Analysis of Regression Algorithms with Unbounded Sampling

In this letter, we study a class of the regularized regression algorithms when the sampling process is unbounded. By choosing different loss functions, the learning algorithms can include a wide range of commonly used algorithms for regression. Unlike the prior work on theoretical analysis of unbounded sampling, no constraint on the output variables is specified in our setting. By an elegant error analysis, we prove consistency and finite sample bounds on the excess risk of the proposed algorithms under regular conditions.

在这封信中，我们研究了当采样过程无界时的一类正则化回归算法。通过选择不同的损失函数，学习算法可以涵盖多种常用的回归算法。与先前关于无界采样的理论分析工作不同，在我们的设定中没有对输出变量施加约束。通过一种精妙的误差分析，我们证明了在正则条件下所提出算法的超额风险的一致性以及有限样本界。