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The $F$-adjoined Gauss map and Gaussian likelihood geometry

Lukas Gustafsson

Vol. 16 (2025), No. 1, 29–53
Abstract

We introduce the F-adjoined Gauss map. We use it to express the Gaussian maximum likelihood degree as a product of two invariants. As an application of our product formula, we classify all projective curves of Gaussian maximum likelihood degree 1. We also provide a formula for the generic Gaussian maximum likelihood degree of a projective variety X in terms of its polar classes. The renowned polar class formula for generic Euclidean distance degree is a special case of our formula.

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Keywords
algebraic statistics, rational MLE, maximum likelihood degree
Mathematical Subject Classification
Primary: 14E05, 35C11, 35F20, 62R01
Milestones
Received: 5 December 2023
Accepted: 23 July 2024
Published: 10 December 2024
Authors
Lukas Gustafsson
Kungliga Tekniska Högskolan
Stockholm
Sweden