## Bayesian Inference in the Presence of Determinism (2003)

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Venue: | In AI-STATS-2003 |

Citations: | 28 - 9 self |

### BibTeX

@INPROCEEDINGS{Larkin03bayesianinference,

author = {David Larkin and Rina Dechter},

title = {Bayesian Inference in the Presence of Determinism},

booktitle = {In AI-STATS-2003},

year = {2003}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper, we consider the problem of performing inference on Bayesian networks which exhibit a substantial degree of determinism.

### Citations

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Probabilistic reasoning in intelligent systems: networks of plausible inference
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Citation Context ...o light by constraint propagation may be exploited to a much greater extent than has been previously possible. This is confirmed with theoretical and empirical studies. 1 Introduction Belief networks =-=[9]-=- are a popular model for reasoning with uncertainty in Artificial Intelligence. In general, performing inference on a belief network is NPhard. However, tractable subclasses have been identified. The ... |

1283 |
Local computations with probabilities on graphical structures and their application to expert systems
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- 1988
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Citation Context ...rk is NPhard. However, tractable subclasses have been identified. The most important of these is the case when the network graph can be embedded in a triangulated (chordal) graph of bounded treewidth =-=[8, 13, 3]-=-. It is also possible to e#ciently process networks with a special structure in their quantitative component, such as the common case of Noisy-OR gates [9], or contextspecific independence [1]. In thi... |

757 |
Database System Concepts
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- 1996
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Citation Context ...r Elim-Sparse (d tuples of size n each). E#- cient operations to work with these functions are also available. These are mainly based on the Hash-Join procedure which is well-known in database theory =-=[6]-=-. The product of two functions is computed by hashing every tuple in the smaller function into a hash table on the basis of its assignments to the common variables. Then every tuple in the larger func... |

370 | Algorithms for constraint-satisfaction problems : A survey
- KUMAR
- 1992
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Citation Context ...The main motivation for our study is the similarity that exists between belief networks that exhibit many functional relationships and deterministic networks, such as constraint satisfaction problems =-=[7, 2]-=-. Since these belief networks have a substantial deterministic substructure beneath their probabilistic facade, it would seem logical that the sophisticated techniques developed by the constraint sati... |

288 | Context-specific independence in Bayesian networks
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Citation Context ... [8, 13, 3]. It is also possible to e#ciently process networks with a special structure in their quantitative component, such as the common case of Noisy-OR gates [9], or contextspecific independence =-=[1]-=-. In this paper, building upon research reported in [4], we identify another tractable class, the case when the network exhibits a high degree of determinism. With a deterministic relation, such as x ... |

270 | Bucket elimination: A unifying framework for reasoning
- Dechter
- 1999
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Citation Context ...rk is NPhard. However, tractable subclasses have been identified. The most important of these is the case when the network graph can be embedded in a triangulated (chordal) graph of bounded treewidth =-=[8, 13, 3]-=-. It is also possible to e#ciently process networks with a special structure in their quantitative component, such as the common case of Noisy-OR gates [9], or contextspecific independence [1]. In thi... |

133 |
An algebra of Bayesian belief universes for knowledge-based systems
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Citation Context ...yed our simpler method for the purposes of this study. More sophisticated sparse table methods [11] are also available. Investigating the impact these might have is an open question. In previous work =-=[5]-=-, sparse representations have been used to speed Bayesian inference. The sum and product operations have also been previously expressed as relational database operators [12], which coincides with our ... |

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Storing a sparse table
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Citation Context ...tation, without being constrained to respect the structure of partialassignment space. Therefore we employed our simpler method for the purposes of this study. More sophisticated sparse table methods =-=[11]-=- are also available. Investigating the impact these might have is an open question. In previous work [5], sparse representations have been used to speed Bayesian inference. The sum and product operati... |

37 | Probabilistic partial evaluation: Exploiting rule structure in probabilistic inference
- Poole
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Citation Context ...present, the overhead of manipulating nearly full tuple lists can be much larger than dealing with a table. Other structured function representations, such as decision trees [1] or rule-based systems =-=[10]-=- might seem appropriate in this case. These systems partition the domain space of functions into regions of equal value, which only requires one function definition per region. The regions are defined... |

30 | Hybrid processing of beliefs and constraints
- Dechter, Larkin
- 2001
(Show Context)
Citation Context ...per, we consider the problem of performing inference on Bayesian networks which exhibit a substantial degree of determinism. We improve upon the determinismexploiting inference algorithm presented in =-=[4]-=-, showing that the information brought to light by constraint propagation may be exploited to a much greater extent than has been previously possible. This is confirmed with theoretical and empirical ... |

17 |
An Extended Relational Data Model for Probabilistic Reasoning
- Wong
- 1997
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Citation Context ... question. In previous work [5], sparse representations have been used to speed Bayesian inference. The sum and product operations have also been previously expressed as relational database operators =-=[12]-=-, which coincides with our own interpretation. Our main contribution here is to show how the sparse representation can amplify the gain that results from constraint propagation. This can make higher l... |

4 |
A simple algorithm for bayesian network computations
- Zhang, Poole
- 1994
(Show Context)
Citation Context ...rk is NPhard. However, tractable subclasses have been identified. The most important of these is the case when the network graph can be embedded in a triangulated (chordal) graph of bounded treewidth =-=[8, 13, 3]-=-. It is also possible to e#ciently process networks with a special structure in their quantitative component, such as the common case of Noisy-OR gates [9], or contextspecific independence [1]. In thi... |

3 |
Constraint satisfaction. Survey ECS
- Dechter, Rossi
- 2000
(Show Context)
Citation Context ...The main motivation for our study is the similarity that exists between belief networks that exhibit many functional relationships and deterministic networks, such as constraint satisfaction problems =-=[7, 2]-=-. Since these belief networks have a substantial deterministic substructure beneath their probabilistic facade, it would seem logical that the sophisticated techniques developed by the constraint sati... |