Bayesian Error-Bars for Belief Net Inference
Full Text:
ErrBar.ps
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 P(H | E)?'' query. This paper investigates the distribution of this response, shows that it is asymptotically normal, and derives closed-form 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 --- ie, 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.
Citation
T. Van Allen,
R. Greiner,
P. Hooper.
"Bayesian Error-Bars for Belief Net Inference".
Conference on Uncertainty in Artificial Intelligence (UAI), Seattle, Washington, USA, August 2001.
Keywords: |
error bars, belief nets, inference, probabilistic graphical models, theoretical, empirical, machine learning |
Category: |
In Conference |
BibTeX
@incollection{VanAllen+al:UAI01,
author = {Tim Van Allen and Russ Greiner and Peter Hooper},
title = {Bayesian Error-Bars for Belief Net Inference},
booktitle = {Conference on Uncertainty in Artificial Intelligence (UAI)},
year = 2001,
}
Last Updated: April 24, 2007
Submitted by Christian Smith