A Constructive Method to Maximize Entropy under Marginal Constraints

Pierre Bertrand ()
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Pierre Bertrand: AMU ECO - Aix-Marseille Université - Faculté d'économie et de gestion - AMU - Aix Marseille Université, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique

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Abstract: We study the problem of maximizing Rényi entropy of order $2$ (equivalently, minimizing the index of coincidence) over the set of joint distributions with prescribed marginals. A closed-form optimizer is known under a feasibility condition on the marginals; we show that this condition is highly restrictive. We then provide an explicit construction of an optimal coupling for arbitrary marginals. Our approach characterizes the optimizer's structure and yields an iterative algorithm that terminates in finite time, returning an exact solution after at most $p-1$ updates, where $p$ is the number of rows.

Keywords: Entropy maximization; Index of coincidence minimization; Coupling; Marginal constraints (search for similar items in EconPapers)
Date: 2026-03-02
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