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.

中文翻译：

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无界采样回归算法分析

在这封信中，我们研究了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，学习算法可以包括多种常用的回归算法。与之前的无界采样理论分析工作不同，我们的设置中没有指定对输出变量的约束。通过优雅的错误分析，我们证明了所提出算法在常规条件下的过度风险的一致性和有限样本界限。