Geometry of Maximum Likelihood Estimation in Gaussian Graphical Models By
نویسنده
چکیده
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum likelihood estimator (MLE) exists with probability one. This is applied to bipartite graphs, grids and colored graphs. We also study the ML degree, and we present the first instance of a graph for which the MLE exists with probability one, even when the number of observations equals the treewidth.
منابع مشابه
A comparison of algorithms for maximum likelihood estimation of Spatial GLM models
In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two n...
متن کاملIMAGE SEGMENTATION USING GAUSSIAN MIXTURE MODEL
Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we have learned Gaussian mixture model to the pixels of an image. The parameters of the model have estimated by EM-algorithm. In addition pixel labeling corresponded to each pixel of true image is made by Bayes rule. In fact, ...
متن کاملImage Segmentation using Gaussian Mixture Model
Abstract: Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we used Gaussian mixture model to the pixels of an image. The parameters of the model were estimated by EM-algorithm. In addition pixel labeling corresponded to each pixel of true image was made by Bayes rule. In fact,...
متن کاملA New Algorithm for Maximum Likelihood Estimation in Gaussian Graphical Models for Marginal Independence
Graphical models with bi-directed edges (↔) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian joint distribution, sometimes termed a covariance graph model. We present a new fitting algorith...
متن کاملParameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation
Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...
متن کامل