The Bradley-Terry model for paired comparison has been popular in many areas. We propose a generalized version in which paired individual comparisons are extended to paired team comparisons. We introduce a simple algorithm with convergence proofs to solve the model and obtain individual skill. A useful application to multi-class probability estimates using error-correcting codes is demonstrated.

We present a generative model and stochastic filtering algorithm for simultaneous tracking of 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 of conditionally 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) and exact 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 both optic 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.

We study a method of optimal data-driven aggregation of classifiers in a convex combination and establish tight upper bounds on its excess risk with respect to a convex loss function under the assumption that the solution of optimal aggregation problem is sparse. We use a boosting type algorithm of optimal aggregation to develop aggregate classifiers of activation patterns in fMRI based on locally trained SVM classifiers. The aggregation coefficients are then used to design a "boosting map" of the brain needed to identify the regions with most significant impact on classification.

In the analysis of natural images, Gaussian scale mixtures (GSM) have been used to account for the statistics of filter responses, and to inspire hierarchical cortical representational learning schemes. GSMs pose a critical assignment problem, working out which filter responses were generated by a common multiplicative factor. We present a new approach to solving this assignment problem through a probabilistic extension to the basic GSM, and show how to perform inference in the model using Gibbs sampling. We demonstrate the efficacy of the approach on both synthetic and image data. Understanding the statistical structure of natural images is an important goal for visual neuroscience. Neural representations in early cortical areas decompose images (and likely other sensory inputs) in a way that is sensitive to sophisticated aspects of their probabilistic structure. This structure also plays a key role in methods for image processing and coding. A striking aspect of natural images that has reflections in both top-down and bottom-up modeling is coordination across nearby locations, scales, and orientations. From a topdown perspective, this structure has been modeled using what is known as a Gaussian Scale Mixture model (GSM).

Two neural networks that are trained on their mutual output synchronize to an identical time dependant weight vector. This novel phenomenon can be used for creation of a secure cryptographic secret-key using a public channel. Several models for this cryptographic system have been suggested, and have been tested for their security under different sophisticated attack strategies. The most promising models are networks that involve chaos synchronization. The synchronization process of mutual learning is described analytically using statistical physics methods.

The NIPS 2003 workshops included a feature selection competition organized by the authors. We provided participants with five datasets from different application domains and called for classification results using a minimal number of features. The competition took place over a period of 13 weeks and attracted 78 research groups. Participants were asked to make online submissions on the validation and test sets, with performance on the validation set being presented immediately to the participant and performance on the test set presented to the participants at the workshop. In total 1863 entries were made on the validation sets during the development period and 135 entries on all test sets for the final competition. The winners used a combination of Bayesian neural networks with ARD priors and Dirichlet diffusion trees. Other top entries used a variety of methods for feature selection, which combined filters and/or wrapper or embedded methods using Random Forests, kernel methods, or neural networks as a classification engine. The results of the benchmark (including the predictions made by the participants and the features they selected) and the scoring software are publicly available. The benchmark is available at www.nipsfsc.ecs.soton.ac.uk for post-challenge submissions to stimulate further research.

We present a novel approach to collaborative prediction, using low-norm instead of low-rank factorizations. The approach is inspired by, and has strong connections to, large-margin linear discrimination. We show how to learn low-norm factorizations by solving a semi-definite program, and discuss generalization error bounds for them.

We show that anomaly detection can be interpreted as a binary classification problem. Using this interpretation we propose a support vector machine (SVM) for anomaly detection. We then present some theoretical results which include consistency and learning rates. Finally, we experimentally compare our SVM with the standard one-class SVM.

We consider an MDP setting in which the reward function is allowed to change during each time step of play (possibly in an adversarial manner), yet the dynamics remain fixed. Similar to the experts setting, we address the question of how well can an agent do when compared to the reward achieved under the best stationary policy over time. We provide efficient algorithms, which have regret bounds with no dependence on the size of state space. Instead, these bounds depend only on a certain horizon time of the process and logarithmically on the number of actions. We also show that in the case that the dynamics change over time, the problem becomes computationally hard.

Successful application of reinforcement learning algorithms often involves considerable handcrafting of the necessary nonlinear features to reduce the complexity of the value functions and hence to promote convergence of the algorithm. In contrast, the human brain readily and autonomously finds the complex features when provided with sufficient training. Recent work in machine learning and neurophysiology has demonstrated the role of the basal ganglia and the frontal cortex in mammalian reinforcement learning. This paper develops and explores new reinforcement learning algorithms inspired by neurological evidence that provides potential new approaches to the feature construction problem. The algorithms are compared and evaluated on the Acrobot task.