A Conditional Distribution Equality Testing Framework using Deep Generative Learning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909925201936384 |
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| author | Zheng, Siming Wang, Tong Lan, Meifang Lin, Yuanyuan |
| author_facet | Zheng, Siming Wang, Tong Lan, Meifang Lin, Yuanyuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Conditional Distribution Equality Testing Framework using Deep Generative Learning Zheng, Siming Wang, Tong Lan, Meifang Lin, Yuanyuan Machine Learning Statistics Theory Methodology 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. |
| title | A Conditional Distribution Equality Testing Framework using Deep Generative Learning |
| topic | Machine Learning Statistics Theory Methodology |
| url | https://arxiv.org/abs/2509.17729 |