High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality

Yong-Syun Cao; Shinpei Imori; Ching-Kang Ing

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arXiv · 2505.06531

High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality

Yong-Syun Cao·Shinpei Imori·Ching-Kang Ing

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Abstract

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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BibTeX RIS

Yong-Syun Cao, Shinpei Imori, Ching-Kang Ing. 2025-05-10. High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality. https://arxiv.org/abs/2505.06531

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