The support vector machine (SVM) is a state-of-the-art technique for regression and classification, combining excellent generalisation properties with a sparse kernel representation. However, it does suffer from a number of disadvantages, notably the absence of probabilistic outputs, the requirement to estimate a tradeoff parameter and the need to utilise'Mercer' kernel functions. In this paper we introduce the Relevance Vector Machine (RVM), a Bayesian treatment of a generalised linear model of identical functional form to the SVM. The RVM suffers from none of the above disadvantages, and examples demonstrate that for comparable generalisation performance, the RVM requires dramatically fewer kernel functions.

We propose a novel approach for building finite memory predictive models similar in spirit to variable memory length Markov models (VLMMs). The models are constructed by first transforming the n-block structure of the training sequence into a spatial structure of points in a unit hypercube, such that the longer is the common suffix shared by any two n-blocks, the closer lie their point representations. Such a transformation embodies a Markov assumption - n-blocks with long common suffixes are likely to produce similar continuations. Finding a set of prediction contexts is formulated as a resource allocation problem solved by vector quantizing the spatial n-block representation. We compare our model with both the classical and variable memory length Markov models on three data sets with different memory and stochastic components. Our models have a superior performance, yet, their construction is fully automatic, which is shown to be problematic in the case of VLMMs.

In this paper we will treat input selection for a radial basis function (RBF) like classifier within a Bayesian framework. We approximate the a-posteriori distribution over both model coefficients and input subsets by samples drawn with Gibbs updates and reversible jump moves. Using some public datasets, we compare the classification accuracy of the method with a conventional ARD scheme. These datasets are also used to infer the a-posteriori probabilities of different input subsets. 1 Introduction Methods that aim to determine relevance of inputs have always interested researchers in various communities. Classical feature subset selection techniques, as reviewed in [1], use search algorithms and evaluation criteria to determine one optimal subset.

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 to use 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.

Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified

We provide an analysis of the turbo decoding algorithm (TDA) in a setting involving Gaussian densities. In this context, we are able to show that the algorithm converges and that - somewhat surprisingly - though the density generated by the TDA may differ significantly from the desired posterior density, the means of these two densities coincide.

Fishers linear discriminant analysis (LDA) is a classical multivariate technique both for dimension reduction and classification. The data vectors are transformed into a low dimensional subspace such that the class centroids are spread out as much as possible. In this subspace LDA works as a simple prototype classifier with linear decision boundaries. However, in many applications the linear boundaries do not adequately separate the classes. We present a nonlinear generalization of discriminant analysis that uses the kernel trick of representing dot products by kernel functions.

The idea of a large minimum margin [17] explains the good generalization performance of AdaBoost in the low noise regime. However, AdaBoost performs worse on noisy tasks [10, 11], such as the iris and the breast cancer benchmark data sets [1]. On the latter tasks, a large margin on all training points cannot be achieved without adverse effects on the generalization error. This experimental observation was supported by the study of [13] where the generalization error of ensemble methods was bounded by the sum of the fraction of training points which have a margin smaller than some value p, say, plus a complexity term depending on the base hypotheses and p. While this bound can only capture part of what is going on in practice, it nevertheless already conveys the message that in some cases it pays to allow for some points which have a small margin, or are misclassified, if this leads to a larger overall margin on the remaining points. To cope with this problem, it was mandatory to construct regularized variants of AdaBoost, which traded off the number of margin errors and the size of the margin 562 G. Riitsch, B. Sch6lkopf, A. J. Smola, K.-R.

In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the difficult problem of finding the "right" number of mixture components. Inference in the model is done using an efficient parameter-free Markov Chain that relies entirely on Gibbs sampling.

We present a new learning architecture: the Decision Directed Acyclic Graph (DDAG), which is used to combine many two-class classifiers into a multiclass classifier. For an N -class problem, the DDAG contains N(N - 1)/2 classifiers, one for each pair of classes. We present a VC analysis of the case when the node classifiers are hyperplanes; the resulting bound on the test error depends on N and on the margin achieved at the nodes, but not on the dimension of the space. This motivates an algorithm, DAGSVM, which operates in a kernel-induced feature space and uses two-class maximal margin hyperplanes at each decision-node of the DDAG. The DAGSVM is substantially faster to train and evaluate than either the standard algorithm or Max Wins, while maintaining comparable accuracy to both of these algorithms. 1 Introduction The problem of multiclass classificatIon, especially for systems like SVMs, doesn't present an easy solution. It is generally simpler to construct classifier theory and algorithms for two mutually-exclusive classes than for N mutually-exclusive classes.