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

arXiv: https://arxiv.org/abs/2505.06531 · HTML: https://mlsanity.com/paper/2505.06531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 7 references that are in the map.
- First posted on arXiv 10 May 2025.

## Builds on (most cited first, 3 of 3)

- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Model selection for high-dimensional linear regression with dependent observations](https://mlsanity.com/paper/1906.07395/) (2019)

## Abstract (arXiv)

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.