학술논문
Embedded Stochastic Syntactic Processes: A Class of Stochastic Grammars Equivalent by Embedding to a Markov Process
Document Type
Periodical
Author
Source
IEEE Transactions on Aerospace and Electronic Systems IEEE Trans. Aerosp. Electron. Syst. Aerospace and Electronic Systems, IEEE Transactions on. 57(4):1996-2005 Aug, 2021
Subject
Language
ISSN
0018-9251
1557-9603
2371-9877
1557-9603
2371-9877
Abstract
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.