Not Logged In

Improved Mean and Variance Approximations for Belief Net Responses via Network Doubling

Full Text: doubling-uai2009.pdf PDF
Other Attachments: Poster.pdf [Poster] PDF

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.

Citation

P. Hooper, Y. Abbasi-Yadkori, R. Greiner, B. Hoehn. "Improved Mean and Variance Approximations for Belief Net Responses via Network Doubling". Conference on Uncertainty in Artificial Intelligence (UAI), June 2009.

Keywords: machine learning, belief network, inference, variance
Category: In Conference

BibTeX

@incollection{Hooper+al:UAI09,
  author = {Peter Hooper and Yasin Abbasi-Yadkori and Russ Greiner and Bret
    Hoehn},
  title = {Improved Mean and Variance Approximations for Belief Net Responses
    via Network Doubling},
  booktitle = {Conference on Uncertainty in Artificial Intelligence (UAI)},
  year = 2009,
}

Last Updated: June 16, 2009
Submitted by Russ Greiner

University of Alberta Logo AICML Logo