{"ID":2867689,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.17729","arxiv_id":"2509.17729","title":"A Conditional Distribution Equality Testing Framework using Deep Generative Learning","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.","short_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 testi...","url_abs":"https://arxiv.org/abs/2509.17729","url_pdf":"https://arxiv.org/pdf/2509.17729v3","authors":"[\"Siming Zheng\",\"Tong Wang\",\"Meifang Lan\",\"Yuanyuan Lin\"]","published":"2025-09-22T12:59:18Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}