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Testing Conditional Independence on Discrete Data using Stochastic Complexity

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Marx,  Alexander
Databases and Information Systems, MPI for Informatics, Max Planck Society;

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Vreeken,  Jilles
Databases and Information Systems, MPI for Informatics, Max Planck Society;

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Fulltext (public)

arXiv:1903.04829.pdf
(Preprint), 923KB

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Citation

Marx, A., & Vreeken, J. (2019). Testing Conditional Independence on Discrete Data using Stochastic Complexity. Retrieved from http://arxiv.org/abs/1903.04829.


Cite as: http://hdl.handle.net/21.11116/0000-0004-027A-1
Abstract
Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple variables. We focus on discrete data and propose a new test based on the notion of algorithmic independence that we instantiate using stochastic complexity. Amongst others, we show that our proposed test, SCI, is an asymptotically unbiased as well as $L_2$ consistent estimator for conditional mutual information (CMI). Further, we show that SCI can be reformulated to find a sensible threshold for CMI that works well on limited samples. Empirical evaluation shows that SCI has a lower type II error than commonly used tests. As a result, we obtain a higher recall when we use SCI in causal discovery algorithms, without compromising the precision.