English

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

Machine Learning 2025-05-13 v1 Machine Learning Statistics Theory Statistics Theory

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.

Cite

@article{arxiv.2505.06531,
  title  = {High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality},
  author = {Yong-Syun Cao and Shinpei Imori and Ching-Kang Ing},
  journal= {arXiv preprint arXiv:2505.06531},
  year   = {2025}
}
R2 v1 2026-06-28T23:27:58.955Z