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Title: On the scalability of conditional particle filters Authors:  Matti Vihola - University of Jyväskylä (Finland) [presenting]
Anthony Lee - University of Warwick (United Kingdom)
Sumeetpal Singh - Cambridge University (United Kingdom)
Abstract: Hidden Markov models (HMMs) are a flexible framework for time-series modelling. Full Bayesian inference of non-linear and/or non-Gaussian HMMs has remained a challenge until the recently introduced particle Markov chain Monte Carlo methods. In particular, the conditional particle filter (CPF), and its backward sampling variant (CBPF), have been found efficient in many challenging settings. We discuss the scalability properties of the CPF and the CBPF with respect to the time horizon (length of the time series). Our theoretical results align well with the empirical observations about the efficiency. In particular, our findings about the CBPF confirm the long held view that the CBPF remains an effective sampler with a fixed number of samples even as the time horizon increases. Our analysis of the CBPF relies on analysis of a so-called coupled conditional backward sampling particle filter (CCBPF) algorithm, which is interesting on its own right. Indeed, CCBPF is a simple algorithmic variant of PREVIOUS methods suggested for unbiased estimation with respect to the smoothing distribution of a HMM.