### Abstract

We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the treereweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the standard TRW formulation for the ground graphical model. Compared to earlier work on lifted belief propagation, our formulation leads to a convex optimization problem for lifted marginal inference and provides an upper bound on the partition function. We provide two approaches for improving the lifted TRW upper bound. The first is a method for efficiently computing maximum spanning trees in highly symmetric graphs, which can be used to optimize the TRW edge appearance probabilities. The second is a method for tightening the relaxation of the marginal polytope using lifted cycle inequalities and novel exchangeable cluster consistency constraints.

Original language | English (US) |
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Title of host publication | Uncertainty in Artificial Intelligence - Proceedings of the 30th Conference, UAI 2014 |

Editors | Nevin L. Zhang, Jin Tian |

Publisher | AUAI Press |

Pages | 92-101 |

Number of pages | 10 |

ISBN (Electronic) | 9780974903910 |

State | Published - Jan 1 2014 |

Event | 30th Conference on Uncertainty in Artificial Intelligence, UAI 2014 - Quebec City, Canada Duration: Jul 23 2014 → Jul 27 2014 |

### Publication series

Name | Uncertainty in Artificial Intelligence - Proceedings of the 30th Conference, UAI 2014 |
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### Other

Other | 30th Conference on Uncertainty in Artificial Intelligence, UAI 2014 |
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Country | Canada |

City | Quebec City |

Period | 7/23/14 → 7/27/14 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence

### Cite this

*Uncertainty in Artificial Intelligence - Proceedings of the 30th Conference, UAI 2014*(pp. 92-101). (Uncertainty in Artificial Intelligence - Proceedings of the 30th Conference, UAI 2014). AUAI Press.