Over local fields, the maximum likelihood Gaussian is the span of the data, conditional independence is an F_q-realizable matroid, and in dimension 2 the tropicalized Gaussian is exactly a supermodular tropical polynomial.
Tropical Gaussians: A Brief Survey
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abstract
We review the existing analogues of the Gaussian measure in the tropical semiring and outline various research directions.
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Statistics and tropicalization of local field Gaussian measures
Over local fields, the maximum likelihood Gaussian is the span of the data, conditional independence is an F_q-realizable matroid, and in dimension 2 the tropicalized Gaussian is exactly a supermodular tropical polynomial.