A Spectral Approach for Probabilistic Grammatical Inference on Trees

Raphaël Bailly (1) , Amaury Habrard (1) , Francois Denis (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

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.

Mots clés: weighted tree automata; stochastic languages; spectral methods

Domaines: Apprentissage [cs.LG]

Raphaël Bailly, Amaury Habrard, Francois Denis. A Spectral Approach for Probabilistic Grammatical Inference on Trees. 21st International Conference on Algorithmic Learning Theory (ALT 2010), Oct 2010, Australia. pp.74-88. ⟨hal-00607096⟩