Signed and unsigned partial information decompositions of continuous network interactions. (10th September 2022) - Milzman, Jesse; Lyzinski, Vince
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 Williams & Beer (2010, Nonnegative decomposition of multivariate information, CoRR, arXiv:2106.12393) and Finn & Lizier (2018, Entropy, 20, 297), 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.