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Maximizing multi-information. (English) Zbl 1249.82011

Summary: Stochastic interdependence of a probability distribution on a product space is measured by its Kullback-Leibler distance from the exponential family of product distributions (called multi-information). Here, we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure.
Based on a detailed description of the structure of probability distributions with globally maximal multi-information, we obtain our main result: the exponential family of pure pair interactions contains all global maximizers of the multi-information in its closure.

MSC:

82C32 Neural nets applied to problems in time-dependent statistical mechanics
62B10 Statistical aspects of information-theoretic topics
94A15 Information theory (general)
68T05 Learning and adaptive systems in artificial intelligence
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