English
Related papers

Related papers: Sparse Inverse Covariance Matrix Estimation Using …

200 papers

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

Machine Learning · Statistics 2011-06-28 Suvrit Sra , Dongmin Kim

In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the…

Methodology · Statistics 2023-05-12 Ghania Fatima , Prabhu Babu , Petre Stoica

The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A…

Machine Learning · Statistics 2018-06-08 Richard Y. Zhang , Salar Fattahi , Somayeh Sojoudi

Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…

Machine Learning · Computer Science 2022-01-25 Shahaf E. Finder , Eran Treister , Oren Freifeld

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…

Machine Learning · Computer Science 2010-11-02 Katya Scheinberg , Shiqian Ma , Donald Goldfarb

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…

Methodology · Statistics 2011-02-14 Tony Cai , Weidong Liu , Xi Luo

We propose an l1-regularized likelihood method for estimating the inverse covariance matrix in the high-dimensional multivariate normal model in presence of missing data. Our method is based on the assumption that the data are missing at…

Methodology · Statistics 2012-02-28 Nicolas Städler , Peter Bühlmann

We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…

Information Theory · Computer Science 2016-09-06 Steffen Limmer , Sławomir Stańczak

Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse…

Machine Learning · Computer Science 2012-06-18 John Duchi , Stephen Gould , Daphne Koller

We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our…

Machine Learning · Computer Science 2018-11-16 Jean Honorio , Tommi S. Jaakkola

The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood…

Machine Learning · Computer Science 2024-04-15 Yakov Medvedovsky , Eran Treister , Tirza Routtenberg

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Machine Learning · Statistics 2015-06-15 Zhaoshi Meng , Dennis Wei , Ami Wiesel , Alfred O. Hero

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…

Machine Learning · Computer Science 2012-02-28 Christopher C. Johnson , Ali Jalali , Pradeep Ravikumar

We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to…

Machine Learning · Statistics 2015-03-17 Gui-Bo Ye , Jian-Feng Cai , Xiaohui Xie

The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In…

Computation · Statistics 2012-11-28 Dominique Guillot , Bala Rajaratnam , Benjamin T. Rolfs , Arian Maleki , Ian Wong

Estimating the unconstrained mean and covariance matrix is a popular topic in statistics. However, estimation of the parameters of $N_p(\mu,\Sigma)$ under joint constraints such as $\Sigma\mu = \mu$ has not received much attention. It can…

Methodology · Statistics 2023-01-25 Anupam Kundu , Mohsen Pourahmadi

We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…

Machine Learning · Statistics 2021-11-08 Dimitris Bertsimas , Jourdain Lamperski , Jean Pauphilet

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

Artificial Intelligence · Computer Science 2007-07-06 Onureena Banerjee , Laurent El Ghaoui , Alexandre d'Aspremont

We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…

Statistics Theory · Mathematics 2015-09-02 Yves F. Atchadé , Rahul Mazumder , Jie Chen

We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…

Methodology · Statistics 2025-07-31 Konstantin E. Avrachenkov , Leonid B. Freidovich
‹ Prev 1 2 3 10 Next ›