English
Related papers

Related papers: Objective Bayes Covariate-Adjusted Sparse Graphica…

200 papers

We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear recursive structural equation model (SEM) with the associated…

Statistics Theory · Mathematics 2025-08-05 Anamitra Chaudhuri , Anirban Bhattacharya , Yang Ni

We study submodels of Gaussian DAG models defined by partial homogeneity constraints imposed on the model error variances and structural coefficients. We represent these models with colored DAGs and investigate their properties for use in…

Statistics Theory · Mathematics 2025-12-12 Tobias Boege , Kaie Kubjas , Pratik Misra , Liam Solus

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the…

Machine Learning · Statistics 2013-11-15 Po-Ling Loh , Peter Bühlmann

Background: In epidemiology, causal inference and prediction modeling methodologies have been historically distinct. Directed Acyclic Graphs (DAGs) are used to model a priori causal assumptions and inform variable selection strategies for…

Methodology · Statistics 2020-07-03 Marco Piccininni , Stefan Konigorski , Jessica L Rohmann , Tobias Kurth

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

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

We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…

Methodology · Statistics 2025-09-16 Gregor Zens , Mark F. J. Steel

Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal…

Statistics Theory · Mathematics 2022-12-20 Robin J. Evans

The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated…

Methodology · Statistics 2021-03-15 J. Mulder , H. Hoijtink , X. Gu

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

Methodology · Statistics 2012-07-02 Ricardo Silva , Zoubin Ghahramani

We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…

Methodology · Statistics 2025-08-25 Xuan Cao , Kyoungjae Lee

Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov…

Machine Learning · Computer Science 2021-06-15 Yashas Annadani , Jonas Rothfuss , Alexandre Lacoste , Nino Scherrer , Anirudh Goyal , Yoshua Bengio , Stefan Bauer

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Methodology · Statistics 2023-08-08 Sagnik Bhadury , Riten Mitra , Jeremy T. Gaskins

Estimation of the covariance matrix for high-dimensional multivariate datasets is a challenging and important problem in modern statistics. In this paper, we focus on high-dimensional Gaussian DAG models where sparsity is induced on the…

Statistics Theory · Mathematics 2019-03-11 Xuan Cao , Kshitij Khare , Malay Ghosh

Directed Acyclic Graphs (DAGs) are solid structures used to describe and infer the dependencies among variables in multivariate scenarios. Having a thorough comprehension of the accurate DAG-generating model is crucial for causal discovery…

Methodology · Statistics 2024-09-09 S. Nazari , M. Arashi , A. Sadeghkhani

We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…

Methodology · Statistics 2020-09-22 Angelos Alexopoulos , Leonardo Bottolo

We establish a novel framework for learning a directed acyclic graph (DAG) when data are generated from a Gaussian, linear structural equation model. It consists of two parts: (1) introduce a permutation matrix as a new parameter within a…

Machine Learning · Statistics 2021-07-06 Aramayis Dallakyan , Mohsen Pourahmadi

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

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…

Statistics Theory · Mathematics 2016-09-30 Emilie Devijver , Mélina Gallopin

Estimating the structure of Bayesian networks as directed acyclic graphs (DAGs) from observational data is a fundamental challenge, particularly in causal discovery. Bayesian approaches excel by quantifying uncertainty and addressing…

Machine Learning · Computer Science 2026-02-17 Edwin V. Bonilla , Pantelis Elinas , He Zhao , Maurizio Filippone , Vassili Kitsios , Terry O'Kane