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Traditionally, Bayesian network structure learning is often carried out at a central site, in which all data is gathered. However, in practice, data may be distributed across different parties (e.g., companies, devices) who intend to…
Learning the structure of Bayesian networks (BNs) from data is challenging, especially for datasets involving a large number of variables. The recently proposed divide-and-conquer (D\&D) strategies present a promising approach for learning…
Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents…
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…
Naive Bayes is a simple Bayesian classifier with strong independence assumptions among the attributes. This classifier, desipte its strong independence assumptions, often performs well in practice. It is believed that relaxing the…
Previous work has shown that the problem of learning the optimal structure of a Bayesian network can be formulated as a shortest path finding problem in a graph and solved using A* search. In this paper, we improve the scalability of this…
We study the problem of learning hypergraphs with shortest-path queries (SP-queries), and present the first provably optimal online algorithm for a broad and natural class of hypertrees that we call orderly hypertrees. Our online algorithm…
Sum-product networks (SPNs) are flexible density estimators and have received significant attention due to their attractive inference properties. While parameter learning in SPNs is well developed, structure learning leaves something to be…
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…
Dealing with uncertainty in Bayesian Network structures using maximum a posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often intractable due to the superexponential number of possible directed, acyclic graphs. When the…
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…
We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
Estimating dependence relationships between variables is a crucial issue in many applied domains, such as medicine, social sciences and psychology. When several variables are entertained, these can be organized into a network which encodes…
The score-based structure learning of Bayesian network (BN) is an effective way to learn BN models, which are regarded as some of the most compelling probabilistic graphical models in the field of representation and reasoning under…
Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
The limit of infinite width allows for substantial simplifications in the analytical study of over-parameterised neural networks. With a suitable random initialisation, an extremely large network exhibits an approximately Gaussian…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…