A Sample Efficient Conditional Independence Test in the Presence of Discretization

TL;DR

This paper introduces a new sample-efficient conditional independence test that accurately infers relationships in discretized data without information loss, outperforming existing binarization-based methods.

Contribution

The paper proposes a novel CI test leveraging GMM and nodewise regression to avoid binarization, improving accuracy with less data in discretized settings.

Findings

The proposed test outperforms existing methods in various datasets.

The test accurately reflects CI relationships in discretized data.

Theoretical analysis confirms asymptotic correctness.

Abstract

In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect conclusions. To address this, recent advancements have sought to infer the correct CI relationship between the latent variables through binarizing observed data. However, this process inevitably results in a loss of information, which degrades the test's performance. Motivated by this, this paper introduces a sample-efficient CI test that does not rely on the binarization process. We find that the independence relationships of latent continuous variables can be established by addressing an over-identifying restriction problem with Generalized Method of Moments (GMM). Based on this insight, we derive an appropriate test statistic and establish its asymptotic distribution correctly reflecting CI by leveraging nodewise regression. Theoretical findings and Empirical results across various datasets demonstrate that the superiority and effectiveness of our proposed test. Our code implementation is provided in https://github.com/boyangaaaaa/DCT