Basic Methods of Probabilistic Context Free Grammars

In automatic speech recognition, language models can be represented by Probabilistic Context Free Grammars (PCFGs). In this lecture we review some known algorithms which handle PCFGs; in particular an algorithm for the computation of the total probability that a PCFG generates a given sentence (Inside), an algorithm for finding the most probable parse tree (Viterbi), and an algorithm for the estimation of the probabilities of the rewriting rules of a PCFG given a corpus (Inside-Outside). Moreover, we introduce the Left-to-Right Inside algorithm, which computes the probability that successive applications of the grammar rewriting rules (beginning with the sentence start symbol s) produce a word string whose initial substring is a given one.