提出高维加权信息准则，实现模型选择的最优偏差-方差平衡。
High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality
- 基于重要性加权正交贪心算法，构建可调迭代次数的模型选择框架。
- 理论证明该方法在高维误设回归下达到最优预测误差收敛速率。
- 适用于存在协变量偏移的高维数据建模，尤其适合精准预测场景。
Imori 和 Ing（2025）提出了重要性加权正交贪心算法（IWOGA），用于在协变量偏移条件下进行高维误设回归模型选择。为确定 IWOGA 的迭代次数，他们引入了高维重要性加权信息准则（HDIWIC）。作者认为，将 IWOGA 与 HDIWIC 结合使用（即 IWOGA + HDIWIC）可在方差与平方偏差之间实现最优权衡，从而在条件均方预测误差意义上达到最优收敛率。本文在一组合理假设下，对该结论提供了理论验证，证明了 IWOGA + HDIWIC 的最优性。
原文摘要 · Abstract (English)
Imori and Ing (2025) proposed the importance-weighted orthogonal greedy algorithm (IWOGA) for model selection in high-dimensional misspecified regression models under covariate shift. To determine the number of IWOGA iterations, they introduced the high-dimensional importance-weighted information criterion (HDIWIC). They argued that the combined use of IWOGA and HDIWIC, IWOGA + HDIWIC, achieves an optimal trade-off between variance and squared bias, leading to optimal convergence rates in terms of conditional mean squared prediction error. In this article, we provide a theoretical justification for this claim by establishing the optimality of IWOGA + HDIWIC under a set of reasonable assumptions.
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