Non-Reversible Markov Chain Monte Carlo

The application of Markov Chain Monte Carlo (MCMC) has exploded in the last decades, as it allows for efficient sampling of high-dimensional probability distributions for a very broad range of models, such as ones found in statistical mechanics, Bayesian statistics, artificial intelligence, computational chemistry, digital signal processing. The samples generated are then applied to make inference, for example calculating expectations or estimating probabilities. To make these algorithms efficient and scalable, they need to quickly converge to the desired distribution. Based on research by Diaconis, Holmes and Neal (2000) and more recently on the vorticity methodology of Sun et al. (2010) and Bierkens (2016), this project, covering both statistics and applied probability, will attempt to improve the fundamental MCMC models by introducing non-reversibility into the model design, which for example can be done by adding a direction vector to the exploratory process, or by lifting (in a suitable sense) the Markov chain to a larger state space while it remains invariant with respect to the desired probability distribution. Intuitively, the goal is to explore a space quicker by avoiding to spend too much time in places already visited. As model complexity grows with the advent of high-performance cloud computing and large amounts of data, the project also needs to consider computational implementations, for example by devising methods that does not increase the time complexity.

Bierkens, Joris. "Non-reversible metropolis-hastings." Statistics and Computing 26.6 (2016): 1213-1228.

Diaconis, Persi, Susan Holmes, and Radford M. Neal. "Analysis of a nonreversible Markov chain sampler." Annals of Applied Probability (2000): 726-752.

Sun, Yi, Jurgen Schmidhuber, and Faustino J. Gomez. "Improving the asymptotic performance of Markov chain Monte-Carlo by inserting vortices." Advances in Neural Information Processing Systems. 2010.