This article addresses the problem of suitably defining statistical models of languages derived from context-free grammars (CFGs), where the observed strings may be corrupted by noise or other mechanisms. This article uses the concept of a stochastic syntactic process (SSP), which we have introduced in previous work. An SSP is a stochastic process taking values in the set of all parse trees of a CFG. Inference problems such as estimating a parse tree for “noisy” processes are of obvious significance, particularly in the motivating example of metalevel target tracking. This article demonstrates that by careful application of the theory of probability, an SSP can be embedded into a Markov random field (MRF), thus opening up the possibility of the application of advanced machine learning algorithms based on graphical models to inference problems involving sophisticated target behavior at the “meta” level. This article provides a simple example of how a simple CFG can be embedded in an MRF. Extensions to context-sensitive grammars are discussed.

中文翻译：

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嵌入随机句法过程：一类通过嵌入马尔可夫过程等价的随机语法

本文解决了适当定义源自上下文无关文法 (CFG) 的语言统计模型的问题，其中观察到的字符串可能会被噪声或其他机制破坏。这篇文章使用了一个概念随机句法过程（SSP），我们在之前的工作中已经介绍过。SSP 是一个随机过程，它在 CFG 的所有解析树的集合中取值。诸如估计“嘈杂”过程的解析树之类的推理问题具有明显的意义，特别是在元级目标跟踪的激励示例中。本文证明，通过仔细应用概率理论，可以将 SSP 嵌入到马尔可夫随机场 (MRF) 中，从而开辟了将基于图形模型的高级机器学习算法应用于涉及复杂目标的推理问题的可能性。 “元”级别的行为。本文提供了一个简单的示例，说明如何将简单的 CFG 嵌入到 MRF 中。讨论了上下文相关语法的扩展。