Sample-efficient neural likelihood-free Bayesian inference of implicit HMMs

TL;DR

This paper introduces a novel, sample-efficient likelihood-free method for accurately estimating the hidden states in implicit Hidden Markov Models using autoregressive flows, significantly reducing computational costs.

Contribution

It proposes a new approach that directly learns the high-dimensional posterior of hidden states in implicit HMMs, addressing limitations of existing likelihood-free methods.

Findings

Estimates are comparable to expensive SMC algorithms.

Method reduces simulation burden in Bayesian inference.

Effective for high-dimensional hidden states.

Abstract

Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable model, such as a Hidden Markov model (HMM), these methods are designed to only estimate the parameters, rather than the joint distribution of the parameters and the hidden states. Naive application of these methods to a HMM, ignoring the inference of this joint posterior distribution, will thus produce an inaccurate estimate of the posterior predictive distribution, in turn hampering the assessment of goodness-of-fit. To rectify this problem, we propose a novel, sample-efficient likelihood-free method for estimating the high-dimensional hidden states of an implicit HMM. Our approach relies on learning directly the intractable posterior distribution of the hidden states, using an autoregressive-flow, by exploiting the Markov property. Upon evaluating our approach on some implicit HMMs, we found that the quality of the estimates retrieved using our method is comparable to what can be achieved using a much more computationally expensive SMC algorithm.