### Abstract

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.

Original language | English |
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Pages (from-to) | 474-484 |

Number of pages | 11 |

Journal | International Journal of Approximate Reasoning |

Volume | 51 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2010 |

### Keywords

- Loopy belief propagation

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## Cite this

Antonucci, A., Yi, S., de Campos, C. P., & Zaffalon, M. (2010). Generalized loopy 2U: A new algorithm for approximate inference in credal networks.

*International Journal of Approximate Reasoning*,*51*(5), 474-484. https://doi.org/10.1016/j.ijar.2010.01.007