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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 introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

Methodology · Statistics 2024-09-25 Anwesha Chakravarti , Naveen N. Narishetty , Feng Liang

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

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Applications · Statistics 2018-08-07 Donald R. Williams , Juho Piironen , Aki Vehtari , Philippe Rast

In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant…

Statistics Theory · Mathematics 2017-12-11 Guo Yu , Jacob Bien

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

Computation · Statistics 2019-04-23 Linda S. L. Tan , David J. Nott

This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the precision and the observations, we show that the sample…

Statistics Theory · Mathematics 2025-03-25 Jiaheng Chen , Daniel Sanz-Alonso

Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…

Methodology · Statistics 2025-10-07 Thomas Muschinski , Georg J. Mayr , Thorsten Simon , Nikolaus Umlauf , Achim Zeileis

Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…

Methodology · Statistics 2024-10-17 Yuan Gao , Zhiyuan Zhang , Zhanrui Cai , Xuening Zhu , Tao Zou , Hansheng Wang

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…

Machine Learning · Computer Science 2013-06-14 Cho-Jui Hsieh , Matyas A. Sustik , Inderjit S. Dhillon , Pradeep Ravikumar

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…

Methodology · Statistics 2013-03-18 Kei Hirose , Michio Yamamoto

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…

Machine Learning · Statistics 2012-01-11 Shuheng Zhou , Philipp Rutimann , Min Xu , Peter Buhlmann

Given n observations of a p-dimensional random vector, the covariance matrix and its inverse (precision matrix) are needed in a wide range of applications. Sample covariance (e.g. its eigenstructure) can misbehave when p is comparable to…

Methodology · Statistics 2008-07-24 Guilherme V. Rocha , Peng Zhao , Bin Yu

This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approximator for the output of probabilistic ensemble models used for dense image prediction tasks. This is achieved through a convolutional neural…

Computer Vision and Pattern Recognition · Computer Science 2022-03-30 Ivor J. A. Simpson , Sara Vicente , Neill D. F. Campbell

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

Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential…

Methodology · Statistics 2019-02-20 Mitchell Krock , William Kleiber , Stephen Becker

In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a…

Statistics Theory · Mathematics 2015-10-30 Degui Li , Yuan Ke , Wenyang Zhang

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

Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…

Methodology · Statistics 2018-02-13 Jonathan P Williams , Jan Hannig

Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…

Numerical Analysis · Computer Science 2016-07-04 Eran Treister , Javier S. Turek , Irad Yavneh