PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Relevant Representations for the Inference of Rational Stochastic Tree Languages
François Denis, Edouard Gilbert, Amaury Habrard, Faissal Ouardi and Marc Tommasi
In: 9th International Colloquium on Grammatical Inference (ICGI 2008), Saint Malo, France(2008).

Abstract

Recently, an algorithm - dees - was proposed for learning rational stochastic tree languages. Given a sample of trees independently and identically drawn according to a distribution defined by a rational stochastic language, dees outputs a linear representation of a rational series which converges to the target. dees can then be used to identify in the limit with probability one rational stochastic tree languages. However, when dees deals with finite samples, it often outputs a rational tree series which does not define a stochastic language. Moreover, the linear representation can not be directly used as a generative model. In this paper, we show that any representation of a rational stochastic tree language can be transformed in a reduced normalised representation that can be used to generate trees from the underlying distribution. We also study some properties of consistency for rational stochastic tree languages and discuss their implication for the inference. We finally consider the applicability of \dees to trees built over an unranked alphabet.

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EPrint Type:Conference or Workshop Item (Paper)
Additional Information:This version is a long version of the paper published in the ICGI proceedings.
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:4493
Deposited By:Amaury Habrard
Deposited On:13 March 2009