Signed and Unsigned Partial Information Decompositions of Continuous Network Interactions

TL;DR

This paper compares two partial information decomposition frameworks for identifying significant interactions in continuous systems, extending them analytically and numerically, and analyzing their sensitivity and specificity in detecting true network edges.

Contribution

It extends both the $I_{ ext{cap}}^{ ext{min}}$ and $I_{ ext{cap}}^{ ext{PM}}$ PIDs to continuous systems and evaluates their effectiveness for edge detection.

Findings

$I_{ ext{cap}}^{ ext{PM}}$ atoms are sensitive to high mutual information regardless of interaction.

$I_{ ext{cap}}^{ ext{min}}$ is more specific but less sensitive.

Both frameworks provide insights into information sharing in network interactions.

Abstract

We investigate the partial information decomposition (PID) framework as a tool for edge nomination. We consider both the $I_{\cap}^{\text{min}}$ and $I_{\cap}^{\text{PM}}$ 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 $I_{\cap}^{\text{min}}$ and $I_{\cap}^{\text{PM}}$ 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 $I_{\cap}^{\text{PM}}$ 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 $I_{\cap}^{\text{min}}$ PID is quite specific, although simulations suggest that it lacks sensitivity.