MAP estimation of context-free grammars

Abstract In this paper Bayesian inference is used to recover, from a finite set of candidate grammars, the most probable grammar (and derivation) that generated the non-noisy version of an observed noisy string. It is assumed that the noise process is iid and defined by an arbitrary stochastic matrix. It is shown that if the grammars are context-free or stochastic context-free, this problem is solvable in polynomial time. Generalizations are also discussed.