Simpler PAC-Bayesian bounds for hostile data
Simpler PAC-Bayesian bounds for hostile data
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DOI：
10.1007/s10994-017-5690-0
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发表时间：
2018-05-01
期刊：
影响因子：
7.5
通讯作者：
Guedj, Benjamin
中科院分区：
文献类型：
--
作者：
Alquier, Pierre;Guedj, Benjamin
PAC-Bayesian学习边界是学习社区最感兴趣的。它们的作用是将聚集分布的泛化能力与其经验风险以及相对于某些先验分布的Kullback-Leibler散度联系起来。不幸的是，大多数可用的边界通常依赖于沉重的假设，如有界性和独立的观察。本文旨在放松这些限制，并提供PAC贝叶斯学习界限，持有依赖，重尾观测（以下简称为敌对数据）。在这些界限中，Kullack-Leibler分歧被Csiszar f-分歧的一般版本所取代。我们证明了一个一般的PAC贝叶斯界，并展示了如何使用它在各种敌对的设置。
PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution to its empirical risk and to its Kullback-Leibler divergence with respect to some prior distribution . Unfortunately, most of the available bounds typically rely on heavy assumptions such as boundedness and independence of the observations. This paper aims at relaxing these constraints and provides PAC-Bayesian learning bounds that hold for dependent, heavy-tailed observations (hereafter referred to as hostile data). In these bounds the Kullack-Leibler divergence is replaced with a general version of Csiszar's f-divergence. We prove a general PAC-Bayesian bound, and show how to use it in various hostile settings.