Extra Samples can Reduce the Communication for Independence Testing

By K. R. Sahasranand, Himanshu Tyagi. 2018

12 citations recorded by the source corpus.

Two parties observing sequences of bits want to determine if their bits were generated independently or not. To that end, the first party communicates to the second. A simple communication scheme involves taking as few sample bits as determined by the sample complexity of independence testing and sending it to the second party. But is there a scheme that uses fewer bits of communication than the sample complexity, perhaps by observing more sample bits? We show that the answer to this question is in the affirmative when the joint distribution is a binary symmetric source. More generally, for any given joint distribution, we present a distributed independence test that uses linear correlation between functions of the observed random variables. Furthermore, we provide lower bounds for the general setting that use hypercontractivity and reverse hypercontractivity to obtain a measure change bound between the joint and the independent distributions. The resulting bounds are tight for both a binary symmetric source and a Gaussian symmetric source.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Statistics and Probability

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Citations in the corpus

Inference Under Information Constraints I: Lower Bounds From Chi-Square Contraction (2018, background): “Recent results in this area have focused on more complicated communication models [53], [54] and, more recently, on the minimum communication requirements for large sample sizes [6], [44].”