2019-05-22
10:15 at HCP F 43.4

Accelerated sampling of multimodal probability distributions

Benedict Leimkuhler

The University of Edinburgh, Scotland

We have been working on the design of efficient algorithms for sampling intractable probability distributions, motivated by problems in molecular dynamics and, lately, statistics. Exploration is impeded by multimodality and poor scaling; standard sampling procedures waste resource in redundant local exploration. I will discuss the design of innovative algorithms based on extensions or modifications of Langevin dynamics for enhancing sampling in such applications, including preconditioning schemes [1], simulated tempering methods [2], and methods based on diffusion maps [3]. If time permits (or even if it doesn’t) I will also plug our new software package, the Thermodynamic Analytics ToolkIt [4], which brings a versatile sampling framework to the Tensorflow universe.

[1] B. Leimkuhler, C. Matthews and J. Weare, Ensemble preconditiong for Markov Chain Monte Carlo simulation, Statistics and Computing, 28:277-290, 2018.
[2] A. Martinsson, J. Lu, B. Leimkuhler, and E. Vanden-Eijnden, The simulated tempering method in the infinite switch limit with adaptive weight learning, Journal of Statistical Mechanics: Theory and Experiment, 013207, 2019.
[3] Z. Trstanova, B. Leimkuhler and T. Lelievre, Local and global perspectives on diffusion maps in the analysis of molecular systems, 2019. https://arxiv.org/abs/1901.06936
[4] F. Heber, Z. Trstanova and B. Leimkuhler, TATi - Thermodynamic Analytics ToolkIt: TensorFlow-based software for posterior sampling in machine learning applications, 2019. https://arxiv.org/abs/1903.08640.