  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.
