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Content available remote Perfect tree-like Markovian distributions
EN
We show that if a strictly positive joint probability distribution for a set of binary variables factors according to a tree, then vertex separation represents all and only the independence relations encoded in the distribution. The same result is show to hold also for multivariate nondegenerate normal distributions. Our proof uses a new property of conditional independence that holds for these two classes of probabilisty distributions.
EN
We address the problem of evaluating the quality of cluster assignment of individual items in a classification. The problem can also be viewed as outlier detection in classifications. We describe simple methods for this task based on the use of Naive Bayes classification. Applied to two existing classifications of 5313 strains of bacteria the method indicated that one classification is far more robust than the other. The observations that fit badly to their clusters are typically items whose classification is suspect also from other considerations. Removing these elements from the data set, performing clustering on the reduced data set, and adding the outliers back one-by-one yielded a clustering that has a higher likelihood than the previous accepted classifications. Investigation of this new clustering lead to suggested changes in the classification of 69 strains in the material.
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