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.
This work was partially supported by the ANR LAMPADA ANR-09-EMER-007 project and by the IST Programme of the European Community, under the PASCAL2 Network of Excellence, IST-2007-216886. This publication only reflects the authors’ views.
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Bailly, R., Habrard, A., Denis, F. (2010). A Spectral Approach for Probabilistic Grammatical Inference on Trees. In: Hutter, M., Stephan, F., Vovk, V., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2010. Lecture Notes in Computer Science(), vol 6331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16108-7_10
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DOI: https://doi.org/10.1007/978-3-642-16108-7_10
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