A comparison of collapsed Bayesian methods for probabilistic finite automata

This paper describes several collapsed Bayesian methods, which work by first marginalizing out transition probabilities, for inferring several kinds of probabilistic finite automata. The methods include collapsed Gibbs sampling (CGS) and collapsed variational Bayes, as well as two new methods. Their targets range over general probabilistic finite automata, hidden Markov models, probabilistic deterministic finite automata, and variable-length grams. We implement and compare these algorithms over the data sets from the Probabilistic Automata Learning Competition (PAutomaC), which are generated by various types of automata. We report that the CGS-based algorithm designed to target general probabilistic finite automata performed the best for any types of data.