论文标题
Chernoff在单位间隔中绑定随机变量的注释
A Note on the Chernoff Bound for Random Variables in the Unit Interval
论文作者
论文摘要
Chernoff Bound是一种众所周知的工具，可根据其样本平均值获得高概率与Bernoulli随机变量的期望。这种结合通常在统计学习理论中使用，以在二进制数据值损失函数的情况下，以其对持有数据的经验风险来限制假设的概括风险。但是，在单位间隔中以随机变量为单位变量的情况的扩展在社区中不太了解。在本说明中，我们提供了此扩展名的证明，以方便和将来参考。
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the generalisation risk of a hypothesis in terms of its empirical risk on held-out data, for the case of a binary-valued loss function. However, the extension of this bound to the case of random variables taking values in the unit interval is less well known in the community. In this note we provide a proof of this extension for convenience and future reference.
