Optimizing Bivariate Partial Information Decomposition
Abstract
None of the BROJA information decomposition measures SI, CI, UIy, UIz are convex or concave over the probability simplex. In this paper, we provide formulas for the sub-gradient and super-gradients of any of the information decomposition measures. Then we apply these results to obtain an optimum of some of these information decomposition measures when optimized over a constrained set of probability distributions.
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