Learning Probabilistic Automata Using Residuals

A probabilistic automaton is a non-deterministic finite automaton with probabilities assigned to transitions and states that define a distribution on the set of all strings. In general, there are distributions generated by automata with a non-deterministic structure that cannot be generated by a deterministic one. There exist several methods in machine learning that can be used to approximate the probabilities of an automaton given its structure and a finite number of strings independently drawn with respect to an unknown distribution. In this paper, we efficiently construct a probabilistic automaton from a sample by first learning its non-deterministic structure using residual languages and then assigning appropriate probabilities to the transitions and states. We show that our method learns the structure of the automaton precisely for a class of probabilistic automata strictly including deterministic one and give some experimental results to compare the learned distribution with respect to other methods. To this end, we present a novel algorithm to compute the Euclidean distance between two weighted graphs effectively.