Statistics – Methodology
Scientific paper
2011-08-24
Statistics
Methodology
13 pages, 6 figures
Scientific paper
In this paper we introduce a statistical model based on a permanental process for supervised classification problems. Unlike many research work in the literature, we assume only exchangeability instead of independence on observations. Regardless of the number of classes or the dimension of the feature variables, the model may require only 2-3 parameters for fitting the covariance structure within clusters. It works well even if each class occupies non-convex, disjoint regions, or regions overlapped with other classes in the feature space. To calculate the weighted permanental ratio involved, we propose analytic approximations based on its cyclic expansion, which require only polynomial time up to order three. It works well for classification purpose. An application to DNA microarray analysis indicates that the permanental model with cyclic approximations is more capable of handling high-dimensional data. It can employ more feature variables in an efficient way and reduce the prediction error significantly. This is critical when the true classification relies on non-reducible high-dimensional features.
McCullagh Peter
Miescke Klaus
Yang Jie
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