Comparing MCMC Algorithms for Bayesian Hierarchical Gaussian Mixture Models

Folder structure

gmm-mcmc/
  ├── src/
  │   ├── generators/ # code to generate gaussian mixtures
  │   ├── models/ # code to build and validate hierarchical models
  │   ├── utils/
  ├── configs/ # configuration files for experiments
  ├── results/ # experiment resutls
  ├── requirements.txt
  ├── main.py # file to run the experiments
  ├── report.pdf
  └── README.md

Instructions

1. Creating the environment

First of all, clone the repository and create a virtual environment by running the following commands,

git clone https://github.com/alexcaldarone/gmm-mcmc.git
cd gmm-mcmc 
python3 -m venv venv

To activate the environment, if on Windows use:

venv\Scripts\activate

If on MacOs/Linnix use:

source venv/bin/activate

Then install the dependencies by running,

pip install -r requirements.txt

2. Running the experiments

The project allows one to easily run the experiments needed. Here is a breakdown of the steps needed:

1. Change the experiment settings (parameters of the components of the mixture) in the experiment_params.json file (Note: Change only the numerical values, the structure of the dictionary should stay the same)

2. Change the prior parameters of the hierarchical model components in the prior_params.json file (the same note as above holds - only change the numerical values)

3. Run the experiments using the command line by calling:

The main.py allws the user to run the experiments by specifying what set of experiments we are interested in and the sampler to use. The options are:

• Experiment tyepe: univariate (runs the experiments for the mixture of univariate gaussians) or multivariate (runs the experiments for the mixture of multivariate gaussian random variables)
• Sampler: which sampler to use for the experiments. At the moment the supported options are: Metropolis (to use Metropolis-Hastings algorithm) and HMC (to use Hamiltonian Monte Carlo)

In practice, the experiments are run by calling:

python3 main.py --type [type] --sampler [sampler]

Running this command will start the sampling for all the settings specified in the experiment_params.json file. The results will be saved in the results directory, under a folder of the format YYYYMMDD_HHMMSS. In here you will be able to find the traceplots and the summary statistics returned by the sampler.

If you wish to run more than one sampler for the same experiment settings, you will have to run one at a time (so run the above command twice, by changing the sampler option).

If you need extra help on how to manage the command line options, run

python3 main.py --help