Maximum likelihood estimation for linear Gaussian covariance models
By Piotr Zwiernik, Caroline Uhler, Donald St. P. Richards. 2014
64 citations recorded by the source corpus.
We study parameter estimation in linear Gaussian covariance models, which are p‐dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non‐convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill climbing method to converge to the global maximum. Although we are primarily interested in the case in which n≫p, the proofs of our results utilize large sample asymptotic theory under the scheme n/p→γ>1. Remarkably, our numerical simulations indicate that our results remain valid for p as small as 2. An important consequence of this analysis is that, for sample sizes n≃14p, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/e256d411e06bc985fee1cb61ef56e7add940435c
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Citations in the corpus
- Covariance Regression Analysis (2017, unknown): “This type of linear combination structure has been used by Anderson (1973), Szatrowski (1980), and Zwiernik, Uhler, and Richards (2014).”
- Invariant Models for Causal Transfer Learning (2015, background): “The constrained optimization problem can be shown to be convex in the neighborhood of the optimum (Zwiernik et al., 2017, Sec.”
- Causal Transfer in Machine Learning (2015, background): “The constrained optimization problem can be shown to be convex in the neighbourhood of the optimum [Zwiernik et al., 2014, Sec.”