用生成模型解决条件分布相等性检验，适用于协变量偏移与因果发现。
A Conditional Distribution Equality Testing Framework using Deep Generative Learning
- 将条件检验转化为无条件问题，结合生成网络与样本分割。
- 在弱条件下证明了检验一致性，并给出生成器收敛速率。
- 适用于需要检测数据分布差异的机器学习与因果推断场景。
本文提出一个通用框架，用于解决两样本问题中的条件分布相等性检验，该问题与协变量偏移和因果发现密切相关。框架基于神经网络生成方法与样本分割技术，将条件检验问题转化为无条件问题。我们引入基于生成分类准确率的条件分布相等性检验（GCA-CDET）来展示该框架。通过新的偏移Rademacher复杂度结果，建立了生成器的收敛速率，并在温和条件下证明了GCA-CDET的检验一致性。实验部分包括合成数据集和两个真实数据集，验证了方法的有效性。更多关于框架最优性的讨论见在线补充材料。
原文摘要 · Abstract (English)
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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