# When is Importance Weighting Correction Needed for Covariate Shift Adaptation?

arXiv: https://arxiv.org/abs/2303.04020 · HTML: https://mlsanity.com/paper/2303.04020/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 59 references that are in the map.
- First posted on arXiv 7 Mar 2023.

## Builds on (most cited first, 16 of 16)

- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Rethinking Importance Weighting for Deep Learning under Distribution Shift](https://mlsanity.com/paper/2006.04662/) (2020)
- [Marginal Singularity, and the Benefits of Labels in Covariate-Shift](https://mlsanity.com/paper/1803.01833/) (2018)
- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [Near-Optimal Linear Regression under Distribution Shift](https://mlsanity.com/paper/2106.12108/) (2021)
- [Understanding the role of importance weighting for deep learning](https://mlsanity.com/paper/2103.15209/) (2021)
- [A new similarity measure for covariate shift with applications to nonparametric regression](https://mlsanity.com/paper/2202.02837/) (2022)
- [Understanding Why Generalized Reweighting Does Not Improve Over ERM](https://mlsanity.com/paper/2201.12293/) (2022)
- [Generalization Bounds for Domain Adaptation](https://mlsanity.com/paper/1304.1574/) (2013)
- [Is Importance Weighting Incompatible with Interpolating Classifiers?](https://mlsanity.com/paper/2112.12986/) (2021)
- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)

## Built on by (most cited first, 13 of 13)

- [A Short Survey on Importance Weighting for Machine Learning](https://mlsanity.com/paper/2403.10175/) (2024)
- [Towards a Unified Analysis of Kernel-based Methods Under Covariate Shift](https://mlsanity.com/paper/2310.08237/) (2023)
- [Conditional Bayesian Quadrature](https://mlsanity.com/paper/2406.16530/) (2024)
- [High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization](https://mlsanity.com/paper/2406.03171/) (2024)
- [Computational Efficiency under Covariate Shift in Kernel Ridge Regression](https://mlsanity.com/paper/2505.14083/) (2025)
- [Spectral Algorithms under Covariate Shift](https://mlsanity.com/paper/2504.12625/) (2025)
- [Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shift](https://mlsanity.com/paper/2509.05106/) (2025)
- [Towards regularized learning from functional data with covariate shift](https://mlsanity.com/paper/2601.21019/) (2026)
- [Entropic Projection Alignment: Estimating, Explaining, and Improving Model Performance Under Distribution Shift](https://mlsanity.com/paper/2605.31250/) (2026)
- [Convergence Analysis of Nystr"om Subsampling in Covariate Shift Adaptation for Misspecified case](https://mlsanity.com/paper/2606.22259/) (2026)
- [Nonparametric Goodness-of-fit Testing under Covariate Shift](https://mlsanity.com/paper/2608.04860/) (2026)
- [Learning under Target Shift: Optimal Density Ratio Estimation and Importance-Weighted Regression](https://mlsanity.com/paper/2609.15785/) (2026)
- [Domain Adaptation with Target Information via Doubly-Anchored Distributionally Robust Optimization](https://mlsanity.com/paper/2609.32730/) (2026)

## Abstract (arXiv)

This paper investigates when the importance weighting (IW) correction is needed to address covariate shift, a common situation in supervised learning where the input distributions of training and test data differ. Classic results show that the IW correction is needed when the model is parametric and misspecified. In contrast, recent results indicate that the IW correction may not be necessary when the model is nonparametric and well-specified. We examine the missing case in the literature where the model is nonparametric and misspecified, and show that the IW correction is needed for obtaining the best approximation of the true unknown function for the test distribution. We do this by analyzing IW-corrected kernel ridge regression, covering a variety of settings, including parametric and nonparametric models, well-specified and misspecified settings, and arbitrary weighting functions.