ICML 2025

A Sample-Efficient Conditional Independence Test
in the Presence of Discretization
Boyang Sun 1 Yu Yao 2 Xinshuai Dong 3 Zongfang Liu 1 Tongliang Liu 2 1 Yumou Qiu 4 Kun Zhang 3 1
Abstract
In many real-world scenarios, interested variables
are often represented as discretized values due
to measurement limitations.
Applying Condi-
tional 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 ad-
dressing 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 distribu-
tion correctly reflecting CI by leveraging node-
wise regression. Theoretical findings and Empir-
ical results across various datasets demonstrate
that the superiority and effectiveness of our pro-
posed test. Our code implementation is provided
in https://github.com/boyangaaaaa/DCT.
1. Introduction
Conditional independence tests for discrete variables are
fundamental in statistical analysis and widely applied across
various disciplines. Traditional methods including the chi-
squared test (F.R.S., 2009), the G-test (likelihood ratio test)
(McDonald, 2009), and measures based on conditional mu-
tual information (Kubkowski et al., 2021) are well estab-
lished and extensively used. However, a critical yet often
1Mohamed bin Zayed University of Artificial Intelligence
2Sydney AI Centre, The University of Sydney 3Carnegie Mellon
University 4Peking University. Correspondence to: Yumou Q...