Bayesian Error-Bars for Belief Net Inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Using query-specific variance estimates to combine Bayesian classifiers
ICML '06 Proceedings of the 23rd international conference on Machine learning
Discriminative model selection for belief net structures
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
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A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing conditional distributions. The parameters are viewed as random variables to quantify uncertainty about their values. Belief nets are used to compute responses to queries; i.e., conditional probabilities of interest. A query is a function of the parameters, hence a random variable. Van Allen et al. (2001, 2008) showed how to quantify uncertainty about a query via a delta method approximation of its variance. We develop more accurate approximations for both query mean and variance. The key idea is to extend the query mean approximation to a "doubled network" involving two independent replicates. Our method assumes complete data and can be applied to discrete, continuous, and hybrid networks (provided discrete variables have only discrete parents). We analyze several improvements, and provide empirical studies to demonstrate their effectiveness.