Related papers: A partial graphical model with a structural prior …
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…
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…
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…
In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on…
We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…
Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…
Probabilistic graphical models (PGMs) provide a compact and flexible framework to model very complex real-life phenomena. They combine the probability theory which deals with uncertainty and logical structure represented by a graph which…
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…
This paper characterizes the values of partial regression coefficients, defined as projection coefficients onto the space spanned by explanatory variables, for random variables generated by linear structural equation models using graphical…
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…
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…
In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…
The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in…
Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…
One of the challenges with functional data is incorporating spatial structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear…
Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the $\ell_2$ penalty enjoys a smaller…
In the context of undirected Gaussian graphical models, we introduce three estimators based on elastic net penalty for the underlying dependence graph. Our goal is to estimate the sparse precision matrix, from which to retrieve both the…
Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool which allows one to describe the relationships among the variables of interest.…