Modern classification applications necessitate supplementing the few available labeled examples with unlabeled examples to improve classification performance.We present a new tractable algorithm for exploiting unlabeled examples in discriminative classification. This is achieved essentially by expanding the input vectors into longer feature vectors via both labeled and unlabeled examples. The resulting classification method can be interpreted as a discriminative kernel density estimate and is readily trainedvia the EM algorithm, which in this case is both discriminative and achieves the optimal solution. We provide, in addition, a purely discriminative formulationof the estimation problem by appealing to the maximum entropy framework. We demonstrate that the proposed approach requiresvery few labeled examples for high classification accuracy.

We introduce a method of feature selection for Support Vector Machines. The method is based upon finding those features which minimize bounds on the leave-one-out error. This search can be efficiently performed via gradient descent. The resulting algorithms are shown to be superior to some standard feature selection algorithms on both toy data and real-life problems of face recognition, pedestrian detection and analyzing DNA micro array data. 1 Introduction In many supervised learning problems feature selection is important for a variety of reasons: generalizationperformance, running time requirements, and constraints and interpretational issuesimposed by the problem itself.

We present a bound on the generalisation error of linear classifiers in terms of a refined margin quantity on the training set. The result is obtained in a PAC-Bayesian framework and is based on geometrical arguments in the space of linear classifiers. The new bound constitutes an exponential improvement of the so far tightest margin bound by Shawe-Taylor et al. [8] and scales logarithmically in the inverse margin. Even in the case of less training examples than input dimensions sufficiently large margins lead to nontrivial bound values and - for maximum margins - to a vanishing complexity term.Furthermore, the classical margin is too coarse a measure for the essential quantity that controls the generalisation error: the volume ratio between the whole hypothesis space and the subset of consistent hypotheses. The practical relevance of the result lies in the fact that the well-known support vector machine is optimal w.r.t. the new bound only if the feature vectors are all of the same length.

Learning of a smooth but nonparametric probability density can be regularized usingmethods of Quantum Field Theory. We implement a field theoretic prior numerically, test its efficacy, and show that the free parameter ofthe theory (,smoothness scale') can be determined self consistently bythe data; this forms an infinite dimensional generalization of the MDL principle. Finally, we study the implications of one's choice of the prior and the parameterization and conclude that the smoothness scale determination makes density estimation very weakly sensitive to the choice of the prior, and that even wrong choices can be advantageous for small data sets. One of the central problems in learning is to balance'goodness of fit' criteria against the complexity of models. An important development in the Bayesian approach was thus the realization that there does not need to be any extra penalty for model complexity: if we compute the total probability that data are generated by a model, there is a factor from the volume in parameter space-the'Occam factor' -that discriminates against models with more parameters [1, 2].

Classificationis achieved by a linear or nonlinear separating surface in the input space of the dataset. In this work we propose a very fast simple algorithm, based on an active set strategy for solving quadratic programs with bounds [18]. The algorithm is capable of accurately solving problems with millions of points and requires nothing more complicated than a commonly available linear equation solver [17, 1, 6] for a typically small (100) dimensional input space of the problem. Key to our approach are the following two changes to the standard linear SVM: 1. Maximize the margin (distance) between the parallel separating planes with respect to both orientation (w) as well as location relative to the origin b).

We introduce a new, nonparametric and principled, distance based clustering method. This method combines a pairwise based approach witha vector-quantization method which provide a meaningful interpretation to the resulting clusters. The idea is based on turning the distance matrix into a Markov process and then examine the decay of mutual-information during the relaxation of this process. The clusters emerge as quasi-stable structures during thisrelaxation, and then are extracted using the information bottleneck method.

Nearest neighbor classification assumes locally constant class conditional probabilities.This assumption becomes invalid in high dimensions with finite samples due to the curse of dimensionality. Severe bias can be introduced under these conditions when using the nearest neighbor rule. We propose a locally adaptive nearest neighbor classification method to try to minimize bias. We use a Chi-squared distance analysis to compute a flexible metric for producing neighborhoodsthat are elongated along less relevant feature dimensions and constricted along most influential ones. As a result, the class conditional probabilities tend to be smoother in the modified neighborhoods,whereby better classification performance can be achieved. The efficacy of our method is validated and compared against other techniques using a variety of real world data. 1 Introduction

We develop an approach to object recognition based on matching shapesand using a resulting measure of similarity in a nearest neighbor classifier. The key algorithmic problem here is that of finding pointwise correspondences between an image shape and a stored prototype shape. We introduce a new shape descriptor, the shape context, which makes this possible, using a simple and robust algorithm. We demonstrate that shape contexts greatly simplify recovery of correspondences between points of two given shapes. Once shapes are aligned, shape contexts are used to define a robust score for measuring shape similarity.

To control the walking gaits of a four-legged robot we present a novel neuromorphic VLSI chip that coordinates the relative phasing of the robot's legs similar to how spinal Central Pattern Generators are believed to control vertebrate locomotion [3]. The chip controls the leg movements bydriving motors with time varying voltages which are the outputs of a small network of coupled oscillators. The characteristics of the chip's output voltages depend on a set of input parameters. The relationship betweeninput parameters and output voltages can be computed analytically for an idealized system.

Suppose there exists an unknown real-valued property of the feature space, p(¢), that maps from the feature space, ¢ ERn, to R. The property function and a positive set A c