用对称KL信息刻画Gibbs算法的泛化误差
Characterizing the Generalization Error of Gibbs Algorithm with Symmetrized KL information
摘要：
确定监督学习算法的泛化误差是学习理论中的一个重要问题，人们已经提出了各种方法。然而，现有的界限往往是松散的，缺乏保障。因此，它们可能无法表征学习算法的精确泛化能力。我们的主要贡献是一个精确的表征的预期泛化误差的著名的吉布斯算法在输入训练样本和输出假设之间的对称KL信息。该结果可用于收紧已有的期望泛化误差界。我们的分析提供了更多的洞察力的基本作用的对称KL信息控制的泛化误差的吉布斯算法。
英文摘要：
Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm. Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm in terms of symmetrized KL information between the input training samples and the output hypothesis. Such a result can be applied to tighten existing expected generalization error bound. Our analysis provides more insight on the fundamental role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm.
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