A Spectral Approach for Probabilistic Grammatical Inference on Trees

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.
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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⟩

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