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In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation…
Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based…
To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…
Causal Bayesian networks are widely used tools for summarising the dependencies between variables and elucidating their putative causal relationships. By restricting the search to trees, for example, learning the optimum from data is…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
A key problem in statistics and machine learning is the determination of network structure from data. We consider the case where the structure of the graph to be reconstructed is known to be scale-free. We show that in such cases it is…
This paper considers the problem of learning the parameters in Bayesian networks of discrete variables with known structure and hidden variables. Previous approaches in these settings typically use expectation maximization; when the network…
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…
This paper addresses the problem of learning a sparse structure Bayesian network from high-dimensional discrete data. Compared to continuous Bayesian networks, learning a discrete Bayesian network is a challenging problem due to the large…
Learning Bayesian networks from raw data can help provide insights into the relationships between variables. While real data often contains a mixture of discrete and continuous-valued variables, many Bayesian network structure learning…
In this paper we examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional…
Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…
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…
One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NP-hard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but…
Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce…
We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…
Feature selection is an important task in many problems occurring in pattern recognition, bioinformatics, machine learning and data mining applications. The feature selection approach enables us to reduce the computation burden and the…
It has been observed in practical applications and in theoretical analysis that over-parametrization helps to find good minima in neural network training. Similarly, in this article we study widening and deepening neural networks by a…