The Minimax Probability Machine Classification (MPMC) framework [Lanckriet et al., 2002] builds classifiers by minimizing the maximum probability of misclassification, and gives direct estimates of the probabilistic accuracy bound Ω. The only assumptions that MPMC makes is that good estimates of means and covariance matrices of the classes exist. However, as with Support Vector Machines, MPMC is computationally expensive and requires extensive cross validation experiments to choose kernels and kernel parameters that give good performance. In this paper we address the computational cost of MPMC by proposing an algorithm that constructs nonlinear sparse MPMC (SMPMC) models by incrementally adding basis functions (i.e.

The standard 2-norm SVM is known for its good performance in twoclass classi£cation. In this paper, we consider the 1-norm SVM. We argue that the 1-norm SVM may have some advantage over the standard 2-norm SVM, especially when there are redundant noise features. We also propose an ef£cient algorithm that computes the whole solution path of the 1-norm SVM, hence facilitates adaptive selection of the tuning parameter for the 1-norm SVM.

Computer animated agents and robots bring a social dimension to human computer interaction and force us to think in new ways about how computers could be used in daily life. Face to face communication is a real-time process operating at a time scale of less than a second. In this paper we present progress on a perceptual primitive to automatically detect frontal faces in the video stream and code them with respect to 7 dimensions in real time: neutral, anger, disgust, fear, joy, sadness, surprise. The face finder employs a cascade of feature detectors trained with boosting techniques [13, 2]. The expression recognizer employs a novel combination of Adaboost and SVM's. The generalization performance to new subjects for a 7-way forced choice was 93.3% and 97% correct on two publicly available datasets. The outputs of the classifier change smoothly as a function of time, providing a potentially valuable representation to code facial expression dynamics in a fully automatic and unobtrusive manner. The system was deployed and evaluated for measuring spontaneous facial expressions in the field in an application for automatic assessment of human-robot interaction.

We compute approximate analytical bootstrap averages for support vector classification using a combination of the replica method of statistical physics and the TAP approach for approximate inference. We test our method on a few datasets and compare it with exact averages obtained by extensive Monte-Carlo sampling.

Knowledge about local invariances with respect to given pattern transformations can greatly improve the accuracy of classification. Previous approaches are either based on regularisation or on the generation of virtual (transformed) examples. We develop a new framework for learning linear classifiers under known transformations based on semidefinite programming. We present a new learning algorithm-- the Semidefinite Programming Machine (SDPM)--which is able to find a maximum margin hyperplane when the training examples are polynomial trajectories instead of single points. The solution is found to be sparse in dual variables and allows to identify those points on the trajectory with minimal real-valued output as virtual support vectors. Extensions to segments of trajectories, to more than one transformation parameter, and to learning with kernels are discussed. In experiments we use a Taylor expansion to locally approximate rotational invariance in pixel images from USPS and find improvements over known methods.

The standard 2-norm SVM is known for its good performance in twoclass classi£cation. In this paper, we consider the 1-norm SVM. We argue that the 1-norm SVM may have some advantage over the standard 2-norm SVM, especially when there are redundant noise features. We also propose an ef£cient algorithm that computes the whole solution path of the 1-norm SVM, hence facilitates adaptive selection of the tuning parameter for the 1-norm SVM.

We consider the question of predicting nonlinear time series. Kernel Dynamical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows strong connection with the classic Kalman Filter model, with the kernel feature space as hidden state space. Kernel Dynamical Modeling is tested against two benchmark time series and achieves high quality predictions.

Many classification algorithms, including the support vector machine, boosting and logistic regression, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0-1 loss function. We characterize the statistical consequences of using such a surrogate by providing a general quantitative relationship between the risk as assessed using the 0-1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial bounds under the weakest possible condition on the loss function--that it satisfy a pointwise form of Fisher consistency for classification. The relationship is based on a variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise. Finally, we present applications of our results to the estimation of convergence rates in the general setting of function classes that are scaled hulls of a finite-dimensional base class.

We compute approximate analytical bootstrap averages for support vector classification using a combination of the replica method of statistical physics and the TAP approach for approximate inference. We test our method on a few datasets and compare it with exact averages obtained by extensive Monte-Carlo sampling.

This article addresses the issues of colour classification and collision detection as they occur in the legged league robot soccer environment of RoboCup. We show how the method of one-class classification with support vector machines (SVMs) can be applied to solve these tasks satisfactorily using the limited hardware capacity of the prescribed Sony AIBO quadruped robots. The experimental evaluation shows an improvement over our previous methods of ellipse fitting for colour classification and the statistical approach used for collision detection.