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Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…

Applications · Statistics 2016-05-24 Adria Caballe , Natalia Bochkina , Claus Mayer

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…

Methodology · Statistics 2013-03-05 Fabian Scheipl , Thomas Kneib , Ludwig Fahrmeir

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…

We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…

Methodology · Statistics 2015-12-24 Bryon Aragam , Qing Zhou

Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the…

Methodology · Statistics 2023-11-16 Jack Storror Carter , David Rossell , Jim Q. Smith

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…

Machine Learning · Statistics 2019-02-07 Zehang Richard Li , Tyler H. McCormick

Associated to each graph G is a Gaussian graphical model. Such models are often used in high-dimensional settings, i.e. where there are relatively few data points compared to the number of variables. The maximum likelihood threshold of a…

Statistics Theory · Mathematics 2023-12-07 Daniel Irving Bernstein , Hayden Outlaw

In many applied fields, such as genomics, different types of data are collected on the same system, and it is not uncommon that some of these datasets are subject to censoring as a result of the measurement technologies used, such as data…

Methodology · Statistics 2020-05-04 Luigi Augugliaro , Gianluca Sottile , Veronica Vinciotti

We consider a method to jointly estimate sparse precision matrices and their underlying graph structures using dependent high-dimensional datasets. We present a penalized maximum likelihood estimator which encourages both sparsity and…

Applications · Statistics 2016-08-22 Adria Caballe , Natalia Bochkina , Claus Mayer

We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…

Computation · Statistics 2016-03-29 Julio E. Castrillon-Candas , Marc G. Genton , Rio Yokota

In this paper, we study properties of penalized and structured M-estimators of multivariate scatter, based on geodesically convex but not necessarily smooth penalty functions. Existence and uniqueness conditions for these penalized and…

Methodology · Statistics 2026-03-31 Mengxi Yi , David Tyler

We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose…

Statistics Theory · Mathematics 2012-07-24 Helene Gehrmann , Steffen L. Lauritzen

Modeling the complex relationships between multiple categorical response variables as a function of predictors is a fundamental task in the analysis of categorical data. However, existing methods can be difficult to interpret and may lack…

Methodology · Statistics 2024-10-08 Hongru Zhao , Aaron J. Molstad , Adam J. Rothman

This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between…

Statistics Theory · Mathematics 2021-05-25 Eunice Okome Obiang , Pascal Jézéquel , Frédéric Proïa

Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…

Machine Learning · Statistics 2009-12-01 Ali Shojaie , George Michailidis

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…

Methodology · Statistics 2017-11-01 Alexander J. Gibberd , James D. B. Nelson

Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…

Statistics Theory · Mathematics 2013-05-07 Elizabeth Gross , Mathias Drton , Sonja Petrović

Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where…

Methodology · Statistics 2022-05-13 Alessandro Casa , Andrea Cappozzo , Michael Fop

In this work, we consider a manufactory process which can be described by a multiple-instance logistic regression model. In order to compute the maximum likelihood estimation of the unknown coefficient, an expectation-maximization algorithm…

Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of…

Machine Learning · Statistics 2019-09-13 Faïcel Chamroukhi , Florian Lecocq , Hien D. Nguyen