文章基本信息

标题：New Lower Bounds for Statistical Query Learning
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作者：Ke Yang
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2002
卷号：2002
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We prove two lower bounds on the Statistical Query (SQ) learning model. The first lower bound is on weak-learning. We prove that for a concept class of SQ-dimension d , a running time of ( d log d ) is needed. The SQ-dimension of a concept class is defined to be the maximum number of concepts that are ``uniformly correlated'', in that each pair of them have nearly the same correlation. This lower bound matches the upper bound in~\cite{BFJ+94}, up to a logarithmic factor. We prove this lower bound against an ``honest SQ-oracle'', which gives a stronger result than the ones against the more frequently used ``adversarial SQ-oracles''. The second lower bound is more general. It gives a continuous trade-off between the ``advantage'' of an algorithm in learning the target function and the number of queries it needs to make, where the advantage of an algorithm is the probability it succeeds in predicting a label minus the probability it doesn't. Both lower bounds extend and/or strengthen previous results, and solved an open problem left in~\cite{Y01}. A preliminary version of this paper appeared in the Proceedings of the Fifteenth Annual Conference on Computational Learning Theory, 2002 (COLT 2002)
关键词：KL-divergence , lower bound , PAC learning , Singular Value Decomposition , statistical query