from incomplete data is conceptually similar to the estimation of latent-variable models, where powerful tools such as variational inference (VI) exist. However, in contrast to standard latent-variable models, parameter estimation with incomplete data often requires estimating exponentially-many conditional distributions of the missing variables, hence making standard VI methods intractable. We address this gap by introducing variational Gibbs inference (VGI), a new general-purpose method to estimate the parameters of statistical models from incomplete data.

We invite the readers of the paper to also see the Jupyter notebook, where we demonstrate VGI on two statistical models and animate the learning process to help better understand the method.

Below is an animation from the notebook of a Gaussian Mixture Model fitted from incomplete data using the VGI algorithm (left), and the variational Gibbs conditional approximations (right) throughout iterations.

Install python dependencies from conda and the cdi project package with

conda env create -f environment.yml
conda activate cdi
python setup.py develop

If the dependencies in environment.yml change, update dependencies with

conda env update --file environment.yml

All data used in the paper are stored in data directory and the corresponding data loaders can be found in cdi/data directory.

The main code to the various methods used in the paper can be found in cdi/trainers directory.

• trainer_base.py implements the main data loading and preprocessing code.
• variational_cdi.py and cdi.py implement the key code for variational Gibbs inference (VGI).
• mcimp.py implements the code for variational block-Gibbs inference (VBGI) used in the VAE experiments.
• The other scripts in cdi/trainers implement the comparison methods and variational conditional pre-training.

The code for the statistical (factor analysis, VAEs, and flows) and the variational models are located in cdi/models.

The experiment_configs directory contains the configuration files for all experiments. The config files include all the hyperparameter settings necessary to reproduce our results. The config files are in a json format. They are passed to the main running script as a command-line argument and values in them can be overriden with additional command-line arguments.

train.py is the main code we use to run the experiments, and test.py is the main script to produce analysis results presented in the paper.

The Jupyter notebooks in notebooks directory contain the code which was used to analysis the method and produce figures in the paper. You should also be able to use these notebooks to find the corresponding names of the config files for the experiments in the paper.

Before running any code you'll need to activate the cdi conda environment (and make sure you've installed the dependencies)

conda activate cdi

To train a model use the train.py script, for example, to fit a rational-quadratic spline flow on 50% missing MiniBooNE dataset

python train.py --config=experiment_configs/flows_uci/learning_experiments/3/rqcspline_miniboone_chrqsvar_cdi_uncondgauss.json

Any parameters set in the config file can be overriden by passing additionals command-line arguments, e.g.

python train.py --config=experiment_configs/flows_uci/learning_experiments/3/rqcspline_miniboone_chrqsvar_cdi_uncondgauss.json --data.total_miss=0.33

Some VGI experiments use variational model "warm-up", which pre-trains the variational model on observed data as probabilistic regressors. The experiment configurations for these runs will have var_pretrained_model set to the name of the pre-trained model. To run the corresponding pre-training script run, e.g.

python train.py --config=experiment_configs/flows_uci/learning_experiments/3/miniboone_chrqsvar_pretraining_uncondgauss.json

For model evaluation use test.py with the corresponding test config, e.g.

python test.py --test_config=experiment_configs/flows_uci/eval_loglik/3/rqcspline_miniboone_chrqsvar_cdi_uncondgauss.json

This will store all results in a file that we then analyse in the provided notebook.

For the VAE evaluation, where variational distribution fine-tuning is required for test log-likelihood evaluation use retrain_all_ckpts_on_test_and_run_test.py.

While the main purpose of this repository is reproducibility of the research paper and a demonstration of the method, you should be able to adapt the code to fit your statistical models. We would advise you to first see the Jupyter notebook demo. The notebook provides an example of how to implement the target statistical model as well as the variational model of the conditionals, you can find further examples in cdi/models directory. If you intend to use a variational family that is different to ours you will also need to implement the corresponding sampling functions here.