A spectral approach for probabilistic grammatical inference on trees

Authors:
Raphaël Bailly;Amaury Habrard;François Denis
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille, UMR CNRS, Aix-Marseille Université, CMI, Marseille cedex 13, France;Laboratoire d'Informatique Fondamentale de Marseille, UMR CNRS, Aix-Marseille Université, CMI, Marseille cedex 13, France;Laboratoire d'Informatique Fondamentale de Marseille, UMR CNRS, Aix-Marseille Université, CMI, Marseille cedex 13, France
Venue:
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Year:
2010

Citing 8
Cited 0

Stochastic Inference of Regular Tree Languages

Machine Learning
A Hilbert Space Embedding for Distributions

ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Learning Rational Stochastic Tree Languages

ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Relevant Representations for the Inference of Rational Stochastic Tree Languages

ICGI '08 Proceedings of the 9th international colloquium on Grammatical Inference: Algorithms and Applications
On Rational Stochastic Languages

Fundamenta Informaticae
Bisimulation Minimisation of Weighted Automata on Unranked Trees

Fundamenta Informaticae
Grammatical inference as a principal component analysis problem

ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Languages as hyperplanes: grammatical inference with string kernels

ECML'06 Proceedings of the 17th European conference on Machine Learning

Quantified Score

Hi-index	0.00

Visualization

Abstract

We focus on the estimation of a probability distribution over a set of trees. We consider here the class of distributions computed by weighted automata - a strict generalization of probabilistic tree automata. This class of distributions (called rational distributions, or rational stochastic tree languages - RSTL) has an algebraic characterization: All the residuals (conditional) of such distributions lie in a finite-dimensional vector subspace. We propose a methodology based on Principal Components Analysis to identify this vector subspace. We provide an algorithm that computes an estimate of the target residuals vector subspace and builds a model which computes an estimate of the target distribution.