High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality
This work addresses model selection in high-dimensional regression with covariate shift, offering a theoretical foundation for practitioners, but it is incremental as it builds on prior methods.
The authors provided theoretical justification for the IWOGA + HDIWIC method, showing it achieves an optimal trade-off between variance and squared bias, leading to optimal convergence rates in conditional mean squared prediction error for high-dimensional misspecified regression under covariate shift.
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.