Recurrent networks that perform a winner-take-all computation have been studied extensively. Although some of these studies include spiking networks, they consider only analog input rates. We present results of this winner-take-all computation on a network of integrate-and-fire neurons which receives spike trains as inputs. We show how we can configure the connectivity in the network so that the winner is selected after a predetermined number of input spikes. We discuss spiking inputs with both regular frequencies and Poisson-distributed rates. The robustness of the computation was tested by implementing the winner-take-all network on an analog VLSI array of 64 integrate-and-fire neurons which have an innate variance in their operating parameters.

We prove the strongest known bound for the risk of hypotheses selected from the ensemble generated by running a learning algorithm incrementally on the training data. Our result is based on proof techniques that are remarkably different from the standard risk analysis based on uniform convergence arguments.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learning result and works for hundred thousands of examples or hundreds of kernels to be combined.

We analyze classification error on unseen cases, i.e. cases that are different from those in the training set. Unlike standard generalization error, this off-training-set error may differ significantly from the empirical error with high probability even with large sample sizes. We derive a datadependent bound on the difference between off-training-set and standard generalization error. Our result is based on a new bound on the missing mass, which for small samples is stronger than existing bounds based on Good-Turing estimators. As we demonstrate on UCI data-sets, our bound gives nontrivial generalization guarantees in many practical cases. In light of these results, we show that certain claims made in the No Free Lunch literature are overly pessimistic.

Sparse PCA seeks approximate sparse "eigenvectors" whose projections capture the maximal variance of data. As a cardinality-constrained and non-convex optimization problem, it is NPhard and is encountered in a wide range of applied fields, from bio-informatics to finance. Recent progress has focused mainly on continuous approximation and convex relaxation of the hard cardinality constraint. In contrast, we consider an alternative discrete spectral formulation based on variational eigenvalue bounds and provide an effective greedy strategy as well as provably optimal solutions using branch-and-bound search. Moreover, the exact methodology used reveals a simple renormalization step that improves approximate solutions obtained by any continuous method. The resulting performance gain of discrete algorithms is demonstrated on real-world benchmark data and in extensive Monte Carlo evaluation trials.

Brain-Computer Interface (BCI) systems create a novel communication channel from the brain to an output device by bypassing conventional motor output pathways of nerves and muscles. Therefore they could provide a new communication and control option for paralyzed patients. Modern BCI technology is essentially based on techniques for the classification of single-trial brain signals. Here we present a novel technique that allows the simultaneous optimization of a spatial and a spectral filter enhancing discriminability of multi-channel EEG single-trials. The evaluation of 60 experiments involving 22 different subjects demonstrates the superiority of the proposed algorithm. Apart from the enhanced classification, the spatial and/or the spectral filter that are determined by the algorithm can also be used for further analysis of the data, e.g., for source localization of the respective brain rhythms.

We investigate the learning of the appearance of an object from a single image of it. Instead of using a large number of pictures of the object to recognize, we use a labeled reference database of pictures of other objects to learn invariance to noise and variations in pose and illumination. This acquired knowledge is then used to predict if two pictures of new objects, which do not appear on the training pictures, actually display the same object. We propose a generic scheme called chopping to address this task. It relies on hundreds of random binary splits of the training set chosen to keep together the images of any given object. Those splits are extended to the complete image space with a simple learning algorithm. Given two images, the responses of the split predictors are combined with a Bayesian rule into a posterior probability of similarity.

In this paper we propose a general framework to study the generalization properties of binary classifiers trained with data which may be dependent, but are deterministically generated upon a sample of independent examples. It provides generalization bounds for binary classification and some cases of ranking problems, and clarifies the relationship between these learning tasks.

Images represent an important and abundant source of data. Understanding their statistical structure has important applications such as image compression and restoration. In this paper we propose a particular kind of probabilistic model, dubbed the "products of edge-perts model" to describe the structure of wavelet transformed images. We develop a practical denoising algorithm based on a single edge-pert and show state-ofthe-art denoising performance on benchmark images.

This paper presents a non-asymptotic statistical analysis of Kernel-PCA with a focus different from the one proposed in previous work on this topic. Here instead of considering the reconstruction error of KPCA we are interested in approximation error bounds for the eigenspaces themselves. We prove an upper bound depending on the spacing between eigenvalues but not on the dimensionality of the eigenspace. As a consequence this allows to infer stability results for these estimated spaces.