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We consider the classification problem on the cube $[0,1]^d$ when the Bayes rule is known to belong to some new functions classes. These classes are made of prediction rules satisfying some conditions...
Let $(X,Y)$ be a random variable consisting of an observed feature vector $X in XX$ and an unobserved class label $Y in {1,2,ldots,L}$ with unknown joint distribution. In addition, let $DD$ be a train...
Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984) classifiers are obtained under a margin condition in the binary supervised classification framework. These risk bound...
The spatial structure of a class of superprocesses which arise as limits in distribution of a class of interacting particle systems with location dependent branching is investigated. The criterion of ...
Given a training sample of size m from a d-dimensional population, we wish to allocate a new observation Z ∈ IRd to this population or to the noise. We suppose that the difference between the distri...
Often in discriminant analysis several models are estimated but based on some validation criterion, a single model is selected. In the purpose of taking profit from several potential models, classif...
Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of ...
The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN ...
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms...
Let F be a set of M classification procedures with values in [−1, 1]. Given a loss function, we want to construct a procedure which mimics at the best possible rate the best procedure in F. Th...
For many classification and regression problems, a large number of features are available for possible use — this is typical of DNA microarray data on gene expression, for example. Often,for computat...

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