The primary use of any probabilistic model involving a set of random variables is to run inference and sampling queries on it. Inference queries in classical probabilistic models is concerned by the computation of marginal or conditional probabilities of events given as an input. When the probabilistic model is sequential, more sophisticated marginal inference queries involving complex grammars may be of interest in fields such as computational linguistics and NLP. In this work, we address the question of computing the likelihood of context-free grammars (CFGs) in Hidden Markov Models (HMMs). We provide a dynamic algorithm for the exact computation of the likelihood for the class of unambiguous context-free grammars. We show that the problem is NP-Hard, even with the promise that the input CFG has a degree of ambiguity less than or equal to 2. We then propose a fully polynomial randomized approximation scheme (FPRAS) algorithm to approximate the likelihood for the case of polynomially-bounded ambiguous CFGs.

本文提出了一种计算隐马尔可夫模型中上下文无关文法概率的算法，解决了计算一类非二义性上下文无关文法概率的问题，并提出了一种可用于多项式绑定的二义性上下文无关文法概率的随机多项式算法。

在上下文无关文法约束下的隐藏马尔可夫模型中的边际推理查询