Testing Conditional Independence on Discrete Data using Stochastic Complexity

12 Mar 2019  ·  Alexander Marx, Jilles Vreeken ·

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.

PDF Abstract
No code implementations yet. Submit your code now

Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here