## On The Complexity of Inference About Probabilistic Relational Models (1999)

Venue: | Artificial Intelligence |

Citations: | 15 - 2 self |

### BibTeX

@ARTICLE{Jaeger99onthe,

author = {Manfred Jaeger},

title = {On The Complexity of Inference About Probabilistic Relational Models},

journal = {Artificial Intelligence},

year = {1999},

volume = {117},

pages = {297--308}

}

### OpenURL

### Abstract

We investigate the complexity of probabilistic inference from knowledge bases that encode probability distributions on nite domain relational structures. Our interest here lies in the complexity in terms of the domain under consideration in a specic application instance. We obtain the result that assuming NETIME6=ETIME this problem is not polynomial for reasonably expressive representation systems. The main consequence of this result is that it is unlikely to nd inference techniques with a better worst-case behavior than the commonly employed strategy of constructing standard Bayesian networks over ground atoms (knowledge based model construction). Key words: Knowledge based model construction, Bayesian networks, rst-order logic 1

### Citations

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Citation Context ...xponential blowup in n is inherent in the problem, and cannot be avoided by other inference techniques. Note, in particular, that the well-known complexity results for inference in Bayesian networks (=-=Cooper 1990-=-) are not applicable here, because we cannot represent a suitable class of Bayesian networks that shows that inference is NP-hard in the network size as the set of auxiliary networks constructed for a... |

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Citation Context ...e will be unable to derive from (1) any nontrivial bounds for . In purely propositional settings, Bayesian networks have proven to be more useful in practice than propositional probabilistic logics (N=-=ilsson 1-=-986, Frisch & Haddaway 1994) because they dene a unique probability distribution on the set of propositional models (i.e. truth assignments), and therefore (at the cost of a greater specication eort) ... |

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Citation Context ...awy 1997, Jaeger 1997, Koller & Pfeer 1998). These systems have evolved out of earlier frameworks that were developed as specication languages for structurally uniform classes of Bayesian networks (Po=-=ole 199-=-3, Breese 1992, Saotti & Umkehrer 1994). Given a particular probabilistic query, a specication in such a language would serve as the blueprint for the automatic generation of a Bayesian network in whi... |

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Citation Context ...ve evidence q(a; b) the rule allows us to compute a posterior probability of 0.3 for p(a; b) 1 (if (1) expresses statistical knowledge, this computation would be an instance of direct inference, cf. (=-=Bacchus 199-=-0)). This coincides with the interpretation of similar rules in certain probabilistic logics (Ng & Subrahmanian 1992, Lakshmanan & Sadri 1994). The dierence between knowledge based model construction ... |

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Citation Context ...g probabilities P n (r(m)). To see why, consider an algorithm that produces random samples M i 2 Mod n (S) according to the distributionsP n . As in logic sampling for standard Bayesian networks (He=-=nrion 198-=-8) we could use the fraction of structures M i with M i j= r(m) in a random samplesM 1 ; : : : ; M n as an estimate for P n (r(m)). This is usually not the best use we can make of the sample M 1 ; : ... |

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Citation Context ... for the specication of probability distributions on relational structures, or, in the terminology of Friedman et al. (1999), the construction of probabilistic relational models (Ngo & Haddawy 1997, J=-=aeger 19-=-97, Koller & Pfeer 1998). These systems have evolved out of earlier frameworks that were developed as specication languages for structurally uniform classes of Bayesian networks (Poole 1993, Breese 19... |

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Citation Context ...eger 1997, Koller & Pfeer 1998). These systems have evolved out of earlier frameworks that were developed as specication languages for structurally uniform classes of Bayesian networks (Poole 1993, Br=-=eese 199-=-2, Saotti & Umkehrer 1994). Given a particular probabilistic query, a specication in such a language would serve as the blueprint for the automatic generation of a Bayesian network in which the probab... |

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Citation Context ...e proposed representation systems with additional syntactic constructs that in the knowledge base declare how several applicable clauses are to be combined. Relational Bayesian networks (Jaeger 1997, =-=Jaeger 1998-=-) can be understood as a representation formalism that goes one step further by compiling sets of clauses (1), and the necessary additional conventions for their combination, into a single functional ... |

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