We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images. 1 Introduction In this article we consider the rather general learning problem of finding a dependency between inputs x E X and outputs y E Y given a training set (Xl,yl),...,(xm, Ym) E X x Y This includes conventional pattern recognition and regression estimation. It also encompasses more complex dependency estimation tasks, e.g mapping of a certain class of strings to a certain class of graphs (as in text parsing) or the mapping of text descriptions to images.

Several authors have suggested viewing boosting as a gradient descent search for a good fit in function space. We apply gradient-based boosting methodology to the unsupervised learning problem of density estimation. We show convergence properties of the algorithm and prove that a strength of weak learnability property applies to this problem as well. We illustrate the potential of this approach through experiments with boosting Bayesian networks to learn density models.

In this work, we study an information filtering model where the relevance labels associated to a sequence of feature vectors are realizations of an unknown probabilistic linear function. Building on the analysis of a restricted version of our model, we derive a general filtering rule based on the margin of a ridge regression estimator. While our rule may observe the label of a vector only by classfying the vector as relevant, experiments on a real-world document filtering problem show that the performance of our rule is close to that of the online classifier which is allowed to observe all labels. These empirical results are complemented by a theoretical analysis where we consider a randomized variant of our rule and prove that its expected number of mistakes is never much larger than that of the optimal filtering rule which knows the hidden linear model.

Prototypes based algorithms are commonly used to reduce the computational complexity of Nearest-Neighbour (NN) classifiers. In this paper we discuss theoretical and algorithmical aspects of such algorithms. On the theory side, we present margin based generalization bounds that suggest that these kinds of classifiers can be more accurate then the 1-NN rule. Furthermore, we derived a training algorithm that selects a good set of prototypes using large margin principles. We also show that the 20 years old Learning Vector Quantization (LVQ) algorithm emerges naturally from our framework.

We investigate the generalization performance of some learning problems in Hilbert function Spaces. We introduce a concept of scalesensitive effective data dimension, and show that it characterizes the convergence rate of the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to nonparametric kernel learning methods. We derive upper bounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.

We consider a statistical framework for learning in a class of networks of spiking neurons. Our aim is to show how optimal local learning rules can be readily derived once the neural dynamics and desired functionality of the neural assembly have been specified, in contrast to other models which assume (sub-optimal) learning rules. Within this framework we derive local rules for learning temporal sequences in a model of spiking neurons and demonstrate its superior performance to correlation (Hebbian) based approaches. We further show how to include mechanisms such as synaptic depression and outline how the framework is readily extensible to learning in networks of highly complex spiking neurons. A stochastic quantal vesicle release mechanism is considered and implications on the complexity of learning discussed.

Language acquisition is a special kind of learning problem because the outcome of learning of one generation is the input for the next. That makes it possible for languages to adapt to the particularities of the learner. In this paper, I show that this type of language change has important consequences for models of the evolution and acquisition of syntax.

Prototypes based algorithms are commonly used to reduce the computational complexityof Nearest-Neighbour (NN) classifiers. In this paper we discuss theoretical and algorithmical aspects of such algorithms. On the theory side, we present margin based generalization bounds that suggest thatthese kinds of classifiers can be more accurate then the 1-NN rule. Furthermore, we derived a training algorithm that selects a good set of prototypes using large margin principles. We also show that the 20 years old Learning Vector Quantization (LVQ) algorithm emerges naturally fromour framework.

We investigate the generalization performance of some learning problems inHilbert function Spaces. We introduce a concept of scalesensitive effectivedata dimension, and show that it characterizes the convergence rateof the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to nonparametric kernel learning methods. We derive upperbounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.

Jason Weston, Olivier Chapelle, Andre Elisseeff, Bernhard Scholkopf and Vladimir Vapnik* Max Planck Institute for Biological Cybernetics, 72076 Tubingen, Germany *NEC Research Institute, Princeton, NJ 08540 USA Abstract We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions,thus embedding the objects into vector spaces. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images. 1 Introduction In this article we consider the rather general learning problem of finding a dependency betweeninputs x E X and outputs y E Y given a training set (Xl,yl), ...,(xm, Ym) This includes conventional pattern recognition and regression estimation. It also encompasses more complex dependency estimation tasks, e.g mapping of a certain class of strings to a certain class of graphs (as in text parsing) or the mapping of text descriptions to images.