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Minimization with respect to divergences and applications


We apply divergences to project a prior guess discrete probability law on pq elements towards a subspace defined by fixed margins constraints µ and ν on p and q elements respectively. We justify why the Kullback-Leibler and the Chi-square divergences are two canonical choices based on a 1991 work of Imre Csiszár. Besides we interpret the so called indetermination resulting from the second divergence as a construction to reduce couple matchings. Eventually, we demonstrate how both resulting probabilities arise in two information theory applications: guessing problem and task partitioning where some optimization remains to minimize a divergence projection.
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hal-03329875 , version 1 (31-08-2021)



Pierre Bertrand, Michel Broniatowski, Jean-François Marcotorchino. Minimization with respect to divergences and applications. GSI 2021: Geometric Science of Information, pp.818-828, 2021, ⟨10.1007/978-3-030-80209-7_88⟩. ⟨hal-03329875⟩
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