Related papers: Bayesian Networks for Max-linear Models

Max-linear Bayesian networks are recursive max-linear structural equation models represented by an edge weighted directed acyclic graph (DAG). The identifiability and estimation of max-linear Bayesian networks is an intricate issue as…

Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for…

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…

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…

Given a Bayesian network structure (directed acyclic graph), the celebrated d-separation algorithm efficiently determines whether the network structure implies a given conditional independence relation. We show that this changes drastically…

We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods…

Discrete max-linear Bayesian networks are directed graphical models specified by the same recursive structural equations as max-linear models but with discrete innovations. When all of the random variables in the model are binary, these…

Max-linear Bayesian networks have emerged as highly applicable models for causal inference via extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian…

Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning…

We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data, learning an undirected graph we call the unconditional dependence graph. We show that unconditional dependence graphs…

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…

We characterise the likelihood function computed from a Bayesian network with latent variables as root nodes. We show that the marginal distribution over the remaining, manifest, variables also factorises as a Bayesian network, which we…

Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in terms of the max-plus algebra by taking its logarithm. Then,…

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…

Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…

Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to…

This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How can…

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…

We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…

AThe paper gives a few arguments in favour of the use of chain graphs for description of probabilistic conditional independence structures. Every Bayesian network model can be equivalently introduced by means of a factorization formula with…