A Lower Bound for Learning Distributions Generated by Probabilistic Automata [chapter]

Borja Balle, Jorge Castro, Ricard Gavaldà
2010 Lecture Notes in Computer Science  
Known algorithms for learning PDFA can only be shown to run in time polynomial 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 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 these queries can be simulated from samples and observe that known PAC
more » ... orithms for learning PDFA can be rewritten to access its target using L∞-queries and standard Statistical Queries. Finally, we show a lower bound: every algorithm to learn PDFA using queries with a resonable tolerance needs a number of queries larger than (1/µ) c for every c < 1.
doi:10.1007/978-3-642-16108-7_17 fatcat:xknfxptpsfhvra7udyy4dn47mu