We introduce a novel adaptive nonparametric anomaly detection approach, called GEM, that is based on the minimal covering properties of K-point entropic graphs when constructed on N training samples from a nominal probability distribution. Such graphs have the property that as N their span recovers the entropy minimizing set that supports at least ρ K/N(100)% of the mass of the Lebesgue part of the distribution. When a test sample falls outside of the entropy minimizing set an anomaly can be declared at a statistical level of significance α 1 ρ. A method for implementing this nonparametric anomaly detector is proposed that approximates this minimum entropy set by the influence region of a K-point entropic graph built on the training data. By implementing an incremental leave-one-out k-nearest neighbor graph on resampled subsets of the training data GEM can efficiently detect outliers at a given level of significance and compute their empirical p-values. We illustrate GEM for several simulated and real data sets in high dimensional feature spaces.

It has been established that a neuron reproduces highly precise spike response to identical fluctuating input currents. We wish to accurately predict the firing times of a given neuron for any input current. For this purpose we adopt a model that mimics the dynamics of the membrane potential, and then take a cue from its dynamics for predicting the spike occurrence for a novel input current. It is found that the prediction is significantly improved by observing the state space of the membrane potential and its time derivative(s) in advance of a possible spike, in comparison to simply thresholding an instantaneous value of the estimated potential.

In many modern large-scale learning applications, the amount of unlabeled data far exceeds that of labeled data. A common instance of this problem is the transductive setting where the unlabeled test points are known to the learning algorithm. This paper presents a study of regression problems in that setting. It presents explicit VC-dimension error bounds for transductive regression that hold for all bounded loss functions and coincide with the tight classification bounds of Vapnik when applied to classification. It also presents a new transductive regression algorithm inspired by our bound that admits a primal and kernelized closedform solution and deals efficiently with large amounts of unlabeled data. The algorithm exploits the position of unlabeled points to locally estimate their labels and then uses a global optimization to ensure robust predictions. Our study also includes the results of experiments with several publicly available regression data sets with up to 20,000 unlabeled examples. The comparison with other transductive regression algorithms shows that it performs well and that it can scale to large data sets.

In large-scale applications, the data are often highly sparse. CRS combines sketching and sampling in that it converts sketches of the data into conditional random samples online in the estimation stage, with the sample size determined retrospectively.

We propose a family of kernels for structured objects which is based on the bag-ofcomponents paradigm. However, rather than decomposing each complex object into the single histogram of its components, we use for each object a family of nested histograms, where each histogram in this hierarchy describes the object seen from an increasingly granular perspective. We use this hierarchy of histograms to define elementary kernels which can detect coarse and fine similarities between the objects. We compute through an efficient averaging trick a mixture of such specific kernels, to propose a final kernel value which weights efficiently local and global matches. We propose experimental results on an image retrieval experiment which show that this mixture is an effective template procedure to be used with kernels on histograms.

The performance of EEGbased Brain-Computer-Interfaces (BCIs) critically depends on the extraction of features from the EEG carrying information relevant for the classification of different mental states. For BCIs employing imaginary movements of different limbs, the method of Common Spatial Patterns (CSP) has been shown to achieve excellent classification results. The CSP-algorithm however suffers from a lack of robustness, requiring training data without artifacts for good performance. To overcome this lack of robustness, we propose an adaptive spatial filter that replaces the training data in the CSP approach by a-priori information. More specifically, we design an adaptive spatial filter that maximizes the ratio of the variance of the electric field originating in a predefined region of interest (ROI) and the overall variance of the measured EEG. Since it is known that the component of the EEG used for discriminating imaginary movements originates in the motor cortex, we design two adaptive spatial filters with the ROIs centered in the hand areas of the left and right motor cortex. We then use these to classify EEG data recorded during imaginary movements of the right and left hand of three subjects, and show that the adaptive spatial filters outperform the CSP-algorithm, enabling classification rates of up to 94.7 % without artifact rejection.

A new bottom-up visual saliency model, Graph-Based Visual Saliency (GBVS), is proposed. It consists of two steps: rst forming activation maps on certain feature channels, and then normalizing them in a way which highlights conspicuity and admits combination with other maps. The model is simple, and biologically plausible insofar as it is naturally parallelized. This model powerfully predicts human xations on 749 variations of 108 natural images, achieving 98% of the ROC area of a human-based control, whereas the classical algorithms of Itti & Koch ([2], [3], [4]) achieve only 84%.

We propose a new kernel-based data transformation technique. It is founded on the principle of maximum entropy (MaxEnt) preservation, hence named kernel MaxEnt. The key measure is Renyi's entropy estimated via Parzen windowing. We show that kernel MaxEnt is based on eigenvectors, and is in that sense similar to kernel PCA, but may produce strikingly different transformed data sets. An enhanced spectral clustering algorithm is proposed, by replacing kernel PCA by kernel MaxEnt as an intermediate step. This has a major impact on performance.

This paper addresses the bottom-up influence of local image information on human eye movements. Most existing computational models use a set of biologically plausible linear filters, e.g., Gabor or Difference-of-Gaussians filters as a front-end, the outputs of which are nonlinearly combined into a real number that indicates visual saliency. Unfortunately, this requires many design parameters such as the number, type, and size of the front-end filters, as well as the choice of nonlinearities, weighting and normalization schemes etc., for which biological plausibility cannot always be justified. As a result, these parameters have to be chosen in a more or less ad hoc way. Here, we propose to learn a visual saliency model directly from human eye movement data. The model is rather simplistic and essentially parameter-free, and therefore contrasts recent developments in the field that usually aim at higher prediction rates at the cost of additional parameters and increasing model complexity. Experimental results show that--despite the lack of any biological prior knowledge--our model performs comparably to existing approaches, and in fact learns image features that resemble findings from several previous studies. In particular, its maximally excitatory stimuli have center-surround structure, similar to receptive fields in the early human visual system.

This paper proposes a PAC-Bayes bound to measure the performance of Support Vector Machine (SVM) classifiers. The bound is based on learning a prior over the distribution of classifiers with a part of the training samples. Experimental work shows that this bound is tighter than the original PAC-Bayes, resulting in an enhancement of the predictive capabilities of the PAC-Bayes bound. In addition, it is shown that the use of this bound as a means to estimate the hyperparameters of the classifier compares favourably with cross validation in terms of accuracy of the model, while saving a lot of computational burden.