Generalized linear models are the most commonly used tools to describe the stimulus selectivity of sensory neurons.

In many real-world statistical problems, we would like to fit a model with a large number of dependent variables to a training sample with very many cases.

This makes Gaussian process regression too slow for large datasets. In this paper, we present a fast approximation method, based on kd-trees, that significantly reduces both the prediction and the training times of Gaussian process regression.

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 under strong restrictions on time and memory requirements.

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 inO(d) rather than O(n), d n, n the number of training points), but also to perform training under strong restrictions on time and memory requirements.

We propose the framework of mutual information kernels for learning covariance kernels, as used in Support Vector machines and Gaussian process classifiers, from unlabeled task data using Bayesian techniques. We describe an implementation of this framework which uses variational Bayesian mixtures of factor analyzers in order to attack classification problems in high-dimensional spaces where labeled data is sparse, but unlabeled data is abundant.

We propose the framework of mutual information kernels for learning covariance kernels, as used in Support Vector machines and Gaussian process classifiers, from unlabeled task data using Bayesian techniques. We describe an implementation of this framework whichuses variational Bayesian mixtures of factor analyzers in order to attack classification problems in high-dimensional spaces where labeled data is sparse, but unlabeled data is abundant.

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We present a variational Bayesian method for model selection over families of kernels classifiers like Support Vector machines or Gaussian processes.The algorithm needs no user interaction and is able to adapt a large number of kernel parameters to given data without having to sacrifice training cases for validation. This opens the possibility touse sophisticated families of kernels in situations where the small "standard kernel" classes are clearly inappropriate. We relate the method to other work done on Gaussian processes and clarify the relation between Support Vector machines and certain Gaussian process models. 1 Introduction Bayesian techniques have been widely and successfully used in the neural networks and statistics community and are appealing because of their conceptual simplicity, generality and consistency with which they solve learning problems. In this paper we present a new method for applying the Bayesian methodology to Support Vector machines. We will briefly review Gaussian Process and Support Vector classification in this section and clarify their relationship by pointing out the common roots. Although we focus on classification here, it is straightforward to apply the methods to regression problems as well. In section 2 we introduce our algorithm and show relations to existing methods. Finally, we present experimental results in section 3 and close with a discussion in section 4. Let X be a measure space (e.g.