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.

We consider multi-agent systems whose agents compete for resources by striving to be in the minority group. The agents adapt to the environment by reinforcement learning of the preferences of the policies they hold. Diversity of preferences of policies is introduced by adding random biases to the initial cumulative payoffs of their policies. We explain and provide evidence that agent cooperation becomes increasingly important when diversity increases. Analyses of these mechanisms yield excellent agreement with simulations over nine decades of data.

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 show how to build hierarchical, reduced-rank representation for large stochastic matrices and use this representation to design an efficient algorithm for computing the largest eigenvalues, and the corresponding eigenvectors. In particular, the eigen problem is first solved at the coarsest level of the representation. The approximate eigen solution is then interpolated over successive levels of the hierarchy. A small number of power iterations are employed at each stage to correct the eigen solution. The typical speedups obtained by a Matlab implementation of our fast eigensolver over a standard sparse matrix eigensolver [13] are at least a factor of ten for large image sizes. The hierarchical representation has proven to be effective in a min-cut based segmentation algorithm that we proposed recently [8].

In this paper we propose to combine two powerful ideas, boosting and manifold learning.

We propose a sequential information maximization model as a general strategy for programming eye movements.

We describe a novel method for real-time, simultaneous multi-view face detection and facial pose estimation. The method employs a convolutional network to map face images to points on a manifold, parametrized by pose, and non-face images to points far from that manifold. This network is trained by optimizing a loss function of three variables: image, pose, and face/non-face label. We test the resulting system, in a single configuration, on three standard data sets - one for frontal pose, one for rotated faces, and one for profiles - and find that its performance on each set is comparable to previous multi-view face detectors that can only handle one form of pose variation. We also show experimentally that the system's accuracy on both face detection and pose estimation is improved by training for the two tasks together.

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.

Decision trees are surprisingly adaptive in three important respects: They automatically (1) adapt to favorable conditions near the Bayes decision boundary; (2) focus on data distributed on lower dimensional manifolds; (3) reject irrelevant features. In this paper we examine a decision tree based on dyadic splits that adapts to each of these conditions to achieve minimax optimal rates of convergence. The proposed classifier is the first known to achieve these optimal rates while being practical and implementable.

We use unsupervised probabilistic machine learning ideas to try to explain the kinds of learning observed in real neurons, the goal being to connect abstract principles of self-organisation to known biophysical processes. For example, we would like to explain Spike Timing-Dependent Plasticity (see [5,6] and Figure 3A), in terms of information theory. Starting out, we explore the optimisation of a network sensitivity measure related to maximising the mutual information between input spike timings and output spike timings. Our derivations are analogous to those in ICA, except that the sensitivity of output timings to input timings is maximised, rather than the sensitivity of output'firing rates' to inputs. ICA and related approaches have been successful in explaining the learning of many properties of early visual receptive fields in rate coding models, and we are hoping for similar gains in understanding of spike coding in networks, and how this is supported, in principled probabilistic ways, by cellular biophysical processes. For now, in our initial simulations, we show that our derived rule can learn synaptic weights which can unmix, or demultiplex, mixed spike trains. That is, it can recover independent point processes embedded in distributed correlated input spike trains, using an adaptive single-layer feedforward spiking network.