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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Francois Denis, Amaury Habrard. Learning rational stochastic tree languages. Proceedings of the 18th International Conference on Algorithmic Learning Theory (ALT'07), 2007, Japan. p.242-256. ⟨hal-00192401v2⟩

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