Related papers: Parameter Priors for Directed Acyclic Graphical Mo…
We develop simple methods for constructing parameter priors for model choice among Directed Acyclic Graphical (DAG) models. In particular, we introduce several assumptions that permit the construction of parameter priors for a large number…
In this paper, we consider Gaussian models Markov with respect to an arbitrary DAG. We first construct a family of conjugate priors for the Cholesky parametrization of the covariance matrix of such models. This family has as many shape…
Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG…
Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph $G$. These models are distinctly different from the traditional concentration graph models (often also…
When considering a graphical Gaussian model ${\mathcal{N}}_G$ Markov with respect to a decomposable graph $G$, the parameter space of interest for the precision parameter is the cone $P_G$ of positive definite matrices with fixed zeros…
Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate…
Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…
In Gaussian graphical models, the zero entries in the precision matrix determine the dependence structure, so estimating that sparse precision matrix and, thereby, learning this underlying structure, is an important and challenging problem.…
We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time…
In this paper, we first develop a new family of conjugate prior distributions for the cell parameters of discrete graphical models Markov with respect to a set P of moral directed acyclic graphs with skeleton a given decomposable graph G.…
Directed Gaussian graphical models are statistical models that use a directed acyclic graph (DAG) to represent the conditional independence structures between a set of jointly normal random variables. The DAG specifies the model through…
The Wishart distribution is the standard conjugate prior for the precision of the multivariate Gaussian likelihood, when the mean is known -- while the normal-Wishart can be used when the mean is also unknown. It is however not so obvious…
Deep kernel processes are a recently introduced class of deep Bayesian models that have the flexibility of neural networks, but work entirely with Gram matrices. They operate by alternately sampling a Gram matrix from a distribution over…
We present an objective Bayes method for covariance selection in Gaussian multivariate regression models whose error term has a covariance structure which is Markov with respect to a Directed Acyclic Graph (DAG). The scope is…
In probabilstic supervised learning of an input-output relationship - as a sample function of a Gaussian Process (GP) - priors are typically specified for the hyperparameters of the kernel that parametrises the covariance function of the…
Directed acyclic graphical models (DAGs) are often used to describe common structural properties in a family of probability distributions. This paper addresses the question of classifying DAGs up to an isomorphism. By considering Gaussian…
Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…
For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such…
We propose an approach termed ``qDAGx'' for Bayesian covariate-dependent quantile directed acyclic graphs (DAGs) where these DAGs are individualized, in the sense that they depend on individual-specific covariates. The individualized DAG…
We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined…