研究分布漂移下加权风险最小化的预测误差，给出理论保证。
Fast Rates for Nonstationary Weighted Risk Minimization
- 分解误差为学习项与漂移项，建立统一的泛化界。
- 在混合条件下证明了学习误差的枢轴不等式，适用于任意权重类。
- 在回归问题中恢复最优率，适合关注非平稳数据的研究者。
加权经验风险最小化是应对分布漂移的常见预测方法。本文研究其在非平稳条件下的泛化误差。我们给出了过剩风险的一般分解，包括学习项和与分布漂移相关的误差项，并在混合条件下证明了学习误差的枢轴不等式。该学习界对任意权重类一致成立，考虑了权重向量带来的有效样本量、权重与假设类的复杂度，以及潜在的数据依赖性。我们在线性模型、基函数逼近和神经网络的(自)回归问题中展示了结果的应用性与紧致性，在未加权且平稳的情形下恢复了最小最大最优率（至对数因子）。
原文摘要 · Abstract (English)
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a learning term and an error term associated with distribution drift, and prove oracle inequalities for the learning error under mixing conditions. The learning bound holds uniformly over arbitrary weight classes and accounts for the effective sample size induced by the weight vector, the complexity of the weight and hypothesis classes, and potential data dependence. We illustrate the applicability and sharpness of our results in (auto-) regression problems with linear models, basis approximations, and neural networks, recovering minimax-optimal rates (up to logarithmic factors) when specialized to unweighted and stationary settings.
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