Learning rational stochastic languages

TL;DR

This paper introduces an efficient algorithm, DEES, for inferring rational stochastic languages generated by Multiplicity Automata, which can accurately estimate the target distribution from samples and converge to the true language.

Contribution

The paper presents DEES, a novel algorithm for inferring minimal normal representations of rational stochastic languages, with proven strong identification in the limit.

Findings

DEES efficiently estimates rational stochastic languages from samples.

The intermediary automata produced by DEES converge to the target language.

Rational stochastic languages can be closely approximated by the outputs of DEES.

Abstract

Given a finite set of words w1,...,wn independently drawn according to a fixed unknown distribution law P called a stochastic language, an usual goal in Grammatical Inference is to infer an estimate of P in some class of probabilistic models, such as Probabilistic Automata (PA). Here, we study the class of rational stochastic languages, which consists in stochastic languages that can be generated by Multiplicity Automata (MA) and which strictly includes the class of stochastic languages generated by PA. Rational stochastic languages have minimal normal representation which may be very concise, and whose parameters can be efficiently estimated from stochastic samples. We design an efficient inference algorithm DEES which aims at building a minimal normal representation of the target. Despite the fact that no recursively enumerable class of MA computes exactly the set of rational stochastic languages over Q, we show that DEES strongly identifies tis set in the limit. We study the intermediary MA output by DEES and show that they compute rational series which converge absolutely to one and which can be used to provide stochastic languages which closely estimate the target.