一般损失函数的无集中学习
Learning without Concentration for General Loss Functions
摘要：
我们研究预测和估计问题，使用经验风险最小化，相对于一般的凸损失函数。即使浓度是假的或非常有限的，例如，在重尾的情况下，我们得到尖锐的错误率。我们的研究结果表明，错误率取决于两个参数：一个捕获类的内在复杂性，并基本上导致在无噪声（或可实现）的问题的错误率;其他措施类成员之间的相互作用的目标和损失，并占主导地位时，问题是远离可实现的。我们还解释了如何处理离群值，通过选择损失的方式来校准类的内在复杂性和问题的噪声水平（后者是由目标和类之间的距离来衡量的）。
英文摘要：
We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed scenarios. Our results show that the error rate depends on two parameters: one captures the intrinsic complexity of the class, and essentially leads to the error rate in a noise-free (or realizable) problem; the other measures interactions between class members the target and the loss, and is dominant when the problem is far from realizable. We also explain how one may deal with outliers by choosing the loss in a way that is calibrated to the intrinsic complexity of the class and to the noise-level of the problem (the latter is measured by the distance between the target and the class).
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