Geodesic
Maximizing multi–information
Kybernetika, Tome 42 (2006) no. 5, pp. 517-538

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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.
Classification : 60B10, 82C32, 92B20, 94A15
Keywords: multi-information; exponential family; relative entropy; pair- interaction; infomax principle; Boltzmann machine; neural networks 
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     author = {Ay, Nihat and Knauf, Andreas},
     title = {Maximizing multi{\textendash}information},
     journal = {Kybernetika},
     pages = {517--538},
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     zbl = {1249.82011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006__42_5_a0/}
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Ay, Nihat; Knauf, Andreas. Maximizing multi–information. Kybernetika, Tome 42 (2006) no. 5, pp. 517-538. http://geodesic.mathdoc.fr/item/KYB_2006__42_5_a0/