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Update Rules for Parameter Estimation in Bayesian Networks
Eric Bauer, Daphne Koller, Yoram Singer
Abstract:
This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for parameter estimation that encompasses both on-line learning, where the model is continuously adapted to new data cases as they arrive, and the more traditional batch learning, where a pre-accumulated set of samples is used in a one-time model selection process. In the batch case, our framework encompasses both the gradient projection algorithm and the EM algorithm for Bayesian networks. The framework also leads to new on-line and batch parameter update schemes, including a parameterized version of EM. We provide both empirical and theoretical results indicating that parameterized EM allows faster convergence to the maximum likelihood parameters than does standard EM.
Keywords: Learning Bayesian networks, online learning, EM, parameter estimation,
hidden variab
Pages: 3-13
PS Link: http://robotics.stanford.edu/~koller/papers/uai97em.ps
PDF Link: /papers/97/p3-bauer.pdf
BibTex:
@INPROCEEDINGS{Bauer97,
AUTHOR = "Eric Bauer
and Daphne Koller and Yoram Singer",
TITLE = "Update Rules for Parameter Estimation in Bayesian Networks",
BOOKTITLE = "Proceedings of the Thirteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-97)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1997",
PAGES = "3--13"
}
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