Learning implicit hidden Markov models using neural likelihood-free inference

Likelihood-free inference methods for implicit models based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. However, 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 posterior distribution of both the parameters and the hidden states. Naive application of these methods to a HMM, ignoring the inference of this joint posterior distribution, will result in overestimation of uncertainty of the posterior predictive. We propose a postprocessing step that can rectify this problem. 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 intractable HMMs, we found that the quality of the estimates retrieved using our postprocessing is comparable to what can be achieved using a computationally expensive particle-filtering which additionally requires a tractable data distribution.