In contrast to the equivalence of linear blind source separation and linear independent component analysis it is not possible to recover the original sourcesignal from some unknown nonlinear transformations of the sources using only the independence assumption. Integrating the objectives ofstatistical independence and temporal slowness removes this indeterminacy leading to a new method for nonlinear blind source separation. Theprinciple of temporal slowness is adopted from slow feature analysis, an unsupervised method to extract slowly varying features from a given observed vectorial signal. The performance of the algorithm is demonstrated on nonlinearly mixed speech data.

We present a generative model and stochastic filtering algorithm for simultaneous trackingof 3D position and orientation, nonrigid motion, object texture, and background texture using a single camera. We show that the solution to this problem is formally equivalent to stochastic filtering ofconditionally Gaussian processes, a problem for which well known approaches exist [3, 8]. We propose an approach based on Monte Carlo sampling of the nonlinear component of the process (object motion) andexact filtering of the object and background textures given the sampled motion. The smoothness of image sequences in time and space is exploited by using Laplace's method to generate proposal distributions for importance sampling [7]. The resulting inference algorithm encompasses bothoptic flow and template-based tracking as special cases, and elucidates the conditions under which these methods are optimal. We demonstrate an application of the system to 3D nonrigid face tracking.

Repeated spike patterns have often been taken as evidence for the synfire chain, a phenomenon that a stable spike synchrony propagates through a feedforward network. Inter-spike intervals which represent a repeated spike pattern are influenced by the propagation speed of a spike packet. However, the relation between the propagation speed and network structure isnot well understood. While it is apparent that the propagation speed depends on the excitatory synapse strength, it might also be related to spike patterns. We analyze a feedforward network with Mexican-Hattype connectivity(FMH) using the Fokker-Planck equation. We show that both a uniform and a localized spike packet are stable in the FMH in a certain parameter region. We also demonstrate that the propagation speed depends on the distinct firing patterns in the same network.

We propose to selectively remove examples from the training set using probabilistic estimates related to editing algorithms (Devijver and Kittler, 1982). This heuristic procedure aims at creating a separable distribution of training examples with minimal impact on the position of the decision boundary. It breaks the linear dependency between the number of SVs and the number of training examples, and sharply reduces the complexity of SVMs during both the training and prediction stages.

Computation without stable states is a computing paradigm different fromTuring's and has been demonstrated for various types of simulated neural networks. This publication transfers this to a hardware implemented neural network. Results of a software implementation arereproduced showing that the performance peaks when the network exhibits dynamics at the edge of chaos. The liquid computing approach seems well suited for operating analog computing devices such as the used VLSI neural network.

The standard approach to the classification of objects is to consider the examples as independent and identically distributed (iid). In many real world settings, however, this assumption is not valid, because a topographical relationshipexists between the objects. In this contribution we consider the special case of image segmentation, where the objects are pixels and where the underlying topography is a 2D regular rectangular grid. We introduce a classification method which not only uses measured vectorial feature information but also the label configuration within a topographic neighborhood.Due to the resulting dependence between the labels of neighboring pixels, a collective classification of a set of pixels becomes necessary. We propose a new method called'Topographic Support VectorMachine' (TSVM), which is based on a topographic kernel and a self-consistent solution to the label assignment shown to be equivalent toa recurrent neural network. The performance of the algorithm is compared to a conventional SVM on a cell image segmentation task.

We describe an algorithm for support vector machines (SVM) that can be parallelized efficiently and scales to very large problems with hundreds of thousands of training vectors. Instead of analyzing the whole training set in one optimization step, the data are split into subsets and optimized separately with multiple SVMs. The partial results are combined and filtered again in a'Cascade' of SVMs, until the global optimum is reached. The Cascade SVM can be spread over multiple processors with minimal communication overhead and requires far less memory, since the kernel matrices are much smaller than for a regular SVM. Convergence to the global optimum is guaranteed with multiple passes through the Cascade, but already a single pass provides good generalization. A single pass is 5x - 10x faster than a regular SVM for problems of 100,000 vectors when implemented on a single processor. Parallel implementations on a cluster of 16 processors were tested with over 1 million vectors (2-class problems), converging in a day or two, while a regular SVM never converged in over a week.

It has been demonstrated that basic aspects of human visual motion perception arequalitatively consistent with a Bayesian estimation framework, where the prior probability distribution on velocity favors slow speeds. Here, we present a refined probabilistic model that can account for the typical trial-to-trial variabilities observed in psychophysical speed perception experiments. We also show that data from such experiments can be used to constrain both the likelihood and prior functions of the model. Specifically, we measured matching speeds and thresholds in a two-alternative forced choice speed discrimination task. Parametric fits to the data reveal that the likelihood function is well approximated by a LogNormal distribution with a characteristic contrast-dependent variance, andthat the prior distribution on velocity exhibits significantly heavier tails than a Gaussian, and approximately follows a power-law function.

We introduce a novel active-learning scenario in which a user wants to work with a learning algorithm to identify useful anomalies. These are distinguished from the traditional statistical definition of anomalies as outliers or merely ill-modeled points. Our distinction is that the usefulness ofanomalies is categorized subjectively by the user. We make two additional assumptions. First, there exist extremely few useful anomalies tobe hunted down within a massive dataset.

Clustering and prediction of sets of curves is an important problem in many areas of science and engineering. It is often the case that curves tend to be misaligned from each other in a continuous manner, either in space (across the measurements) or in time. We develop a probabilistic framework that allows for joint clustering and continuous alignment of sets of curves in curve space (as opposed to a fixed-dimensional featurevector space).The proposed methodology integrates new probabilistic alignment models with model-based curve clustering algorithms. The probabilistic approach allows for the derivation of consistent EM learning algorithmsfor the joint clustering-alignment problem. Experimental results are shown for alignment of human growth data, and joint clustering andalignment of gene expression time-course data.