Optimal Thinning od MCMC Output
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