Learning PDFA with Asynchronous Transitions

13 years 2 months ago

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In this paper we extend the PAC learning algorithm due to Clark and Thollard for learning distributions generated by PDFA to automata whose transitions may take varying time lengths, governed by exponential distributions. 1 Motivation The problem of learning (distributions generated by) probabilistic automata and related models has been intensely studied by the grammatical inference community; see [4, 12, 13] and references therein. The problem has also been studied in variants of the PAC model. In particular, it has been observed that polynomial-time learnability of PDFA is feasible if one allows polynomiality not only in the number states but also in other measures of the target automaton complexity. Speciﬁcally, Ron et al. [11] showed that acyclic PDFA can be learned w.r.t. the Kullback–Leibler (KL) divergence in time polynomial in alphabet size, 1/ , 1/δ, number of target states, and 1/µ, where µ denotes the distinguishability of the target automaton. Clark and Thollard exte...

Borja Balle, Jorge Castro, Ricard Gavaldà

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