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Probabilistic reasoning with undefined properties in ontologically-based belief networks

University of British Columbia

This thesis concerns building probabilistic models with an underlying ontology that defines the classes and properties used in the model. In particular, it considers the problem of reasoning with properties that may not always be defined. Furthermore, we may even be uncertain about whether a property is defined for a given individual. One approach is to explicitly add a value "undefined" to the range of random variables, forming (what we call) extended belief networks. Adding an extra value to a random variable's range, however, has a large computational overhead. In this work, we propose an alternative, ontologically-based belief networks, where properties are only used when they are defined. We show how probabilistic reasoning can be carried out without explicitly using the value "undefined" during inference. This, in general, requires that we perform two probabilistic queries to determine (1) the probability that the hypothesis is defined and (2) the probabilities of the hypothesis given it is defined. We prove this is equivalent to reasoning with the corresponding extended belief network and empirically demonstrate on synthetic models that inference becomes more efficient.

Text

2013-10-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/45338

Computer Science

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/