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Learning belief network structure involves a trade-o between network complexity and goodness of t. More complex structures allow for a better t to the data, but suer from a decreased ability to generalize to unseen data. This bias-variance trade-o may be operationalized by a scoring function on structures, called a model selection criterion. We describe various criteria for model selection: a prequential, or Bayesian, criterion, 2-fold cross validation, a bootstrap criterion, Akaike's...