PAC-Bayesian归纳和转换学习
PAC-Bayesian inductive and transductive learning
摘要：
我们在这里提出了一个PAC贝叶斯的观点自适应监督分类。使用凸分析，我们展示了如何获得局部措施的复杂性的分类模型，涉及相对熵的后验分布相对于吉布斯后验措施。我们讨论了相对界限，比较两个分类规则，以显示如何的利润率假设的曼门和Tsybakov可以取代一些经验测量的协方差结构的分类模型。我们还展示了如何关联到任何后验分布的{ \em有效温度}有关它的吉布斯先验分布具有相同水平的预期差错率，以及如何估计这个有效的温度从数据中，导致估计的预期差错率自适应收敛根据最佳可能的功率的样本量。然后，我们介绍了一个PAC-贝叶斯的观点，并使用它来改善已知的Vapnik的泛化界限，将它们扩展到样本独立但不相同分布的情况。最后，我们简要回顾了支持向量机的建设，并展示了如何推导出他们的泛化界限，通过支持向量的数量或通过转导或归纳利润估计来衡量的复杂性。
英文摘要：
We present here a PAC-Bayesian point of view on adaptive supervised classification. Using convex analysis, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior distributions with respect to Gibbs posterior measures. We discuss relative bounds, comparing two classification rules, to show how the margin assumption of Mammen and Tsybakov can be replaced with some empirical measure of the covariance structure of the classification model. We also show how to associate to any posterior distribution an {\em effective temperature} relating it to the Gibbs prior distribution with the same level of expected error rate, and how to estimate this effective temperature from data, resulting in an estimator whose expected error rate adaptively converges according to the best possible power of the sample size. Then we introduce a PAC-Bayesian point of view on transductive learning and use it to improve on known Vapnik's generalization bounds, extending them to the case when the sample is independent but not identically distributed. Eventually we review briefly the construction of Support Vector Machines and show how to derive generalization bounds for them, measuring the complexity either through the number of support vectors or through transductive or inductive margin estimates.
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