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Title:
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CALCULATING THE NORMALIZED MAXIMUM LIKELIHOOD DISTRIBUTION FOR BAYESIAN FORESTS |
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Author(s):
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Hannes Wettig , Petri Kontkanen , Petri Myllymäki |
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ISBN:
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978-972-8924-39-3 |
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Editors:
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António Palma dos Reis, Katherine Blashki and Yingcai Xiao (series editors:Piet Kommers, Pedro Isaías and Nian-Shing Chen) |
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Year:
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2007 |
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Edition:
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Single |
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Keywords:
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Machine Learning, Bayesian Networks, Minimum Description Length, Normalized Maximum Likelihood. |
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Type:
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Full Paper |
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First Page:
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51 |
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Last Page:
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58 |
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Language:
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English |
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Cover:
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Full Contents:
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click to dowload 
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Paper Abstract:
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When learning Bayesian network structures from sample data, an important issue is how to evaluate the goodness of
alternative network structures. Perhaps the most commonly used model (class) selection criterion is the marginal
likelihood, which is obtained by integrating over a prior distribution for the model parameters. However, the problem of
determining a reasonable prior for the parameters is a highly controversial issue, and no completely satisfying Bayesian
solution has yet been presented in the non-informative setting. The normalized maximum likelihood (NML), based on
Rissanen's information-theoretic MDL methodology, offers an alternative, theoretically solid criterion that is objective
and non-informative, while no parameter prior is required. It has been previously shown that for discrete data, this
criterion can be computed in linear time for Bayesian networks with no arcs, and in quadratic time for the so called Naive
Bayes network structure. Here we extend the previous results by showing how to compute the NML criterion in
polynomial time for tree-structured Bayesian networks. The order of the polynomial depends on the number of values of
the variables, but neither on the number of variables itself, nor on the sample size1. |
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