Learning Probabilistic Automata: A Study In State Distinguishability
Borja Balle, Jorge Castro and Ricard Gavaldà
Theoretical Computer Science 2011.

Abstract

Known algorithms for learning PDFA can only be shown to run in time poly- nomial in the so-called distinguishability μ of the target machine, besides the number of states and the usual accuracy and confidence parameters. We show that the dependence on μ is necessary in the worst case for every algorithm whose structure resembles existing ones. As a technical tool, a new variant of Statistical Queries termed L∞ -queries is defined. We show how to simulate L∞ -queries using classical Statistical Queries and show that known PAC algorithms for learning PDFA are in fact statistical query algo- rithms. Our results include a lower bound: every algorithm to learn PDFA with queries using a reasonable tolerance must make Ω(1/μ1−c ) queries for every c > 0. Finally, an adaptive algorithm that PAC-learns w.r.t. another measure of complexity is described. This yields better efficiency in many cases, while retaining the same inevitable worst-case behavior. Our algo- rithm requires less input parameters than previously existing ones, and has a better sample bound. Keywords: Distribution Learning, PAC Learning, Probabilistic Automata, Statistical Queries

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