Estimating linear covariance models with numerical nonlinear algebra
Computation
2020-10-07 v1 Algebraic Geometry
Abstract
Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g. Toeplitz, sparse, trees) that are of interest in statistics. We study the maximum likelihood degree and its dual analogue, and we introduce a new software package LinearCovarianceModels.jl for solving the score equations. All local maxima can thus be computed reliably. In addition we identify several scenarios for which the estimator is a rational function.
Cite
@article{arxiv.1909.00566,
title = {Estimating linear covariance models with numerical nonlinear algebra},
author = {Bernd Sturmfels and Sascha Timme and Piotr Zwiernik},
journal= {arXiv preprint arXiv:1909.00566},
year = {2020}
}
Comments
23 pages, 2 figures, 5 tables