\dm_csml_event_details UCL ELLIS

Optimal Thinning of MCMC Output


Marina Riabiz


King's College London


Friday, 29 September 2023




Function Space, UCL Centre for Artificial Intelligence, 1st Floor, 90 High Holborn, London WC1V 6BH



Event series

DeepMind/ELLIS CSML Seminar Series


The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo (MCMC) can be sub-optimal in terms of the empirical approximations that are produced. Typically, a number of the initial states are attributed to “burn in” and removed, whilst the remainder of the chain is “thinned” if compression is also required. In this talk, I consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel class of methods is proposed, based on minimisation of a kernel Stein discrepancy (KSD), that is suitable when the gradient of the log-target can be evaluated and an approximation using a small number of states is required. To minimize the KSD, we consider greedily scanning the entire MCMC output to select one point at the time, as well as selecting more than one point at a time (making the algorithm non-myopic), and mini-batching the candidate set (making the algorithm non-greedy). Theoretical results guarantee consistency of these methods and their effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations.


Marina Riabiz obtained her undergraduate and master’s degree in Mathematical Engineering from Politecnico di Milano, Italy, specialising in Applied Statistics. She completed her PhD in the Signal Processing Group, Information Engineering, at the University of Cambridge, UK, working on latent variable models for Bayesian inference with stable distribution and processes. She then joined King’s College London in 2018 for her postdoc in the Cardiac Electro-Mechanics Research Group (School of Biomedical Engineering and Imaging Sciences), working on uncertainty quantification for cardiac myocyte models. During this time, she was also a visiting researcher at the Alan Turing Institute. In 2021 Marina joined the Department of Mathematics (KCL) as a Lecturer in Statistics.