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.

Cite

Text

Bailly et al. "A Spectral Approach for Probabilistic Grammatical Inference on Trees." International Conference on Algorithmic Learning Theory, 2010. doi:10.1007/978-3-642-16108-7_10

Markdown

[Bailly et al. "A Spectral Approach for Probabilistic Grammatical Inference on Trees." International Conference on Algorithmic Learning Theory, 2010.](https://mlanthology.org/alt/2010/bailly2010alt-spectral/) doi:10.1007/978-3-642-16108-7_10

BibTeX

@inproceedings{bailly2010alt-spectral,
  title     = {{A Spectral Approach for Probabilistic Grammatical Inference on Trees}},
  author    = {Bailly, Raphaël and Habrard, Amaury and Denis, François},
  booktitle = {International Conference on Algorithmic Learning Theory},
  year      = {2010},
  pages     = {74-88},
  doi       = {10.1007/978-3-642-16108-7_10},
  url       = {https://mlanthology.org/alt/2010/bailly2010alt-spectral/}
}