# A Conditional Distribution Equality Testing Framework using Deep Generative Learning

arXiv: https://arxiv.org/abs/2509.17729 · HTML: https://mlsanity.com/paper/2509.17729/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [Learning with Square Loss: Localization through Offset Rademacher Complexity](https://mlsanity.com/paper/1502.06134/) (2015)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [A new similarity measure for covariate shift with applications to nonparametric regression](https://mlsanity.com/paper/2202.02837/) (2022)
- [Score-based Causal Representation Learning: Linear and General Transformations](https://mlsanity.com/paper/2402.00849/) (2024)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Prediction Sets Adaptive to Unknown Covariate Shift](https://mlsanity.com/paper/2203.06126/) (2022)
- [A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum](https://mlsanity.com/paper/2010.07147/) (2020)
- [Environment Invariant Linear Least Squares](https://mlsanity.com/paper/2303.03092/) (2023)
- [Derandomized Novelty Detection with FDR Control via Conformal E-values](https://mlsanity.com/paper/2302.07294/) (2023)
- [Derandomized knockoffs: leveraging e-values for false discovery rate control](https://mlsanity.com/paper/2205.15461/) (2022)
- [Derandomizing Knockoffs](https://mlsanity.com/paper/2012.02717/) (2020)
- [Testing for the Markov Property in Time Series via Deep Conditional Generative Learning](https://mlsanity.com/paper/2305.19244/) (2023)
- [Conditional Data Synthesis Augmentation](https://mlsanity.com/paper/2504.07426/) (2025)
- [Doubly Robust Conditional Independence Testing with Generative Neural Networks](https://mlsanity.com/paper/2407.17694/) (2024)
- [De-Biased Two-Sample U-Statistics With Application To Conditional Distribution Testing](https://mlsanity.com/paper/2402.00164/) (2024)
- [Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shift](https://mlsanity.com/paper/2306.16406/) (2023)
- [Model-based causal feature selection for general response types](https://mlsanity.com/paper/2309.12833/) (2023)

## Built on by (most cited first, 1 of 1)

- [ANGLE: Angular Neural Generative Learning via Engression](https://mlsanity.com/paper/2607.12833/) (2026)

## Abstract (arXiv)

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.