Mauro Scanagatta

Air pollution prediction via multi-label classification

A Bayesian network classifier can be used to estimate the probability of an air pollutant overcoming a certain threshold. Yet multiple predictions are typically required regarding variables which are stochastically dependent, such as ozone measured in multiple stations or assessed according to by different indicators. The common practice (independent approach) is to devise an independent classifier for each class variable being predicted; yet this approach overlooks the dependencies among the class variables. By appropriately modeling such dependencies one can improve the accuracy of the forecasts. We address this problem by designing a multi-label classifier, which simultaneously predict multiple air pollution variables. To this end we design a multi-label classifier based on Bayesian networks and learn its structure through structural learning. We present experiments in three different case studies regarding the prediction of PM2.5 and ozone. The multi-label classifier outperforms the independent approach, allowing to take better decisions. A multi-label classifier jointly predicts multiple dependent variables.We proposed a Bayesian network multi-label classifier.We learn its structure solving an integer programming problem.We consider the joint prediction of air pollution variables.The multi-label classifier outperforms the usage of multiple independent classifiers.

Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks

This work presents two new score functions based on the Bayesian Dirichlet equivalent uniform (BDeu) score for learning Bayesian network structures. They consider the sensitivity of BDeu to varying parameters of the Dirichlet prior. The scores take on the most adversary and the most beneficial priors among those within a contamination set around the symmetric one. We build these scores in such way that they are decomposable and can be computed efficiently. Because of that, they can be integrated into any state-of-the-art structure learning method that explores the space of directed acyclic graphs and allows decomposable scores. Empirical results suggest that our scores outperform the standard BDeu score in terms of the likelihood of unseen data and in terms of edge discovery with respect to the true network, at least when the training sample size is small. We discuss the relation between these new scores and the accuracy of inferred models. Moreover, our new criteria can be used to identify the amount of data after which learning is saturated, that is, additional data are of little help to improve the resulting model.

Efficient learning of bounded-treewidth Bayesian networks from complete and incomplete data sets

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 experiments we show that it consistently yields higher-scoring structures than its competitors on complete data sets. We then consider the problem of structure learning from incomplete data sets. This can be addressed by structural EM, which however is computationally very demanding. We thus adopt the novel k-MAX algorithm in the maximization step of structural EM, obtaining an efficient computation of the expected sufficient statistics. We test the resulting structural EM method on the task of imputing missing data, comparing it against the state-of-the-art approach based on random forests. Our approach achieves the same imputation accuracy of the competitors, but in about one tenth of the time. Furthermore we show that it has worst-case complexity linear in the input size, and that it is easily parallelizable.

Approximate structure learning for large Bayesian networks

We present approximate structure learning algorithms for Bayesian networks. We discuss the two main phases of the task: the preparation of the cache of the scores and structure optimization, both with bounded and unbounded treewidth. We improve on state-of-the-art methods that rely on an ordering-based search by sampling more effectively the space of the orders. This allows for a remarkable improvement in learning Bayesian networks from thousands of variables. We also present a thorough study of the accuracy and the running time of inference, comparing bounded-treewidth and unbounded-treewidth models.

Entropy-based pruning for learning Bayesian networks using BIC

For decomposable score-based structure learning of Bayesian networks, existing approaches first compute a collection of candidate parent sets for each variable and then optimize over this collection by choosing one parent set for each variable without creating directed cycles while maximizing the total score. We target the task of constructing the collection of candidate parent sets when the score of choice is the Bayesian Information Criterion (BIC). We provide new non-trivial results that can be used to prune the search space of candidate parent sets of each node. We analyze how these new results relate to previous ideas in the literature both theoretically and empirically. We show in experiments with UCI data sets that gains can be significant. Since the new pruning rules are easy to implement and have low computational costs, they can be promptly integrated into all state-of-the-art methods for structure learning of Bayesian networks.