A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum

TL;DR

This paper introduces a novel nonparametric test for comparing conditional distributions between two populations, leveraging conformal prediction and a weighted rank-sum statistic, suitable for high-dimensional data.

Contribution

It develops the first conformal prediction-based hypothesis test for conditional distribution equality, combining recent conformal methods with a new conformity score for enhanced power.

Findings

Test is valid under general settings.

Effective in high-dimensional, large-sample scenarios.

Demonstrated superior performance in numerical examples.

Abstract

We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and statistical inference scenarios, including transfer learning and causal predictive inference. We develop a nonparametric test procedure inspired from the conformal prediction framework. The construction of our test statistic combines recent developments in conformal prediction with a novel choice of conformity score, resulting in a weighted rank-sum test statistic that is valid and powerful under general settings. To our knowledge, this is the first successful attempt of using conformal prediction for testing statistical hypotheses beyond exchangeability. Our method is suitable for modern machine learning scenarios where the data has high dimensionality and large sample sizes, and can be effectively combined with existing classification algorithms to find good conformity score functions. The performance of the proposed method is demonstrated in various numerical examples.