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Properties of unique information

Johannes Rauh, Maik Schünemann, Jürgen Jost (2021)

Kybernetika

We study the unique information function U I ( T : X Y ) defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of U I . We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of T , X and Y . Our results are based on a reformulation of the first order conditions...

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