Krishna Balasubramanian (UC Davis)
Langevin Monte Carlo (LMC) algorithms and their stochastic versions are widely used for sampling and large-scale Bayesian inference. Non-asymptotic properties of the LMC algorithm have been examined intensely over the last decade. However, existing analyses are restricted to the case of light-tailed (yet multi-modal) densities. In this talk, I will first present a variable transformation based approach for sampling from heavy-tailed densities using the LMC algorithm. This algorithm is motivated by a related approach for Metropolis random walk algorithm by Johnson and Geyer, 2013. I will next present non-asymptotic oracle complexity analysis of the proposed algorithm with illustrative examples. It will be shown that the proposed approach ‘works’ as long as the heavy-tailed target density satisfies certain tail conditions closely related to the so-called weak-Poincaré inequality.