GPU accelerated collective Monte Carlo methods

This folder contains the code for the arXiv preprint Collective Proposal Distributions for Nonlinear MCMC samplers: Mean-Field Theory and Fast Implementation.

Please visit our website for a full documentation.

Examples

The target distribution is a mixture of a banana-shaped distribution and three Gaussian distributions in dimension 2. The level sets of the target distribution are shown in red, the N particles in blue and the (rejected) proposals in green.

• The Vanilla CMC algorithm.

banana_CMC.mp4

• The MoKA Markov algorithm (adaptive version with a mixture of proposal distributions with different sizes updated at each iteration).

banana_MoKA_Markov.mp4

• The non-Markovian MoKA algorithm (adaptive version with a mixture of proposal distributions with different sizes updated at each iteration and depending on the past iterations).

banana_MoKA.mp4

• The non-Markovian MoKA algorithm with the KIDS weighting procedure in order to select the best particles.

banana_MoKA_KIDS.mp4

• The classical Metropolis-Hastings algorithm with N independent chains and a large proposal distribution.

banana_PMH.mp4

More examples in the article!

Authors

• Antoine Diez
• Grégoire Clarté
• Jean Feydy