Inside Outside algorithm

This is a Method page for the Inside-outside algorithm.

Background

The inside-outside algorithm is a way of estimating probabilities in a PCFG. It is first introduced [| Baker, 1979]. The inside outside algorithm is in fact a generalization of the forward-backward algorithm (for hidden Markov models) to PCFGs.

It is often used as part of the EM algorithm for computing expectations.

Algorithm

The algorithm is a dynamic programming algorithm that is often used with chart parsers to estimate expected production counts.

The algorithm works by computing

The inside probability is defined as $\beta (A,i,j)=P(A\Rightarrow {\hat {*}}w_{i}...w_{j}|G,\mathbf {w} )$, which is the probability of a nonterminal $A$ generating the word sequence $w_{i}$ to $w_{j}$