Discovering Potential Influence via Information Bottleneck

Discovering a potential influence from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average influence, they fail to discover potential influences. To bridge this gap, (i) we postulate a set of natural axioms that we expect a measure of potential influence to satisfy; (ii) we show that the rate of information bottleneck, i.e., the hypercontractivity coefficient, satisfies all the proposed axioms; (iii) we provide a novel estimator to estimate the hypercontractivity coefficient from samples; and (iv) numerical experiments demonstrate that this proposed estimator discovers a potential influence for various indicators of WHO datasets, robust in discovering gene interactions from gene expression time series data, and is statistically more powerful than the estimators for other correlation measures in binary hypothesis testing of canonical potential influences.