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Tropical toric maximum likelihood estimation

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arxiv 2404.10567 v2 pith:52KQTCCA submitted 2024-04-16 math.AG math.COmath.OC

classification math.AGmath.COmath.OC
keywords tropicalpointscriticallikelihoodtoricaffinecasesestimation
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We consider toric maximum likelihood estimation over the field of Puiseux series and study critical points of the likelihood function using tropical methods. This problem translates to finding the intersection points of a tropical affine space with a classical linear subspace. We derive new structural results on tropical affine spaces and use these to give a complete and explicit description of the tropical critical points in certain cases. In these cases, we associate tropical critical points to the simplices in a regular triangulation of the polytope giving rise to the toric model.

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  1. The Maximum Likelihood Degree of Toric Models is Monotonic

    math.AG 2025-07 accept novelty 8.0 of 10

    The ML degree is monotone with respect to faces of the defining polytope for scaled toric models, settling a conjecture of Coons and Sullivant.

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