Markov Chain Cubature for Bayesian Inference

This repository contains code for simulating Markov chains as a cloud of particles using cubature formulae.

The presentation folder contains slides describing the methodology.

The scripts folder contains the code.

Examples

2D Gaussian Mixture

This will run the cubature algorithm on a 2D Gaussian mixture:

 python gmm_cubature.py

Outputting something like

Time: 18.5 seconds
Number of particles:  1024

Cubature mean vector
[-4.13376   -1.8908577]

Cubature covariance matrix
[[ 2.31224477  1.89332097]
[ 1.89332097 10.73603521]]

Actual mean vector
[-4.148839  -1.8847313]

Actual variances
[2.2467885 10.953863]

Difference in means
0.016276047

An illustration of the resulting particle configurations is given below:

Bayesian Logistic Regression

This runs the algorithm for a Bayesian logistic regression on a binary Covertype dataset (see SVGD paper for details):

python bayesian_logisitc_regression_cubature.py

Outputting something like

Time: 1137.0 seconds
Number of particles:  256
[accuracy, log-likelihood]
[0.7573040282953107, -0.5628809048706431]

The content of markov_chain_cubature_presentation.pdf is licensed under the Creative Commons Attribution 4.0 International license, and the Python code is licensed under the MIT license.