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# Learning rational stochastic tree languages

Abstract : We consider the problem of learning stochastic tree languages from a sample of trees independently drawn from a probability distribution $P$. Usually, from a grammatical inference point of view, we estimate $P$ in a class of model such as probabilistic tree automata. We propose to work in a strictly larger class: the class of rational stochastic tree languages. These languages can, in fact, be computed by rational tree series or, equivalently, by multiplicity tree automata. In this paper, we provide two contributions. First, we show that rational tree series admit a canonical representation with parameters that can be efficiently estimated from samples. Then, we give an efficient inference algorithm that identify the class of rational stochastic tree languages in the limit with probability one.
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https://hal.archives-ouvertes.fr/hal-00192401
Contributor : Amaury Habrard <>
Submitted on : Tuesday, November 27, 2007 - 5:34:46 PM
Last modification on : Thursday, January 11, 2018 - 6:16:32 AM
Long-term archiving on: : Monday, April 12, 2010 - 5:20:12 AM

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• HAL Id : hal-00192401, version 1

### Citation

Francois Denis, Amaury Habrard. Learning rational stochastic tree languages. 2007. ⟨hal-00192401v1⟩

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