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.

翻译：基于神经条件密度估计的无似然推断方法已被证明相较于传统方法（如ABC）能大幅降低模拟负担。当应用于隐马尔可夫模型（HMM）等任何潜变量模型时，这些方法仅设计用于估计参数，而非参数与隐状态的联合分布。若简单将此类方法应用于HMM而忽略联合后验分布的推断，将导致对后验预测分布的估计不准确，从而影响拟合优度评估。为解决这一问题，我们提出一种新颖的样本高效无似然方法，用于估计隐式HMM的高维隐状态。该方法通过利用马尔可夫性，采用自回归流直接学习隐状态的复杂后验分布。在若干隐式HMM上的评估表明，我们的方法所获估计质量可与计算成本高得多的序贯蒙特卡洛算法相媲美。