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

TL;DR

This paper establishes the theoretical optimality of the combined importance-weighted greedy algorithm and information criterion for model selection in high-dimensional, misspecified regression models under covariate shift.

Contribution

It provides a rigorous proof of the optimality of IWOGA combined with HDIWIC, confirming their effectiveness in high-dimensional model selection.

Findings

IWOGA + HDIWIC achieves optimal convergence rates.

Theoretical justification for the optimality of the combined method.

Supports model selection under covariate shift in high dimensions.

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.