Dynamic programming for parsing and estimation of stochastic unification-based grammars

Abstract

Stochastic unification-based grammars (SUBGs) define exponential distributions over the parses generated by a unification-based grammar (UBG). Existing algorithms for parsing and estimation require the enumeration of all of the parses of a string in order to determine the most likely one, or in order to calculate the statistics needed to estimate a grammar from a training corpus. This paper describes a graph-based dynamic programming algorithm for calculating these statistics from the packed UBG parse representations of Maxwell and Kaplan (1995) which does not require enumerating all parses. Like many graphical algorithms, the dynamic programming algorithm's complexity is worst-case exponential, but is often polynomial. The key observation is that by using Maxwell and Kaplan packed representations, the required statistics can be rewritten as either the max or the sum of a product of functions. This is exactly the kind of problem which can be solved by dynamic programming over graphical models.