Maximum likelihood degree, complete quadrics, and \(\mathbb{C}^*\)-action. (English) Zbl 1461.62228
Summary: We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on the variety of complete quadrics. This allows us to provide an explicit and basic, albeit very computationally complex, formula for the ML-degree. The variety of complete quadrics is an exact analogue for symmetric matrices of the permutohedron variety for the diagonal matrices.
MSC:
| 62R01 | Algebraic statistics |
| 62F12 | Asymptotic properties of parametric estimators |
| 60G15 | Gaussian processes |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
| 14M17 | Homogeneous spaces and generalizations |
| 14N10 | Enumerative problems (combinatorial problems) in algebraic geometry |
| 14E05 | Rational and birational maps |
| 14C17 | Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry |
| 14Q15 | Computational aspects of higher-dimensional varieties |
Keywords:
maximum likelihood degree; linear concentration model; Lagrangian Grassmannian; complete quadrics; intersection theoryReferences:
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