Work

Maximum Likelihood for Matrices with Rank Constraints

Year: 2012

Type: preprint

Abstract: Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We determine the maximum likelihood degree for a range of determinantal varieties, and we apply numerical algebraic geometry to compute all critical points of their likelihood functions. This led to the discovery of maximum likelihood duality between matrices of complementary ranks, a result proved subsequently by Draisma and Rodriguez.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1210.0198

Authors: Hauenstein, Jonathan, Rodriguez, Jose, Sturmfels, Bernd

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: EMSW21-RTG: Research Training Group in Interactions of Representation Theory, Geometry and Combinatorics, Computational Methods in Numerical Algebraic Geometry, Applications of Algebraic Geometry

OpenAlex ID: W2950918182

Cites:

Cited by: 5

Related to: 20