论文标题
在无上下文的语法约束下，隐藏的马尔可夫模型中的边际推理查询
Marginal Inference queries in Hidden Markov Models under context-free grammar constraints
论文作者
论文摘要
任何涉及一组随机变量的概率模型的主要用途是在其上运行推理和采样查询。经典概率模型中的推理查询是通过计算作为输入事件的边际或条件概率的计算。当概率模型是顺序的时，涉及复杂语法的更复杂的边际推理查询可能会在计算语言学和NLP等领域中引起人们的关注。在这项工作中，我们解决了在隐藏的马尔可夫模型（HMMS）中计算无上下文语法（CFG）的可能性的问题。我们提供了一种动态算法，用于确切计算明确的无上下文语法类别的可能性。我们表明问题是NP-HARD，即使输入CFG的歧义性程度小于或等于2。然后，我们提出了一种完全多项式的随机近似方案（FPRAS）算法，以近似多种含有歧义的歧义CFG的可能性。
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.
