Learning Probabilistic Automata Using Residuals

• Published in: Theoretical Aspects of Computing - ICTAC 2021 Vol. 12819; pp. 295 - 313
• Main Authors: Chu, Wenjing, Chen, Shuo, Bonsangue, Marcello
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: distance between discrete distributions; Learning automata; Probabilistic automata; Residual finite state automata
• ISBN: 3030853144; 9783030853143
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-85315-0_17

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.