We introduce the Generalized2 Linear2 Model, a statistical estimator whichcombines features of nonlinear regression and factor analysis.

In this paper we present a new algorithm suitable for matching discrete objects such as strings and trees in linear time, thus obviating dynarrtic programming with quadratic time complexity. Furthermore, prediction cost in many cases can be reduced to linear cost in the length of the sequence tobe classified, regardless of the number of support vectors. This improvement on the currently available algorithms makes string kernels a viable alternative for the practitioner.

This paper presents two new formulations of multiple-instance learning as a maximum margin problem. The proposed extensions of the Support Vector Machine (SVM) learning approach lead to mixed integer quadratic programs that can be solved heuristically. Our generalization of SVMs makes a state-of-the-art classification technique, including nonlinear classification via kernels, available to an area that up to now has been largely dominated by special purpose methods. We present experimental results on a pharmaceutical dataset and on applications in automated image indexing and document categorization. 1 Introduction Multiple-instance learning (MIL) [4] is a generalization of supervised classification in which training class labels are associated with sets of patterns, or bags, instead of individual patterns. While every pattern may possess an associated true label, it is assumed that pattern labels are only indirectly accessible through labels attached to bags.

This paper introduces an algorithm for the automatic relevance determination ofinput variables in kernelized Support Vector Machines. Relevance is measured by scale factors defining the input space metric, and feature selection is performed by assigning zero weights to irrelevant variables. The metric is automatically tuned by the minimization of the standard SVM empirical risk, where scale factors are added to the usual set of parameters defining the classifier. Feature selection is achieved by constraints encouraging the sparsity of scale factors. The resulting algorithm compares favorably to state-of-the-art feature selection procedures anddemonstrates its effectiveness on a demanding facial expression recognition problem.

We consider the problem of multi-step ahead prediction in time series analysis using the nonparametric Gaussian process model.

Prior knowledge in the form of multiple polyhedral sets, each belonging toone of two categories, is introduced into a reformulation of a linear support vector machine classifier. The resulting formulation leadsto a linear program that can be solved efficiently. Real world examples, from DNA sequencing and breast cancer prognosis, demonstrate the effectiveness of the proposed method. Numerical results show improvement in test set accuracy after the incorporation ofprior knowledge into ordinary, data-based linear support vector machine classifiers. One experiment also shows that a linear classifier,based solely on prior knowledge, far outperforms the direct application of prior knowledge rules to classify data.

In this paper we consider formulations of multi-class problems based on a generalized notion of a margin and using output coding. This includes, but is not restricted to, standard multi-class SVM formulations. Differently frommany previous approaches we learn the code as well as the embedding function. We illustrate how this can lead to a formulation that allows for solving a wider range of problems with for instance many classes or even "missing classes". To keep our optimization problems tractable we propose an algorithm capable of solving them using twoclass classifiers,similar in spirit to Boosting.

Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may be for the user to manually tweak the metric until sufficiently good clusters are found. For these and other applications requiring good metrics, it is desirable that we provide a more systematic way for users to indicate what they consider "similar."For

A distance-based conditional model on the ranking poset is presented for use in classification and ranking. The model is an extension of the Mallows model, and generalizes the classifier combination methods used by several ensemble learning algorithms, including error correcting output codes, discrete AdaBoost, logistic regression and cranking. The algebraic structure of the ranking poset leads to a simple Bayesian interpretation ofthe conditional model and its special cases. In addition to a unifying view, the framework suggests a probabilistic interpretation for error correcting output codes and an extension beyond the binary coding scheme.

A lot of learning machines with hidden variables used in information sciencehave singularities in their parameter spaces. At singularities, the Fisher information matrix becomes degenerate, resulting that the learning theory of regular statistical models does not hold. Recently, it was proven that, if the true parameter is contained in singularities, then the coefficient of the Bayes generalization erroris equal to the pole of the zeta function of the Kullback information.