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Related papers: Sparse Nonparametric Graphical Models

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We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

Statistics Theory · Mathematics 2014-04-08 Sayantan Banerjee , Subhashis Ghosal

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

Methodology · Statistics 2021-12-14 Eunice Okome Obiang , Pascal Jézéquel , Frédéric Proïa

Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions…

Machine Learning · Statistics 2023-02-28 Ricardo Baptista , Youssef Marzouk , Rebecca E. Morrison , Olivier Zahm

The popular generalized additive model framework is extended to allow both the mean curves and the response distribution to be nonparametric. The approach is demonstrated to be a flexible yet parsimonious tool for data analysis in its own…

Methodology · Statistics 2017-09-18 Alan Huang , Nanxi Zhang

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…

Methodology · Statistics 2016-04-04 Anindya Bhadra , Arvind Rao , Veerabhadran Baladandayuthapani

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

Machine Learning · Statistics 2015-11-25 Leo L. Duan , Xia Wang , Rhonda D. Szczesniak

Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…

Methodology · Statistics 2019-04-26 A. Mohammadi , E. C. Wit

A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very…

Statistics Theory · Mathematics 2013-02-14 Lingzhou Xue , Hui Zou

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…

Methodology · Statistics 2016-01-06 Hongxiao Zhu , Nate Strawn , David B. Dunson

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

Machine Learning · Computer Science 2013-02-21 George H. John , Pat Langley

Large real-world graphs tend to be sparse, but they often contain many densely connected subgraphs and exhibit high clustering coefficients. While recent random graph models can capture this sparsity, they ignore the local density, or vice…

Methodology · Statistics 2019-07-18 Sinead A. Williamson , Mauricio Tec

Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…

Machine Learning · Computer Science 2015-06-19 Kenric P. Nelson , Madalina Barbu , Brian J. Scannell

Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…

Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the uncertainty pattern that underlies traffic flow. To address this…

Applications · Statistics 2024-11-25 Yuan-Zheng Lei , Yaobang Gong , Xianfeng Terry Yang

Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…

Methodology · Statistics 2018-02-16 Shota Katayama , Hironori Fujisawa , Mathias Drton

Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high…

Machine Learning · Statistics 2009-03-05 Han Liu , John Lafferty , Larry Wasserman

Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or…

Machine Learning · Statistics 2024-02-15 Konstantin Göbler , Anne Miloschewski , Mathias Drton , Sach Mukherjee

Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization…

Statistics Theory · Mathematics 2010-12-01 Rina Foygel , Mathias Drton

An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph…

Computation · Statistics 2017-06-16 Jarno Hartog , Harry van Zanten

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…

Methodology · Statistics 2017-03-07 Benjamin Frot , Luke Jostins , Gil McVean