We present a learning algorithm for undiscounted reinforcement learning. Our interest lies in bounds for the algorithm's online performance after some finite number of steps. In the spirit of similar methods already successfully applied for the exploration-exploitation tradeoff in multi-armed bandit problems, we use upper confidence bounds to show that our UCRL algorithm achieves logarithmic online regret in the number of steps taken with respect to an optimal policy.

We present a method for learning a low-dimensional representation which is shared across a set of multiple related tasks. The method builds upon the wellknown 1-norm regularization problem using a new regularizer which controls the number of learned features common for all the tasks. We show that this problem is equivalent to a convex optimization problem and develop an iterative algorithm for solving it. The algorithm has a simple interpretation: it alternately performs a supervised and an unsupervised step, where in the latter step we learn commonacross-tasks representations and in the former step we learn task-specific functions using these representations. We report experiments on a simulated and a real data set which demonstrate that the proposed method dramatically improves the performance relative to learning each task independently. Our algorithm can also be used, as a special case, to simply select - not learn - a few common features across the tasks.

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.

We describe an unsupervised method for learning a probabilistic grammar of an object from a set of training examples. Our approach is invariant to the scale and rotation of the objects. We illustrate our approach using thirteen objects from the Caltech 101 database. In addition, we learn the model of a hybrid object class where we do not know the specific object or its position, scale or pose. This is illustrated by learning a hybrid class consisting of faces, motorbikes, and airplanes. The individual objects can be recovered as different aspects of the grammar for the object class.

We describe a nonnegative variant of the "Sparse PCA" problem. The goal is to create a low dimensional representation from a collection of points which on the one hand maximizes the variance of the projected points and on the other uses only parts of the original coordinates, and thereby creating a sparse representation. What distinguishes our problem from other Sparse PCA formulations is that the projection involves only nonnegative weights of the original coordinates -- a desired quality in various fields, including economics, bioinformatics and computer vision. Adding nonnegativity contributes to sparseness, where it enforces a partitioning of the original coordinates among the new axes. We describe a simple yet efficient iterative coordinate-descent type of scheme which converges to a local optimum of our optimization criteria, giving good results on large real world datasets.

We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions between entities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood, information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths, or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given). We discuss properties and variants of SRM and derive an efficient learning algorithm. Very encouraging experimental results are achieved on a toy problem and a user-movie preference link prediction task. In the end we discuss extensions of SRM to general relational learning tasks.

We present a local learning approach for clustering. The basic idea is that a good clustering result should have the property that the cluster label of each data point can be well predicted based on its neighboring data and their cluster labels, using current supervised learning methods. An optimization problem is formulated such that its solution has the above property. Relaxation and eigen-decomposition are applied to solve this optimization problem. We also briefly investigate the parameter selection issue and provide a simple parameter selection method for the proposed algorithm. Experimental results are provided to validate the effectiveness of the proposed approach.

This paper describes a Gaussian process framework for inferring pixel-wise disparity and bi-layer segmentation of a scene given a stereo pair of images.

In many areas of science and engineering, the problem arises how to discover low dimensional representations of high dimensional data. Recently, a number of researchers have converged on common solutions to this problem using methods from convex optimization. In particular, many results have been obtained by constructing semidefinite programs (SDPs) with low rank solutions. While the rank of matrix variables in SDPs cannot be directly constrained, it has been observed that low rank solutions emerge naturally by computing high variance or maximal trace solutions that respect local distance constraints. In this paper, we show how to solve very large problems of this type by a matrix factorization that leads to much smaller SDPs than those previously studied. The matrix factorization is derived by expanding the solution of the original problem in terms of the bottom eigenvectors of a graph Laplacian. The smaller SDPs obtained from this matrix factorization yield very good approximations to solutions of the original problem. Moreover, these approximations can be further refined by conjugate gradient descent. We illustrate the approach on localization in large scale sensor networks, where optimizations involving tens of thousands of nodes can be solved in just a few minutes.

The neurons of the neocortex communicate by asynchronous events called action potentials (or'spikes'). However, for simplicity of simulation, most models of processing by cortical neural networks have assumed that the activations of their neurons can be approximated by event rates rather than taking account of individual spikes. The obstacle to exploring the more detailed spike processing of these networks has been reduced considerably in recent years by the development of hybrid analog-digital Very-Large Scale Integrated (hVLSI) neural networks composed of spiking neurons that are able to operate in real-time. In this paper we describe such a hVLSI neural network that performs an interesting task of selective attentional processing that was previously described for a simulated'pointer-map' rate model by Hahnloser and colleagues. We found that most of the computational features of their rate model can be reproduced in the spiking implementation; but, that spike-based processing requires a modification of the original network architecture in order to memorize a previously attended target.