# Machine-Learning-Assisted Comparison of Regression Functions

arXiv: https://arxiv.org/abs/2510.24714 · HTML: https://mlsanity.com/paper/2510.24714/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum](https://mlsanity.com/paper/2010.07147/) (2020)
- [Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing](https://mlsanity.com/paper/1508.00655/) (2015)
- [Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization](https://mlsanity.com/paper/2502.13030/) (2025)
- [Is a Classification Procedure Good Enough? A Goodness-of-Fit Assessment Tool for Classification Learning](https://mlsanity.com/paper/1911.03063/) (2019)
- [Distance and Kernel-Based Measures for Global and Local Two-Sample Conditional Distribution Testing](https://mlsanity.com/paper/2210.08149/) (2022)
- [Nonparametric Tests for Treatment Effect Heterogeneity with Duration Outcomes](https://mlsanity.com/paper/1612.02090/) (2016)
- [Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders](https://mlsanity.com/paper/2201.00073/) (2021)

## Abstract (arXiv)

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing approaches typically rely on smoothing techniques and are thus hindered by the curse of dimensionality. We propose a generalized notion of kernel-based conditional mean dependence that provides a new characterization of the null hypothesis of equal regression functions. Building on this reformulation, we develop two novel tests that leverage modern machine learning methods for flexible estimation. We establish the asymptotic properties of the test statistics, which hold under both fixed- and high-dimensional regimes. Unlike existing methods that often require restrictive distributional assumptions, our framework only imposes mild moment conditions. The efficacy of the proposed tests is demonstrated through extensive numerical studies.