arXiv 2212.007512022-12-02cs.FLcs.LG

P(Expression|Grammar): Probability of deriving an algebraic expression with a probabilistic context-free grammar

University of Ljubljana（卢布尔雅那大学）；Jožef Stefan Institute（约瑟夫·斯特凡研究所）

Urh Primožič, Ljupčo Todorovski, Matej Petković

英文摘要：

Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence classes of strings derived by grammar and address the problem of calculating the probability of deriving a given expression with a given grammar. We show that the problem is undecidable in general. We then present specific grammars for generating linear, polynomial, and rational expressions, where algorithms for calculating the probability of a given expression exist. For those grammars, we design algorithms for calculating the exact probability and efficient approximation with arbitrary precision.

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