On the Learnability and Usage of Acyclic Probabilistic Finite Automata

We propose and analyze a distribution learning algorithm for a subclass of Acyclic Probabilistic Finite Automata (APFA). This subclass is characterized by a certain distinguishability property of the automata's states. Though hardness results are known for learning distributions generated by general APFAs, we prove that our algorithm can indeed efficiently learn distributions generated by the subclass of APFAs we consider. In particular, we show that the KL-divergence between the distribution generated by the target source and the distribution generated by our hypothesis can be made small with high confidence in polynomial time. We present two applications of our algorithm. In the first, we show how to model cursively written letters. The resulting models are part of a complete cursive handwriting recognition system. In the second application we demonstrate how APFAs can be used to build multiplepronunciation models for spoken words. We evaluate the APFA based pronunciation models on l..