Testing Conditional Independence Between Latent Variables by Independence Residuals
Chen, Zhengming Qiao, Jie Xie, Feng Cai, Ruichu Hao, Zhifeng Zhang, Keli
Chen, Zhengming
Qiao, Jie
Xie, Feng
Cai, Ruichu
Hao, Zhifeng
Zhang, Keli
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Department
Machine Learning
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Journal article
Date
2025
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Language
English
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Abstract
Conditional independence (CI) testing is an important problem, especially in causal discovery. Most testing methods assume that all variables are fully observable and then test the CI among the observed data. Such an assumption is often untenable beyond applications dealing with, e.g., psychological analysis about the mental health status and medical diagnosing (researchers need to consider the existence of latent variables in these scenarios); and typically adopted latent CI test schemes mainly suffer from robust or efficient issues. Accordingly, this article investigates the problem of testing CI between latent variables. To this end, we offer an auxiliary regression-based CI (AReCI) test by taking the measured variable as the surrogate variable of the latent variables to conduct the regression over the latent variables under the linear causal models, in which each latent variable has some certain measured variables. Specifically, given a pair of latent variables LX and LY, and a corresponding latent variable set \mathcal LO, LX ? LY| LO holds if and only if ALX?T1 A?{LO} and A{LY}-?T2A?{LO} are statistically independent, where A? and A? } are the two disjoint subset of the measured variable for the corresponding latent variables, A?{LO} ? A?{LO} = ?, and ?1is a parameter vector characterized from the cross covariance between A{LX} and A?{LO}, and ?2 is a parameter vector characterized from the cross covariance between A{LY} and A?{LO}. We theoretically show that the AReCI test is capable of addressing both Gaussian and non-Gaussian data. In addition, we find that the well-known partial correlation test can be seen as a special case of the AReCI test. Finally, we devise a causal discovery method by using the AReCI test as the CI test. The experimental results on synthetic and real-world data illustrate the effectiveness of our method.
Citation
Z. Chen, J. Qiao, F. Xie, R. Cai, Z. Hao, and K. Zhang, “Testing Conditional Independence Between Latent Variables by Independence Residuals,” IEEE Trans Neural Netw Learn Syst, 2024, doi: 10.1109/TNNLS.2024.3368561.
Source
IEEE Transactions on Neural Networks and Learning Systems
Conference
Keywords
Causal discovery, conditional independence (CI) test, latent variable, latent variable model
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Publisher
IEEE