None of the BROJA information decomposition measures \mboxSI,\mboxCI,\mboxUIy,\mboxUIz 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.
Cite
@article{arxiv.1802.03947,
title = {Optimizing Bivariate Partial Information Decomposition},
author = {Abdullah Makkeh and Dirk Oliver Theis},
journal= {arXiv preprint arXiv:1802.03947},
year = {2018}
}