Signed and Unsigned Partial Information Decompositions of Continuous Network Interactions
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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.
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