Stochastic And-Or grammars (AOG) extend traditional stochastic grammars of language to model other types of data such as images and events. In this paper we propose a representation framework of stochastic AOGs that is agnostic to the type of the data being modeled and thus unifies various domain-specific AOGs. Many existing grammar formalisms and probabilistic models in natural language processing, computer vision, and machine learning can be seen as special cases of this framework. We also propose a domain-independent inference algorithm of stochastic context-free AOGs and show its tractability under a reasonable assumption. Furthermore, we provide an interpretation of stochastic context-free AOGs as a subset of first-order probabilistic logic, which connects stochastic AOGs to the field of statistical relational learning. Based on the interpretation, we clarify the relation between stochastic AOGs and a few existing statistical relational models.
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