  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.
