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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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ISSN: 1646-3692 |
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Editors:
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Pedro Isaías and Marcin Paprzycki |
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Year:
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2007 |
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Edition:
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V II, 2 |
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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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Journal Paper |
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First Page:
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1 |
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Last Page:
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12 |
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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 noninformative
setting. The normalized maximum likelihood (NML), based on Rissanen's informationtheoretic
MDL methodology, offers an alternative, theoretically solid criterion that is objective and noninformative,
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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