Cross-moments computation for stochastic context-free grammars

TL;DR

This paper introduces new algorithms for efficiently computing cross-moments of any order for vector variables in stochastic context-free grammars, extending prior work limited to scalar variables and second order.

Contribution

It develops general algorithms for cross-moments of arbitrary order in stochastic context-free grammars, unifying and extending previous methods.

Findings

Algorithms for arbitrary order cross-moments are proposed.

Previous second-order scalar methods are special cases of the new algorithms.

Efficient computation of cross-moments enhances analysis of stochastic grammars.

Abstract

In this paper we consider the problem of efficient computation of cross-moments of a vector random variable represented by a stochastic context-free grammar. Two types of cross-moments are discussed. The sample space for the first one is the set of all derivations of the context-free grammar, and the sample space for the second one is the set of all derivations which generate a string belonging to the language of the grammar. In the past, this problem was widely studied, but mainly for the cross-moments of scalar variables and up to the second order. This paper presents new algorithms for computing the cross-moments of an arbitrary order, and the previously developed ones are derived as special cases.