Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 59, Issue 1, Pages 573-587Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2012.2212414
Keywords
Dependent observations; generalization bounds; linear prediction; online learning; statistical learning theory
Funding
- Microsoft Research Ph.D. Fellowship
- Google Ph.D. Fellowship
- Department of Defense through a National Defense Science and Engineering Graduate Fellowship
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We study the generalization performance of online learning algorithms trained on samples coming from a dependent source of data. We show that the generalization error of any stable online algorithm concentrates around its regret-an easily computable statistic of the online performance of the algorithm-when the underlying ergodic process is beta- or phi-mixing. We show high-probability error bounds assuming the loss function is convex, and we also establish sharp convergence rates and deviation bounds for strongly convex losses and several linear prediction problems such as linear and logistic regression, least-squares SVM, and boosting on dependent data. In addition, our results have straightforward applications to stochastic optimization with dependent data, and our analysis requires only martingale convergence arguments; we need not rely on more powerful statistical tools such as empirical process theory.
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