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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)

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)

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)

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 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)

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)

We investigate the problem of learning to predict moves in the board game of Go from game records of expert players. In particular, we obtain a probability distribution over legal moves for professional play in a given position. This distribution has numerous applications in computer Go, including serving as an efficient stand-alone Go player. It would also… (More)

We describe a new Bayesian click-through rate (CTR) prediction algorithm used for Sponsored Search in Microsoft's Bing search engine. The algorithm is based on a probit regression model that maps discrete or real-valued input features to probabilities. It maintains Gaussian beliefs over weights of the model and performs Gaussian online updates derived from… (More)