Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Jin, Zekai, Zhang, Yi, Yang, Yun, Shao, Xiaofeng
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7222031731