A Conditional Distribution Equality Testing Framework using Deep Generative Learning

2025/09/22 by Siming Zheng, Zheng, Siming, Tong Wang +5
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Methodology (stat.ME) #Statistics Theory (math.ST) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2509.17729

openalex publication_date 2025/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Conditional Data Synthesis Augmentation
• Doubly Robust Conditional Independence Testing with Generative Neural Networks
• Score-based Causal Representation Learning: Linear and General Transformations
• De-Biased Two-Sample U-Statistics With Application To Conditional Distribution Testing
• Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shift
• Testing for the Markov Property in Time Series via Deep Conditional Generative Learning
• Derandomized Novelty Detection with FDR Control via Conformal E-values
• Flow Matching for Generative Modeling
• Derandomized knockoffs: leveraging e-values for false discovery rate control
• Prediction Sets Adaptive to Unknown Covariate Shift
• A new similarity measure for covariate shift with applications to nonparametric regression
• A Deep Generative Approach to Conditional Sampling
• Deep Nonparametric Regression on Approximate Manifolds: Non-Asymptotic Error Bounds with Polynomial Prefactors
• Derandomizing Knockoffs
• Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation
• Conformal Inference of Counterfactuals and Individual Treatment Effects
• Double Generative Adversarial Networks for Conditional Independence Testing
• Conditional Independence Testing using Generative Adversarial Networks
• Invariance, Causality and Robustness
• On Wasserstein Two Sample Testing and Related Families of Nonparametric\n Tests
• Causal inference using invariant prediction: identification and confidence intervals
• Kernel-based Conditional Independence Test and Application in Causal Discovery
• Modeling wine preferences by data mining from physicochemical properties
• On a new multivariate two-sample test

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• Double Generative Adversarial Networks for Conditional Independence Testing
• Conditional Independence Testing using Generative Adversarial Networks
• Mimic and Classify : A meta-algorithm for Conditional Independence Testing
• Score-based Generative Modeling for Conditional Independence Testing
• Doubly Robust Conditional Independence Testing with Generative Neural Networks