A framework is introduced for assessing the encoding accuracy and the discriminational ability of a population of neurons upon simultaneous presentation of multiple stimuli. Minimal square estimation errors are obtained from a Fisher information analysis in an abstract compound space comprising the features of all stimuli. Even for the simplest case of linear superposition of responses and Gaussian tuning, the symmetries in the compound space are very different from those in the case of a single stimulus. The analysis allows for a quantitative description of attentional effects and can be extended to include neural nonlinearities such as nonclassical receptive fields.

We report a system that classifies and can learn to classify patterns of visual motion online. The complete system is described by the dynamics of its physical network architectures. The combination of the following properties makes the system novel: Firstly, the front-end of the system consists of an aVLSI optical flow chip that collectively computes 2-D global visual motion in real-time [1]. Secondly, the complexity of the classification task is significantly reduced by mapping the continuous motion trajectories to sequences of'motion events'. And thirdly, all the network structures are simple and with the exception of the optical flow chip based on a Winner-Take-All (WTA) architecture. We demonstrate the application of the proposed generic system for a contactless man-machine interface that allows to write letters by visual motion. Regarding the low complexity of the system, its robustness and the already existing front-end, a complete aVLSI system-on-chip implementation is realistic, allowing various applications in mobile electronic devices.

We investigate data based procedures for selecting the kernel when learning with Support Vector Machines. We provide generalization error bounds by estimating the Rademacher complexities of the corresponding function classes. In particular we obtain a complexity bound for function classes induced by kernels with given eigenvectors, i.e., we allow to vary the spectrum and keep the eigenvectors fix. This bound is only a logarithmic factor bigger than the complexity of the function class induced by a single kernel. However, optimizing the margin over such classes leads to overfitting. We thus propose a suitable way of constraining the class. We use an efficient algorithm to solve the resulting optimization problem, present preliminary experimental results, and compare them to an alignment-based approach.

We develop a systems theoretical treatment of a behavioural system that interacts with its environment in a closed loop situation such that its motor actions influence its sensor inputs. The simplest form of a feedback is a reflex. Reflexes occur always "too late"; i.e., only after a (unpleasant, painful, dangerous) reflex-eliciting sensor event has occurred. This defines an objective problem which can be solved if another sensor input exists which can predict the primary reflex and can generate an earlier reaction. In contrast to previous approaches, our linear learning algorithm allows for an analytical proof that this system learns to apply feedforward control with the result that slow feedback loops are replaced by their equivalent feed-forward controller creating a forward model. In other words, learning turns the reactive system into a proactive system. By means of a robot implementation we demonstrate the applicability of the theoretical results which can be used in a variety of different areas in physics and engineering.

W e consider the problem of multi-step ahead prediction in time series analysis using the nonparametric Gaussian process model.

We propose in this paper a probabilistic approach for adaptive inference of generalized nonlinear classification that combines the computational advantage of a parametric solution with the flexibility of sequential sampling techniques. We regard the parameters of the classifier as latent states in a first order Markov process and propose an algorithm which can be regarded as variational generalization of standard Kalman filtering. The variational Kalman filter is based on two novel lower bounds that enable us to use a non-degenerate distribution over the adaptation rate. An extensive empirical evaluation demonstrates that the proposed method is capable of infering competitive classifiers both in stationary and non-stationary environments. Although we focus on classification, the algorithm is easily extended to other generalized nonlinear models.

The responses of cortical sensory neurons are notoriously variable, with the number of spikes evoked by identical stimuli varying significantly from trial to trial. This variability is most often interpreted as'noise', purely detrimental to the sensory system. In this paper, we propose an alternative view in which the variability is related to the uncertainty, about world parameters, which is inherent in the sensory stimulus. Specifically, the responses of a population of neurons are interpreted as stochastic samples from the posterior distribution in a latent variable model. In addition to giving theoretical arguments supporting such a representational scheme, we provide simulations suggesting how some aspects of response variability might be understood in this framework.

We introduce a general family of kernels based on weighted transducers or rational relations, rational kernels, that can be used for analysis of variable-length sequences or more generally weighted automata, in applications such as computational biology or speech recognition. We show that rational kernels can be computed efficiently using a general algorithm of composition of weighted transducers and a general single-source shortest-distance algorithm. We also describe several general families of positive definite symmetric rational kernels. These general kernels can be combined with Support Vector Machines to form efficient and powerful techniques for spoken-dialog classification: highly complex kernels become easy to design and implement and lead to substantial improvements in the classification accuracy. We also show that the string kernels considered in applications to computational biology are all specific instances of rational kernels.

Gaussian process regression allows a simple analytical treatment of exact Bayesian inference and has been found to provide good performance, yet scales badly with the number of training data. In this paper we compare several approaches towards scaling Gaussian processes regression to large data sets: the subset of representers method, the reduced rank approximation, online Gaussian processes, and the Bayesian committee machine. Furthermore we provide theoretical insight into some of our experimental results. We found that subset of representers methods can give good and particularly fast predictions for data sets with high and medium noise levels. On complex low noise data sets, the Bayesian committee machine achieves significantly better accuracy, yet at a higher computational cost.

Problems in which abnormal or novel situations should be detected can be approached by describing the domain of the class of typical examples. These applications come from the areas of machine diagnostics, fault detection, illness identification or, in principle, refer to any problem where little knowledge is available outside the typical class. In this paper we explain why proximities are natural representations for domain descriptors and we propose a simple one-class classifier for dissimilarity representations. By the use of linear programming an efficient one-class description can be found, based on a small number of prototype objects. This classifier can be made (1) more robust by transforming the dissimilarities and (2) cheaper to compute by using a reduced representation set. Finally, a comparison to a comparable one-class classifier by Campbell and Bennett is given.