### Abstract

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.

Original language | English |
---|---|

Pages (from-to) | 603-637 |

Number of pages | 35 |

Journal | Journal of Artificial Intelligence Research |

Volume | 50 |

DOIs | |

Publication status | Published - Jul 2014 |

Externally published | Yes |

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*Journal of Artificial Intelligence Research*,

*50*, 603-637. https://doi.org/10.1613/jair.4355

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*Journal of Artificial Intelligence Research*, vol. 50, pp. 603-637. https://doi.org/10.1613/jair.4355

**Probabilistic inference in credal networks : New complexity results.** / Mauá, Denis Deratani; de Campos, Cassio Polpo; Benavoli, Alessio; Antonucci, Alessandro.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Probabilistic inference in credal networks

T2 - New complexity results

AU - Mauá, Denis Deratani

AU - de Campos, Cassio Polpo

AU - Benavoli, Alessio

AU - Antonucci, Alessandro

PY - 2014/7

Y1 - 2014/7

N2 - Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.

AB - Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.

UR - http://www.scopus.com/inward/record.url?scp=84907362949&partnerID=8YFLogxK

U2 - 10.1613/jair.4355

DO - 10.1613/jair.4355

M3 - Article

VL - 50

SP - 603

EP - 637

JO - Journal of Artificial Intelligence Research

JF - Journal of Artificial Intelligence Research

SN - 1076-9757

ER -