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We present a novel approach for multilabel classification based on an ensemble of Bayesian networks. The class variables are connected by a tree; each model of the ensemble uses a different class as root of the tree. We assume the features to be conditionally independent given the classes, thus generalizing the naive Bayes assumption to the multiclass case.… (More)

Predictions made by imprecise-probability models are often indeterminate (that is, set-valued). Measuring the quality of an indeterminate prediction by a single number is important to fairly compare different models, but a principled approach to this problem is currently missing. In this paper we derive a measure to evaluate the predictions of credal… (More)

- Marco Zaffalon, Giorgio Corani, Denis Deratani Mauá
- Int. J. Approx. Reasoning
- 2012

Predictions made by imprecise-probability models are often indeterminate (that is, set-valued). Measuring the quality of an indeterminate prediction by a single number is important to fairly compare different models, but a principled approach to this problem is currently missing. In this paper we derive, from a set of assumptions, a metric to evaluate the… (More)

This paper presents a new anytime algorithm for the marginal MAP problem in graphical models of bounded treewidth. We show asymptotic convergence and theoretical error bounds for any fixed step. Experiments show that it compares well to a state-of-the-art systematic search algorithm.

- Denis Deratani Mauá, Cassio Polpo de Campos, Marco Zaffalon
- Int. J. Approx. Reasoning
- 2012

Credal networks relax the precise probability requirement of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper, we present a new variable elimination algorithm for exactly computing… (More)

- Denis Deratani Mauá, Cassio Polpo de Campos
- ArXiv
- 2017

We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show np-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability within a sublinear factor. We show that this is a tight bound, as we can find an approximation within a linear factor… (More)

- Giorgio Corani, Alessandro Antonucci, Denis Deratani Mauá, Sandra Gabaglio
- Probabilistic Graphical Models
- 2014

In previous work, we devised an approach for multilabel classification based on an ensemble of Bayesian networks. It was characterized by an efficient structural learning and by high accuracy. Its shortcoming was the high computational complexity of the MAP inference, necessary to identify the most probable joint configuration of all classes. In this work,… (More)

We examine the inferential complexity of Bayesian networks specified through logical constructs. We first consider simple propositional languages, and then move to relational languages. We examine both the combined complexity of inference (as network size and evidence size are not bounded) and the data complexity of inference (where network size is… (More)

- Denis Deratani Mauá, Cassio Polpo de Campos, Marco Zaffalon
- J. Artif. Intell. Res.
- 2012

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly… (More)

This work presents novel algorithms for learning Bayesian networks of bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in sampling k-trees (maximal graphs of treewidth k), and… (More)