标题： 一种新的正则化经验风险最小化中一致性和过拟合的分析方法 显示英文标题

标题： A new analytical approach to consistency and overfitting in regularized empirical risk minimization

摘要： 本文研究了二元分类问题：给定来自某个总体的训练数据$x_1, \dots, x_n$及其关联标签$y_1,\dots, y_n \in \left\{0,1 \right\}$，确定未包含在训练数据中的元素$x$的最佳标签。更具体地说，本文研究了一种正则化的经验风险泛函的变体，该泛函内在地由观测数据定义，并且不依赖于潜在的总体。借助现代分析工具，当正则化参数以与样本大小相关的速率趋于零时，可以得到渐近一致性的简洁证明。这些分析工具为理解过拟合和欠拟合提供了一个新框架，并严格将过拟合的概念与紧致性损失联系起来。 显示英文摘要

摘要： This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$ not among the training data. More specifically, this work considers a variant of the regularized empirical risk functional which is defined intrinsically to the observed data and does not depend on the underlying population. Tools from modern analysis are used to obtain a concise proof of asymptotic consistency as regularization parameters are taken to zero at rates related to the size of the sample. These analytical tools give a new framework for understanding overfitting and underfitting, and rigorously connect the notion of overfitting with a loss of compactness.