Signed and Unsigned Partial Information Decompositions of Continuous Network Interactions

2021/12/23 by Milzman, Jesse, Lyzinski, Vince
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2112.12316

Abstract

We investigate the partial information decomposition (PID) framework as a tool for edge nomination. We consider both the I_∩^min and I_∩^PM PIDs, from arXiv:1004.2515 and arXiv:1801.09010 respectively, and we both numerically and analytically investigate the utility of these frameworks for discovering significant edge interactions. In the course of our work, we extend both the I_∩^min and I_∩^PM PIDs to a general class of continuous trivariate systems. Moreover, we examine how each PID apportions information into redundant, synergistic, and unique information atoms within the source-bivariate PID framework. Both our simulation experiments and analytic inquiry indicate that the atoms of the I_∩^PM PID have a non-specific sensitivity to high predictor-target mutual information, regardless of whether or not the predictors are truly interacting. By contrast, the I_∩^min PID is quite specific, although simulations suggest that it lacks sensitivity.

Related

• Partial information decomposition for mixed discrete and continuous random variables
• Multivariate Partial Information Decomposition: Constructions, Inconsistencies, and Alternative Measures
• A scalable, synergy-first backbone decomposition of higher-order structures in complex systems
• Partial Information Rate Decomposition
• A partial information decomposition for discrete and continuous variables