On concentration of self-bounding functions
On concentration of self-bounding functions
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关于自限函数的集中
DOI：
10.1214/ejp.v14-690
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发表时间：
2009
影响因子：
1.4
通讯作者：
P. Massart
中科院分区：
文献类型：
--
作者：
S. Boucheron;G. Lugosi;P. Massart
我们证明了使用熵方法对自我限制功能的一些新浓度不平等。作为应用程序，我们恢复了Talagrand的凸距离不平等。由于对所谓的赫布斯特论点进行了仔细的分析，因此得出了新的伯恩斯坦般的自我结合功能的不平等现象。后者涉及差异不平等的解决方案之间的比较结果，这本身可能是有趣的。
We prove some new concentration inequalities for self-bounding functions using the entropy method. As an application, we recover Talagrand's convex distance inequality. The new Bernstein-like inequalities for self-bounding functions are derived thanks to a careful analysis of the so-called Herbst argument. The latter involves comparison results between solutions of differential inequalities that may be interesting in their own right.