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 L2 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.
History
Preferred Citation
Alexander Marx and Jilles Vreeken. Testing Conditional Independence on Discrete Data using Stochastic Complexity. In: International Conference on Artificial Intelligence and Statistics (AISTATS). 2019.
Primary Research Area
Empirical and Behavioral Security
Name of Conference
International Conference on Artificial Intelligence and Statistics (AISTATS)
Legacy Posted Date
2019-06-07
Open Access Type
Unknown
BibTeX
@inproceedings{cispa_all_2914,
title = "Testing Conditional Independence on Discrete Data using Stochastic Complexity",
author = "Marx, Alexander and Vreeken, Jilles",
booktitle="{International Conference on Artificial Intelligence and Statistics (AISTATS)}",
year="2019",
}