Related papers: A Prior Distribution over Directed Acyclic Graphs …
Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a…
In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…
Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing…
Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…
Structural learning of directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. We propose a new Gaussian DAG model for dependent data which assumes the observations…
Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…
This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…
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…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…
We consider the problem of Bayesian causal discovery for the standard model of linear structural equations with equivariant Gaussian noise. A uniform prior is placed on the space of directed acyclic graphs (DAGs) over a fixed set of…
Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the…
We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks,…
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…
Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A…
This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a…
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…
In this work, we present a probabilistic model for directed graphs where nodes have attributes and labels. This model serves as a generative classifier capable of predicting the labels of unseen nodes using either maximum likelihood or…
A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling include classification and nonparametric methods. However, both methods often require a large number…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…