English
Related papers

Related papers: Gemini: Graph estimation with matrix variate norma…

200 papers

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in…

Machine Learning · Statistics 2017-10-20 Addison Hu , Sahand Negahban

In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…

Combinatorics · Mathematics 2020-05-25 Israel Rocha , Jeannette Janssen , Nauzer Kalyaniwalla

Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In…

Machine Learning · Statistics 2019-05-16 Aditya Grover , Aaron Zweig , Stefano Ermon

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

Statistics Theory · Mathematics 2008-06-26 Adam J. Rothman , Peter J. Bickel , Elizaveta Levina , Ji Zhu

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

Machine Learning · Computer Science 2017-11-07 Rebecca E. Morrison , Ricardo Baptista , Youssef Marzouk

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 Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

Methodology · Statistics 2007-06-12 Helen Armstrong , Christopher K. Carter , Kevin F. Wong , Robert Kohn

This work considers the distributed computation of the one-to-one vertex correspondences between two undirected and connected graphs, which is called \textit{graph matching}, over multi-agent networks. Given two \textit{isomorphic} and…

Optimization and Control · Mathematics 2020-02-21 Quoc Van Tran , Zhiyong Sun , Brian D. O. Anderson , Hyo-Sung Ahn

The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…

Data Analysis, Statistics and Probability · Physics 2018-02-12 Giulio D'Agostini

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…

Methodology · Statistics 2021-05-17 Peng Tang , Huijing Jiang , Heeyoung Kim , Xinwei Deng

In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery,…

Machine Learning · Computer Science 2012-02-28 Ali Jalali , Chris Johnson , Pradeep Ravikumar

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

Methodology · Statistics 2019-03-06 Xuan Cao , Shaojun Zhang

Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine…

Methodology · Statistics 2014-04-21 Anshumali Shrivastava , Ping Li

Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…

Statistics Theory · Mathematics 2019-04-02 Yabo Niu , Debdeep Pati , Bani Mallick

A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…

Machine Learning · Computer Science 2018-06-11 Qingyun Sun , Mengyuan Yan David Donoho , Stephen Boyd

Distributed estimation methods have recently been used to compute the maximum likelihood estimate of the precision matrix for large graphical Gaussian models. Our aim, in this paper, is to give a Bayesian estimate of the precision matrix…

Methodology · Statistics 2016-05-30 Qiong Li , Xin Gao , Helene Massam

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

Combinatorics · Mathematics 2025-08-08 Catherine Greenhill

The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…

Methodology · Statistics 2025-04-11 Ching Wong , Giusi Moffa , Jack Kuipers

Let $X = \{X_{u}\}_{u \in U}$ be a real-valued Gaussian process indexed by a set $U$. It can be thought of as an undirected graphical model with every random variable $X_{u}$ serving as a vertex. We characterize this graph in terms of the…

Statistics Theory · Mathematics 2023-12-13 Kartik G. Waghmare , Victor M. Panaretos

Graphical Gaussian models with edge and vertex symmetries were introduced by \citet{HojLaur:2008} who also gave an algorithm to compute the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a…

Methodology · Statistics 2015-06-16 Helene Massam , Qiong Li , Xin Gao