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.

We use the k-core decomposition to develop algorithms for the analysis of large scale complex networks. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by progressively focusing on their central cores. By using this strategy we develop a general visualization algorithm that can be used to compare the structural properties of various networks and highlight their hierarchical structure. The low computational complexity of the algorithm, O(n e), where n is the size of the network, and e is the number of edges, makes it suitable for the visualization of very large sparse networks. We show how the proposed visualization tool allows to find specific structural fingerprints of networks.

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 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.

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 under what conditions a neuron can learn by experimentally supported rules for spike timing dependent plasticity (STDP) to predict the arrival times of strong "teacher inputs" to the same neuron. It turns out that in contrast to the famous Perceptron Convergence Theorem, which predicts convergence of the perceptron learning rule for a simplified neuron model whenever a stable solution exists, no equally strong convergence guarantee can be given for spiking neurons with STDP. But we derive a criterion on the statistical dependency structure of input spike trains which characterizes exactly when learning with STDP will converge on average for a simple model of a spiking neuron. This criterion is reminiscent of the linear separability criterion of the Perceptron Convergence Theorem, but it applies here to the rows of a correlation matrix related to the spike inputs. In addition we show through computer simulations for more realistic neuron models that the resulting analytically predicted positive learning results not only hold for the common interpretation of STDP where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.

The Octopus arm is a highly versatile and complex limb. How the Octopus controls such a hyper-redundant arm (not to mention eight of them!) is as yet unknown. Robotic arms based on the same mechanical principles may render present day robotic arms obsolete. In this paper, we tackle this control problem using an online reinforcement learning algorithm, based on a Bayesian approach to policy evaluation known as Gaussian process temporal difference (GPTD) learning. Our substitute for the real arm is a computer simulation of a 2-dimensional model of an Octopus arm. Even with the simplifications inherent to this model, the state space we face is a high-dimensional one. We apply a GPTDbased algorithm to this domain, and demonstrate its operation on several learning tasks of varying degrees of difficulty.

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.

Although nonparametric tests have already been proposed for that purpose, statistical significance tests for nonstandard measures (different from the classification error) are less often used in the literature. This paper is an attempt at empirically verifying how these tests compare with more classical tests, on various conditions. More precisely, using a very large dataset to estimate the whole "population", we analyzed the behavior of several statistical test, varying the class unbalance, the compared models, the performance measure, and the sample size. The main result is that providing big enough evaluation sets nonparametric tests are relatively reliable in all conditions.

Multiple visual cues are used by the visual system to analyze a scene; achromatic cues include luminance, texture, contrast and motion. Singlecell recordings have shown that the mammalian visual cortex contains neurons that respond similarly to scene structure (e.g., orientation of a boundary), regardless of the cue type conveying this information. This paper shows that cue-invariant response properties of simple-and complex-type cells can be learned from natural image data in an unsupervised manner. In order to do this, we also extend a previous conceptual model of cue invariance so that it can be applied to model simple-and complex-cell responses. Our results relate cue-invariant response properties to natural image statistics, thereby showing how the statistical modeling approach can be used to model processing beyond the elemental response properties visual neurons. This work also demonstrates how to learn, from natural image data, more sophisticated feature detectors than those based on changes in mean luminance, thereby paving the way for new data-driven approaches to image processing and computer vision.