Optimal Thinning od MCMC Output

Riabiz Marina, King's College London

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 the 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 a 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.

Area: CS36 - Monte Carlo methods and Applications II (Francesca R Crucinio, Alessandra Iacobucci, Andrea Bertazzi)

Keywords: MCMC postprocessing, Kernel Stein Discrepancy, optimal quantization