On the Computational Complexity of Approximating Distributions by Probabilistic Automata
Machine Learning - Computational learning theory
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SIAM Journal on Computing
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STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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The Journal of Machine Learning Research
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Probabilistic Finite-State Machines-Part I
IEEE Transactions on Pattern Analysis and Machine Intelligence
Prediction, Learning, and Games
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Theoretical Computer Science
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ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
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ECML'06 Proceedings of the 17th European conference on Machine Learning
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Journal of Computer and System Sciences
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Known algorithms for learning PDFA can only be shown to run in time polynomial in the so-called distinguishability @m of the target machine, besides the number of states and the usual accuracy and confidence parameters. We show that the dependence on @m 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 algorithms. Our results include a lower bound: every algorithm to learn PDFA with queries using a reasonable tolerance must make @W(1/@m^1^-^c) queries for every c0. 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 algorithm requires fewer input parameters than previously existing ones, and has a better sample bound.