Testing (Conditional) Mutual Information
Jan Seyfried, Sayantan Sen, Marco Tomamichel

TL;DR
This paper studies the sample complexity of testing mutual and conditional mutual information, providing bounds and methods for distinguishing independence from dependence in complex distributions.
Contribution
It introduces new bounds on sample complexity for mutual information testing and develops novel simulation and estimation techniques for correlated samples.
Findings
Established upper bounds on sample complexity for conditional mutual information testing.
Proved tightness of bounds in several parameter regimes.
Provided a new estimator for equivalence testing with correlated samples.
Abstract
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables with unknown distribution, we want to distinguish between two cases: (i) and are conditionally independent, i.e., , and (ii) and are conditionally dependent, i.e., for some threshold . We establish an upper bound on the number of samples required to distinguish between the two cases with high confidence, as a function of and the three alphabet sizes. We conjecture that our bound is tight and show that this is indeed the case in several parameter regimes. For the special case of mutual information testing (when is trivial), we establish the necessary and sufficient…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Distributed systems and fault tolerance · Random Matrices and Applications
