# A new similarity measure for covariate shift with applications to nonparametric regression

arXiv: https://arxiv.org/abs/2202.02837 · HTML: https://mlsanity.com/paper/2202.02837/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 31 references that are in the map.
- First posted on arXiv 6 Feb 2022.

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

- [Marginal Singularity, and the Benefits of Labels in Covariate-Shift](https://mlsanity.com/paper/1803.01833/) (2018)
- [Near-Optimal Linear Regression under Distribution Shift](https://mlsanity.com/paper/2106.12108/) (2021)
- [Minimax Lower Bounds for Transfer Learning with Linear and One-hidden Layer Neural Networks](https://mlsanity.com/paper/2006.10581/) (2020)

## Built on by (most cited first, 30 of 33)

- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [Adaptive and Robust Multi-Task Learning](https://mlsanity.com/paper/2202.05250/) (2022)
- [The Power and Limitation of Pretraining-Finetuning for Linear Regression under Covariate Shift](https://mlsanity.com/paper/2208.01857/) (2022)
- [Transfer Learning for Contextual Multi-armed Bandits](https://mlsanity.com/paper/2211.12612/) (2022)
- [A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models](https://mlsanity.com/paper/2401.07187/) (2024)
- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)
- [Maximum Likelihood Estimation is All You Need for Well-Specified Covariate Shift](https://mlsanity.com/paper/2311.15961/) (2023)
- [When is Importance Weighting Correction Needed for Covariate Shift Adaptation?](https://mlsanity.com/paper/2303.04020/) (2023)
- [Towards a Unified Analysis of Kernel-based Methods Under Covariate Shift](https://mlsanity.com/paper/2310.08237/) (2023)
- [Double Debiased Covariate Shift Adaptation Robust to Density-Ratio Estimation](https://mlsanity.com/paper/2310.16638/) (2023)
- [Transfer Learning Beyond Bounded Density Ratios](https://mlsanity.com/paper/2403.11963/) (2024)
- [Mitigating Covariate Shift in Misspecified Regression with Applications to Reinforcement Learning](https://mlsanity.com/paper/2401.12216/) (2024)
- [Help Me Help You: The Aggregate Value of Source and Target Data in Transfer Learning](https://mlsanity.com/paper/2408.16189/) (2024)
- [Computational Efficiency under Covariate Shift in Kernel Ridge Regression](https://mlsanity.com/paper/2505.14083/) (2025)
- [Classification Tree Pruning Under Covariate Shift](https://mlsanity.com/paper/2305.04335/) (2023)
- [Transfer Learning for Kernel-based Regression](https://mlsanity.com/paper/2310.13966/) (2023)
- [On the design-dependent suboptimality of the Lasso](https://mlsanity.com/paper/2402.00382/) (2024)
- [Sharp analysis of out-of-distribution error for "importance-weighted" estimators in the overparameterized regime](https://mlsanity.com/paper/2405.06546/) (2024)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Statistical Learning under Heterogeneous Distribution Shift](https://mlsanity.com/paper/2302.13934/) (2023)
- [Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift](https://mlsanity.com/paper/2312.17463/) (2023)
- [Bridging Domains with Approximately Shared Features](https://mlsanity.com/paper/2403.06424/) (2024)
- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)
- [Harnessing the Power of Vicinity-Informed Analysis for Classification under Covariate Shift](https://mlsanity.com/paper/2405.16906/) (2024)
- [A Conditional Distribution Equality Testing Framework using Deep Generative Learning](https://mlsanity.com/paper/2509.17729/) (2025)
- [TILT: Target-induced loss tilting under covariate shift](https://mlsanity.com/paper/2605.14280/) (2026)
- [Covariate shift in nonparametric regression with Markovian design](https://mlsanity.com/paper/2307.08517/) (2023)
- [ADs: Active Data-sharing for Data Quality Assurance in Advanced Manufacturing Systems](https://mlsanity.com/paper/2404.00572/) (2024)
- [Prediction Accuracy & Reliability: Classification and Object Localization under Distribution Shift](https://mlsanity.com/paper/2409.03543/) (2024)
- [Transfer Learning of Surrogate Models: Integrating Domain Warping and Affine Transformations](https://mlsanity.com/paper/2501.18344/) (2025)

## Abstract (arXiv)

We study covariate shift in the context of nonparametric regression. We introduce a new measure of distribution mismatch between the source and target distributions that is based on the integrated ratio of probabilities of balls at a given radius. We use the scaling of this measure with respect to the radius to characterize the minimax rate of estimation over a family of H"older continuous functions under covariate shift. In comparison to the recently proposed notion of transfer exponent, this measure leads to a sharper rate of convergence and is more fine-grained. We accompany our theory with concrete instances of covariate shift that illustrate this sharp difference.