### Abstract

In many practical problems-from tracking aircraft based on radar data to building a bibliographic database based on citation lists-we want to reason about an unbounded number of unseen objects with unknown relations among them. Bayesian networks, which define a fixed dependency structure on a finite set of variables, are not the ideal representation language for this task. This paper introduces contingent Bayesian networks (CBNs), which represent uncertainty about dependencies by labeling each edge with a condition under which it is active. A CBN may contain cycles and have infinitely many variables. Nevertheless, we give general conditions under which such a CBN defines a unique joint distribution over its variables. We also present a likelihood weighting algorithm that performs approximate inference in finite time per sampling step on any CBN that satisfies these conditions.

Original language | English (US) |
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Title of host publication | AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics |

Pages | 238-245 |

Number of pages | 8 |

State | Published - 2005 |

Event | 10th International Workshop on Artificial Intelligence and Statistics, AISTATS 2005 - Hastings, Christ Church, Barbados Duration: Jan 6 2005 → Jan 8 2005 |

### Other

Other | 10th International Workshop on Artificial Intelligence and Statistics, AISTATS 2005 |
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Country | Barbados |

City | Hastings, Christ Church |

Period | 1/6/05 → 1/8/05 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Statistics and Probability

### Cite this

*AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics*(pp. 238-245)

**Approximate inference for infinite contingent Bayesian networks.** / Milch, Brian; Marthi, Bhaskara; Sontag, David; Russell, Stuart; Ong, Daniel L.; Kolobov, Andrey.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics.*pp. 238-245, 10th International Workshop on Artificial Intelligence and Statistics, AISTATS 2005, Hastings, Christ Church, Barbados, 1/6/05.

}

TY - GEN

T1 - Approximate inference for infinite contingent Bayesian networks

AU - Milch, Brian

AU - Marthi, Bhaskara

AU - Sontag, David

AU - Russell, Stuart

AU - Ong, Daniel L.

AU - Kolobov, Andrey

PY - 2005

Y1 - 2005

N2 - In many practical problems-from tracking aircraft based on radar data to building a bibliographic database based on citation lists-we want to reason about an unbounded number of unseen objects with unknown relations among them. Bayesian networks, which define a fixed dependency structure on a finite set of variables, are not the ideal representation language for this task. This paper introduces contingent Bayesian networks (CBNs), which represent uncertainty about dependencies by labeling each edge with a condition under which it is active. A CBN may contain cycles and have infinitely many variables. Nevertheless, we give general conditions under which such a CBN defines a unique joint distribution over its variables. We also present a likelihood weighting algorithm that performs approximate inference in finite time per sampling step on any CBN that satisfies these conditions.

AB - In many practical problems-from tracking aircraft based on radar data to building a bibliographic database based on citation lists-we want to reason about an unbounded number of unseen objects with unknown relations among them. Bayesian networks, which define a fixed dependency structure on a finite set of variables, are not the ideal representation language for this task. This paper introduces contingent Bayesian networks (CBNs), which represent uncertainty about dependencies by labeling each edge with a condition under which it is active. A CBN may contain cycles and have infinitely many variables. Nevertheless, we give general conditions under which such a CBN defines a unique joint distribution over its variables. We also present a likelihood weighting algorithm that performs approximate inference in finite time per sampling step on any CBN that satisfies these conditions.

UR - http://www.scopus.com/inward/record.url?scp=84862596534&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862596534&partnerID=8YFLogxK

M3 - Conference contribution

SN - 097273581X

SN - 9780972735810

SP - 238

EP - 245

BT - AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics

ER -