PAC-Bayesian Inequalities for Martingales

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Date

31 octobre 2011

Type de document
Périmètre
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arXiv

Collection

arXiv

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Cornell University


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Computer Science - Machine Learning Computer Science - Information Theory Statistics - Machine Learning


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Yevgeny Seldin et al., « PAC-Bayesian Inequalities for Martingales », arXiv, ID : 10670/1.76evaq


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We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where martingales are encountered. We also present a comparison inequality that bounds the expectation of a convex function of a martingale difference sequence shifted to the [0,1] interval by the expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma's inequality.

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