In this paper, we study a special kind of learning problem in which each training instance is given a set of (or distribution over) candidate class labels and only one of the candidate labels is the correct one. Such a problem can occur, e.g., in an information retrieval setting where a set of words is associated with an image, or if classes labels are organized hierarchically. We propose a novel discriminative approach for handling the ambiguity of class labels in the training examples. The experiments with the proposed approach over five different UCI datasets show that our approach is able to find the correct label among the set of candidate labels and actually achieve performance close to the case when each training instance is given a single correct label. In contrast, naIve methods degrade rapidly as more ambiguity is introduced into the labels. 1 Introduction Supervised and unsupervised learning problems have been extensively studied in the machine learning literature. In supervised classification each training instance is associated with a single class label, while in unsupervised classification (i.e.

We consider the problem of choosing a kernel suitable for estimation using a Gaussian Process estimator or a Support Vector Machine. A novel solution is presented which involves defining a Reproducing Kernel HilbertSpace on the space of kernels itself. By utilizing an analog of the classical representer theorem, the problem of choosing a kernel from a parameterized family of kernels (e.g. of varying width) is reduced to a statistical estimation problem akin to the problem of minimizing a regularized risk functional. Various classical settings for model or kernel selection are special cases of our framework.

The tangential neurons in the fly brain are sensitive to the typical optic flow patterns generated during self-motion. In this study, we examine whether a simplified linear model of these neurons can be used to estimate self-motionfrom the optic flow. We present a theory for the construction ofan estimator consisting of a linear combination of optic flow vectors that incorporates prior knowledge both about the distance distribution ofthe environment, and about the noise and self-motion statistics of the sensor. The estimator is tested on a gantry carrying an omnidirectional visionsensor. The experiments show that the proposed approach leads to accurate and robust estimates of rotation rates, whereas translation estimatesturn out to be less reliable.

' 1idazolam causes dense,but temporary anterograde amnesia, similar to that produced by-hippocampal

A key challenge for neural modeling is to explain how a continuous stream of multi-modal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real-time. We propose a new computational model that is based on principles of high dimensional dynamical systems in combination with statistical learning theory. It can be implemented on generic evolved or found recurrent circuitry.

We present an automatic alignment procedure which maps the disparate internal representations learned by several local dimensionality reduction experts into a single, coherent global coordinate system for the original data space. Our algorithm can be applied to any set of experts, each of which produces a low-dimensional local representation of a highdimensional input.Unlike recent efforts to coordinate such models by modifying their objective functions [1, 2], our algorithm is invoked after training and applies an efficient eigensolver to post-process the trained models. The post-processing has no local optima and the size of the system itmust solve scales with the number of local models rather than the number of original data points, making it more efficient than model-free algorithms such as Isomap [3] or LLE [4].

We describe a method for computing provably exact maximum a posteriori (MAP)estimates for a subclass of problems on graphs with cycles. The basic idea is to represent the original problem on the graph with cycles asa convex combination of tree-structured problems. A convexity argument then guarantees that the optimal value of the original problem (i.e., the log probability of the MAP assignment) is upper bounded by the combined optimal values of the tree problems. We prove that this upper bound is met with equality if and only if the tree problems share an optimal configurationin common. An important implication is that any such shared configuration must also be the MAP configuration for the original problem. Next we develop a tree-reweighted max-product algorithm for attempting to find convex combinations of tree-structured problems that share a common optimum. We give necessary and sufficient conditions for a fixed point to yield the exact MAP estimate. An attractive feature of our analysis is that it generalizes naturally to convex combinations of hypertree-structured distributions.

This paper introduces an algorithm for the automatic relevance determination of input 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 and demonstrates its effectiveness on a demanding facial expression recognition problem.

Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model. This is of particular importance in identification of nonlinear dynamic systems from experimental data.

We describe a self-configuring neuromorphic chip that uses a model of activity-dependent axon remodeling to automatically wire topographic maps based solely on input correlations. Axons are guided by growth cones, which are modeled in analog VLSI for the first time. Growth cones migrate up neurotropin gradients, which are represented by charge diffusing in transistor channels. Virtual axons move by rerouting address-events. We refined an initially gross topographic projection by simulating retinal wave input.