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A Constructive Method to Maximize Entropy under Marginal Constraints

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  • Pierre Jean-Claude Robert Bertrand

    (Aix Marseille Univ, CNRS, AMSE, Marseille, France)

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.

Suggested Citation

  • Pierre Jean-Claude Robert Bertrand, 2026. "A Constructive Method to Maximize Entropy under Marginal Constraints," AMSE Working Papers 2608, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:2608
    Note: Working paper AMSE 2026-08
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