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The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an…

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 constraint-based structure learning of Markov networks and Bayesian networks in the presence of an unreliable conditional independence oracle that makes at most a bounded number of errors. For Markov networks, we observe that a low…

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…

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…

Bayesian network structure learning algorithms with limited data are being used in domains such as systems biology and neuroscience to gain insight into the underlying processes that produce observed data. Learning reliable networks from…

Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many hardness results are known. In this paper we propose a provably polynomial-time algorithm…

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…

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…

In this report paper we first present a report of the Advanced Machine Learning Course Project on the provided data set and then present a novel heuristic algorithm for exact Bayesian network (BN) structure discovery that uses decomposable…

Learning the structure of Bayesian networks is a difficult combinatorial optimization problem. In this paper, we consider learning of tree-augmented naive Bayes (TAN) structures for Bayesian network classifiers with discrete input features.…

We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…

Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem…

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…

We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees, a rich class of high-dimensional probability distributions and a subclass of Bayesian networks, a widely-studied type of graphical model.…

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…

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…

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…

We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…