Hill-climbing and branch-and-bound algorithms for exact and approximate inference in credal networks

Cano, Andrés; Gómez, Manuel; Moral, Serafı́n; Abellán, Joaquín

doi:10.1016/j.ijar.2006.07.020

Cited by 27 publications

(35 citation statements)

References 11 publications

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“…The code is available as a free software tool. 4 In these experiments, the greedy approach described in Sect. 4 is considered and the algorithm is therefore called G-LP.…”

Section: Methodsmentioning

confidence: 99%

“…Exact approaches have been proposed that implement some branch-and-bound method with local searches [4,6,8,9]. Unfortunately they all suffer from serious efficiency issues unless the credal network is very simple.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, none of these methods can deal well with a binary node having four ternary parents, because this setting is already equivalent to 3 4 = 81 free optimization variables to be chosen, meaning a space of 2 81 possible solutions just locally to this node! On the other hand, approximate methods either are fast and provide no accuracy guarantee [3,4,6] or provide theoretical guarantees but are as slow as exact methods [13]. Moreover, all these approximate methods are only capable of treating credal networks under a vertex-based representation, while a constraint-based specification of credal networks still lacks any practical algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximating Credal Network Inferences by Linear Programming

Antonucci

Campos

Huber

et al. 2013

Lecture Notes in Computer Science

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Abstract. An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to very accurate inferences. The approach can also be specialized to classification with credal networks based on the maximality criterion. A complexity analysis for both the problem and the algorithm is reported together with numerical experiments, which confirm the good performance of the method. While the inner approximation produced by the algorithm gives rise to a classifier which might return a subset of the optimal class set, preliminary empirical results suggest that the accuracy of the optimal class set is seldom affected by the approximate probabilities.

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“…The code is available as a free software tool. 4 In these experiments, the greedy approach described in Sect. 4 is considered and the algorithm is therefore called G-LP.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Approximating Credal Network Inferences by Linear Programming

Antonucci

Campos

Huber

et al. 2013

Lecture Notes in Computer Science

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“…Despite the hardness of the problem, some algorithms are known to perform reasonably well under certain conditions. Exact approaches have been proposed that implement some branch-and-bound method with local searches (da Rocha et al, 2003;de Campos and Cozman, 2005;Cano et al, 2007;de Campos and Cozman, 2007). Unfortunately they all suffer from serious efficiency issues unless the credal network is very simple.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, none of these methods can deal well with a binary node having four ternary parents, because this setting is already equivalent to 3 4 = 81 free optimization variables to be chosen, meaning a space of 2 81 possible solutions just locally on this node! On the other hand, approximate methods either are fast and provide no accuracy guarantee (Cano et al, 2007;da Rocha et al, 2003; or provide theoretical guarantees but are as slow as exact methods (Mauá et al, 2012a). Moreover, all these approximate methods are only capable of treating credal networks whose credal sets are specified by enumerating the extreme points, while a constraint-based specification still lacks any practical algorithm.…”

Section: Introductionmentioning

confidence: 99%

Approximate credal network updating by linear programming with applications to decision making

Antonucci

Campos

Huber

et al. 2015

International Journal of Approximate Reasoning

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Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to accurate inferences. A transformation is also derived to reduce decision making in credal networks based on the maximality criterion to updating. The decision task is proved to have the same complexity of standard inference, being NP PP -complete for general credal nets and NP-complete for polytrees. Similar results are derived for the E-admissibility criterion. Numerical experiments confirm a good performance of the method.

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