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Learning joint probability distributions on n random variables requires exponential sample size in the generic case. Here we consider the case that a temporal (or causal) order of the variables is known and that the (unknown) graph of…
In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown…
Bayesian Networks (BNs) are useful tools giving a natural and compact representation of joint probability distributions. In many applications one needs to learn a Bayesian Network (BN) from data. In this context, it is important to…
Graphical models are usually learned without regard to the cost of doing inference with them. As a result, even if a good model is learned, it may perform poorly at prediction, because it requires approximate inference. We propose an…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…
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…
A classic approach for learning Bayesian networks from data is to identify a maximum a posteriori (MAP) network structure. In the case of discrete Bayesian networks, MAP networks are selected by maximising one of several possible Bayesian…
We commonly assume that data are a homogeneous set of observations when learning the structure of Bayesian networks. However, they often comprise different data sets that are related but not homogeneous because they have been collected in…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
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 neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network…
We present a method for learning the parameters of a Bayesian network with prior knowledge about the signs of influences between variables. Our method accommodates not just the standard signs, but provides for context-specific signs as…
We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to scorebased structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The…
Assumptions about invariances or symmetries in data can significantly increase the predictive power of statistical models. Many commonly used models in machine learning are constraint to respect certain symmetries in the data, such as…
Additive Bayesian networks are types of graphical models that extend the usual Bayesian generalized linear model to multiple dependent variables through the factorisation of the joint probability distribution of the underlying variables.…
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…
In recent years there has been a flurry of works on learning Bayesian networks from data. One of the hard problems in this area is how to effectively learn the structure of a belief network from incomplete data- that is, in the presence of…
Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In…