Related papers: Minimum bounding polytropes for estimation of max-…
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…
We consider the problem of regularized maximum likelihood estimation for the structure and parameters of a high-dimensional, sparse directed acyclic graphical (DAG) model with Gaussian distribution, or equivalently, of a Gaussian structural…
We explore the issue of refining an existent Bayesian network structure using new data which might mention only a subset of the variables. Most previous works have only considered the refinement of the network's conditional probability…
Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…
Bayesian networks are basic graphical models, used widely both in statistics and artificial intelligence. These statistical models of conditional independence structure are described by acyclic directed graphs whose nodes correspond to…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
A Bayesian Network is a directed acyclic graph (DAG) on a set of $n$ random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite…
Recently, there has been much interest in finding globally optimal Bayesian network structures. These techniques were developed for generative scores and can not be directly extended to discriminative scores, as desired for classification.…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
This study proposes the first Bayesian approach for learning high-dimensional linear Bayesian networks. The proposed approach iteratively estimates each element of the topological ordering from backward and its parent using the inverse of a…
Bayesian networks (BN) are directed acyclic graphical (DAG) models that have been adopted into many fields for their strengths in transparency, interpretability, probabilistic reasoning, and causal modeling. Given a set of data, one hurdle…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
Bayesian networks are convenient graphical expressions for high dimensional probability distributions representing complex relationships between a large number of random variables. They have been employed extensively in areas such as…
Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present the first method for fitting these…
Bayesian network (BN) structure discovery algorithms typically either make assumptions about the sparsity of the true underlying network, or are limited by computational constraints to networks with a small number of variables. While these…
This work introduces a novel technique, named structural dimension reduction, to collapse a Bayesian network onto a minimum and localized one while ensuring that probabilistic inferences between the original and reduced networks remain…
Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of…
In networks of dynamic systems, one challenge is to identify the interconnection structure on the basis of measured signals. Inspired by a Bayesian approach in [1], in this paper, we explore a Bayesian model selection method for identifying…
We consider the problem of jointly estimating multiple related directed acyclic graph (DAG) models based on high-dimensional data from each graph. This problem is motivated by the task of learning gene regulatory networks based on gene…
Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme…