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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…

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…

Structure learning is essential for Bayesian networks (BNs) as it uncovers causal relationships, and enables knowledge discovery, predictions, inferences, and decision-making under uncertainty. Two novel algorithms, FSBN and SSBN, based on…

Using a Bayesian network to analyze the causal relationship between nodes is a hot spot. The existing network learning algorithms are mainly constraint-based and score-based network generation methods. The constraint-based method is mainly…

Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact…

In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest model able to…

The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions…

Learning a Bayesian networks with bounded treewidth is important for reducing the complexity of the inferences. We present a novel anytime algorithm (k-MAX) method for this task, which scales up to thousands of variables. Through extensive…

Bayesian networks are probabilistic graphical models often used in big data analytics. The problem of exact structure learning is to find a network structure that is optimal under certain scoring criteria. The problem is known to be NP-hard…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

We introduce a method for the problem of learning the structure of a Bayesian network using the quantum adiabatic algorithm. We do so by introducing an efficient reformulation of a standard posterior-probability scoring function on graphs…

Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that…

Score-based approaches in the structure learning task are thriving because of their scalability. Continuous relaxation has been the key reason for this advancement. Despite achieving promising outcomes, most of these methods are still…

One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is NP-hard.…

Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has…

It is well known in the literature that the problem of learning the structure of Bayesian networks is very hard to tackle: its computational complexity is super-exponential in the number of nodes in the worst case and polynomial in most…

We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…

Learning the structure of Bayesian networks from data is known to be a computationally challenging, NP-hard problem. The literature has long investigated how to perform structure learning from data containing large numbers of variables,…

We study the problem of learning the structure of an optimal Bayesian network when additional constraints are posed on the network or on its moralized graph. More precisely, we consider the constraint that the network or its moralized graph…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…