Bounding the Expectation of the Supremum of an Empirical Process Over a (Weak) VC-Major Class
Bounding the Expectation of the Supremum of an Empirical Process Over a (Weak) VC-Major Class
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DOI：
10.1214/15-ejs1055
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
Y. Baraud
中科院分区：
文献类型：
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作者：
Y. Baraud
给定一个有界函数类G和独立随机变量X1，. . .，Xn，我们提供了一个上界的期望的经验过程的上确界的元素G具有一个小的方差。当G是VC-子图或VC-主图类时，我们的界也适用，并且它的阶数小于用泛熵界得到的阶数。它还涉及显式常数，并且不需要G的熵的知识
Given a bounded class of functions G and independent random variables X1, . . . , Xn, we provide an upper bound for the expectation of the supremum of the empirical process over elements of G having a small variance. Our bound applies in the cases where G is a VC-subgraph or a VC-major class and it is of smaller order than those one could get by using a universal entropy bound over the whole class G . It also involves explicit constants and does not require the knowledge of the entropy of G