Sparse adaptive pre-conditioning for MCMC

We will explore ways to improve the efficiency and accuracy of Markov Chain Monte Carlo (MCMC) algorithms using sparse pre-conditioning and adap ve MCMC methods. Adap ve pre-conditioning is a very effective strategy to speed up the exploration of a distribution using a Markov chain Monte Carlo algorithm, by learning a 'pre-conditioning matrix'. It can, however, be computationally expensive, as O(d^2) matrix entries need to be learned for a d-dimensional problem, and O(d^3) computations may also be needed if done naively. We will explore strategies for imposing sparsity on the pre-conditioning matrix, so that fewer matrix entries need to be learned and that matrix operations can be performed more efficiently. We will develop new theory and methodology for MCMC and also apply the new methods to various application areas.