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- Bernhard Schölkopf, Ralf Herbrich, Alexander J. Smola
- COLT/EuroCOLT
- 2001

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)

- Neil D. Lawrence, Matthias W. Seeger, Ralf Herbrich
- NIPS
- 2002

We present a framework for sparse Gaussian process (GP) methods which uses forward selection with criteria based on informationtheoretic 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 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)

- Ralf Herbrich, Tom Minka, Thore Graepel
- NIPS
- 2006

- Shivani Agarwal, Thore Graepel, Ralf Herbrich, Sariel Har-Peled, Dan Roth
- Journal of Machine Learning Research
- 2005

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 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)

- Ralf Herbrich, Thore Graepel, Colin Campbell
- Journal of Machine Learning Research
- 2001

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)

The perceptron algorithm with margins is a simple, fast and effective learning algorithm for linear classifiers; it produces decision hyperplanes 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. problems… (More)

- David H. Stern, Ralf Herbrich, Thore Graepel
- WWW
- 2009

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)