Testing Conditional Distribution Equality Using Generative Models
Abstract
Conditional distribution equality testing is a core problem with applications in causal inference, model diagnostics, and transfer learning. Existing methods often lose power when the conditioning variable is high-dimensional. We propose a new test that leverages generative models to compare conditional distributions using both observed data and synthetic samples. A sample-splitting and studentization scheme is introduced to control estimation error. Under the null, the test statistic is asymptotically normal, and we establish local power against contiguous alternatives. Our theory under the null and fixed alternative requires only consistency of the learned conditional distribution, allowing for a broad class of generative models. Empirical results demonstrate accurate size control and strong power in high-dimensional settings compared to representative kernel-based conditional and joint two-sample tests.
Related
- Testing the equality of parameters in fixed and increasing dimension
- Testing Equality of Distributions via Repeatedly Integrated Quantile Metrics Under Weak Moment Conditions
- Minimax Rates for Conditional Generative Learning under Wasserstein Loss
- Tight Bounds for Equivalence Testing with Non-Adaptive Conditional Samples
- Sequential Conditional Independence Testing with Machine Learning Models
BibTeX
@misc{jin2026testing,
title = {{Testing Conditional Distribution Equality Using Generative Models}},
author = {Zekai Jin and Yi Zhang and Yun Yang and Xiaofeng Shao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20447},
eprint = {2610.20447},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20447},
}
RIS
TY - UNPB
TI - Testing Conditional Distribution Equality Using Generative Models
AU - Zekai Jin
AU - Yi Zhang
AU - Yun Yang
AU - Xiaofeng Shao
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20447
UR - https://arxiv.org/abs/2610.20447
AB - Conditional distribution equality testing is a core problem with applications in causal inference, model diagnostics, and transfer learning. Existing methods often lose power when the conditioning variable is high-dimensional. We propose a new test that leverages generative models to compare conditional distributions using both observed data and synthetic samples. A sample-splitting and studentization scheme is introduced to control estimation error. Under the null, the test statistic is asymptotically normal, and we establish local power against contiguous alternatives. Our theory under the null and fixed alternative requires only consistency of the learned conditional distribution, allowing for a broad class of generative models. Empirical results demonstrate accurate size control and strong power in high-dimensional settings compared to representative kernel-based conditional and joint two-sample tests.
ER -