Bayesian error-bars for belief net inference

Authors:
Tim Van Allen;Russell Greiner;Peter Hooper
Affiliations:
digiMine, Inc., Bellevue, WA;Dep't of Computing Science, University of Alberta, Edmonton, AB, Canada;Dep't of Mathematical Sciences, University of Alberta, Edmonton, AB, Canada
Venue:
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Year:
2001

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Abstract

A Bayesian Belief Network (BN) is a model of a joint distribution over a finite set of variables, with a DAG structure to represent the immediate dependencies between the variables, and a set of parameters (aka CPTables) to represent the local conditional probabilities of a node, given each assignment to its parents. In many situations, the parameters are themselves treated as random variables -- reflecting the uncertainty remaining after drawing on knowledge of domain experts and/or observing data generated by the network. A distribution over the CPtable parameters induces a distribution for the response the BN will return to any "What is Pr{H/E}?" query. This paper investigates the distribution of this response, shows that it is asymptotically normal, and derives expressions for its mean and asymptotic variance. We show that this computation has the same complexity as simply computing the (mean value of the) response -- i.e., O(n exp(w)), where n is the number of variables and w is the effective tree width. We also provide empirical evidence showing that the error-bars computed from our estimates are fairly accurate in practice, over a wide range of belief net structures and queries.