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Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in terms of the training examples. We generalize the theorem to a larger class of regularizers and empirical risk terms, and give a self-contained proof utilizing the… (More)

In contrast to the standard machine learning tasks of classification and metric regression we investigate the problem of predicting variables of ordinal scale, a setting referred to as ordinal regression. The task of ordinal regression arises frequently in the social sciences and in information retrieval where human preferences play a major role. Also many… (More)

We investigate the problem of predicting variables of ordinal scale. This taks is referred to as ordinal regression and is complementary to the standard machine learning tasks of classification and metric regression. In contrast to statistical models we present a distribution independent formulation of the problem together with uniform bounds of the risk… (More)

We present a framework for sparse Gaussian process (GP) methods which uses forward selection with criteria based on information-theoretic principles, previously suggested for active learning. Our goal is not only to learn d–sparse predictors (which can be evaluated in O(d) rather than O(n), d n, n the number of training points), but also to perform training… (More)

Kernel-classifiers comprise a powerful class of non-linear decision functions for binary classification. The support vector machine is an example of a learning algorithm for kernel classifiers that singles out the consistent classifier with the largest margin, i.e. minimal real-valued output on the training sample, within the set of consistent hypotheses,… (More)

We present a probabilistic model for generating personalised recommendations of items to users of a web service. The Matchbox system makes use of content information in the form of user and item meta data in combination with collaborative filtering information from previous user behavior in order to predict the value of an item for a user. Users and items… (More)

We study generalization properties of the area under the ROC curve (AUC), a quantity that has been advocated as an evaluation criterion for the bipartite ranking problem. The AUC is a different term than the error rate used for evaluation in classification problems; consequently, existing generalization bounds for the classification error rate cannot be… (More)

We investigate the problem of learning a classification task on data represented in terms of their pairwise proximities. This representation does not refer to an explicit feature representation of the data items and is thus more general than the standard approach of using Euclidean feature vectors, from which pairwise proximities can always be calculated.… (More)

The perceptron algorithm with margins is a simple, fast and effective learning algorithm for linear classifiers; it produces decision hy-perplanes within some constant ratio of the maximal margin. In this paper we study this algorithm and a new variant: the perceptron algorithm with uneven margins, tailored for document categorisation problems (i.e.… (More)