The maximum likelihood degree

By F. Catanese, Serkan Hoşten, Amit Khetan, Bernd Sturmfels. 2004

165 citations recorded by the source corpus.

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of bounded regions in the corresponding arrangement of hypersurfaces, and to the Euler characteristic of the complexified complement. Under suitable hypotheses, the maximum likelihood degree equals the top Chern class of a sheaf of logarithmic differential forms. Exact formulae in terms of degrees and Newton polytopes are given for polynomials with generic coefficients.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/354863b9f944d65283c24261ffa1447cd893dc4c

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In Computational Mechanics

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

Algebraic factor analysis: tetrads, pentads and beyond (2005, background): “The ML degree [4] of a statistical model is the number of nontrivial complex zeros of the critical equations for generic data.”
A matroid invariant via the K-theory of the Grassmannian (2006, background): “(p 1,...,pn−1,− Pn−1 i=1 pi) ⊥. I am not aware of a reference which points out the connection between this problem and the intersection theory problem of enumerating Tx∩Ω(ℓ,H). However, theorem 28 of [4] describes the critical points of Φ as the top chern class of a certain sheaf of logarithmic diﬀe”
Algebraic Statistics for Computational Biology: Preface (2005, background): “The connection to maximum likelihood estimation was explored in [Catanese et al., 2005].”