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Population Size Extrapolation in Relational Probabilistic Modelling

David Poole; David Buchman; Seyed Mehran Kazemi; Kristian Kersting; Sriraam Natarajan
In: Umberto Straccia; Andrea Calì (Hrsg.). Scalable Uncertainty Management - 8th International Conference, SUM 2014, Proceedings. Scalable Uncertainty Management (SUM-2014), September 15-17, Oxford, United Kingdom, Pages 292-305, Lecture Notes in Computer Science (LNAI), Vol. 8720, Springer, 2014.


When building probabilistic relational models it is often difficult to determine what formulae or factors to include in a model. Different models make quite different predictions about how probabilities are affected by population size. We show some general patterns that hold in some classes of models for all numerical parametrizations. Given a data set, it is often easy to plot the dependence of probabilities on population size, which, together with prior knowledge, can be used to rule out classes of models, where just assessing or fitting numerical parameters will be misleading. In this paper we analyze the dependence on population for relational undirected models (in particular Markov logic networks) and relational directed models (for relational logistic regression). Finally we show how probabilities for real data sets depend on the population size.

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