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arXiv · 2509.17729

A Conditional Distribution Equality Testing Framework using Deep Generative Learning

Siming Zheng·Tong Wang·Meifang Lan·Yuanyuan Lin
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Abstract

In this paper, we propose a general framework for testing the conditional distribution equality in a two-sample problem, which is most relevant to covariate shift and causal discovery. Our framework is built on neural network-based generative methods and sample splitting techniques by transforming the conditional testing problem into an unconditional one. We introduce the generative classification accuracy-based conditional distribution equality test (GCA-CDET) to illustrate the proposed framework. We establish the convergence rate for the learned generator by deriving new results related to the recently-developed offset Rademacher complexity and prove the testing consistency of GCA-CDET under mild conditions.Empirically, we conduct numerical studies including synthetic datasets and two real-world datasets, demonstrating the effectiveness of our approach. Additional discussions on the optimality of the proposed framework are provided in the online supplementary material.

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Siming Zheng, Tong Wang, Meifang Lan, Yuanyuan Lin. 2025-09-22. A Conditional Distribution Equality Testing Framework using Deep Generative Learning. https://arxiv.org/abs/2509.17729

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