A Conditional Independence Test in the Presence of Discretization
Sun, Boyang Yao, Yu Hao, Guang-Yuan Qiu, Zhang, Kun
Sun, Boyang
Yao, Yu
Hao, Guang-Yuan
Qiu,
Zhang, Kun
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Department
Machine Learning
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Conference proceeding
Date
2025
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English
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Abstract
Testing conditional independence (CI) has many important applications, such as Bayesian network learning and causal discovery. Although several approaches have been developed for inferring CI relationships among observed variables, these existing methods generally fail when the variables of interest cannot be directly observed and only discretized values of those variables are available. For example, if X1, X̃2 and X3 are the observed variables, where X̃2 is a discretization of the latent variable X2, applying the existing methods to the observations of X1, X̃2 and X3 would lead to a false conclusion about the underlying CI of variables X1, X2 and X3. Motivated by this, we propose a CI test specifically designed to accommodate the presence of discretization. To achieve this, a bridge equation and nodewise regression are used to recover the precision coefficients reflecting the conditional dependence of the latent continuous variables under the nonparanormal model. We propose a test statistic and derive its asymptotic distribution under the null hypothesis of CI. Theoretical analysis, along with empirical validation on various datasets, rigorously demonstrates the effectiveness of our testing methods. Our code implementation can be found in https://github.com/boyangaaaaa/DCT. © 2025 13th International Conference on Learning Representations, ICLR 2025. All rights reserved.
Citation
B. Sun, Y. Yao, G.-Y. Hao, Y. Qiu, and K. Zhang, “A Conditional Independence Test in the Presence of Discretization,” International Conference on Representation Learning, vol. 2025, pp. 2907–2939, May 2025
Source
13th International Conference on Learning Representations, ICLR 2025
Conference
13th International Conference on Learning Representations, ICLR 2025
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Source
13th International Conference on Learning Representations, ICLR 2025
Publisher
International Conference on Learning Representations, ICLR