Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by kernel PCA live in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approximate pre-images, focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.

In High Energy Physics experiments one has to sort through a high flux of events, at a rate of tens of MHz, and select the few that are of interest. One of the key factors in making this decision is the location of the vertex where the interaction, that led to the event, took place. Here we present a novel solution to the problem of finding the location of the vertex, based on two feedforward neural networks with fixed architectures, whose parameters are chosen so as to obtain a high accuracy. The system is tested on simulated data sets, and is shown to perform better than conventional algorithms. 1 Introduction An event in High Energy Physics (HEP) is the experimental result of an interaction during the collision of particles in an accelerator. The result of this interaction is the production of tens of particles, each of which is ejected in a different direction and energy. Due to the quantum mechanical effects involved, the events differ from one another in the number of particles produced, the types of particles, and their energies. The trajectories of produced particles are detected by a very large and sophisticated detector.

We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classification models with Gaussian processes. In contrast to previous approaches, no knowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given.

Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

We will also introduce a regularization strategy (analogous to weight decay) into boosting. This strategy uses slack variables to achieve a soft margin (section 4). Numerical experiments show the validity of our regularization approach in section 5 and finally a brief conclusion is given. 2 AdaBoost Algorithm Let {ht(x): t 1,...,T} be an ensemble of T hypotheses defined on input vector x and e

Lazy learning is a memory-based technique that, once a query is received, extracts a prediction interpolating locally the neighboring examples of the query which are considered relevant according to a distance measure. In this paper we propose a data-driven method to select on a query-by-query basis the optimal number of neighbors to be considered for each prediction. As an efficient way to identify and validate local models, the recursive least squares algorithm is introduced in the context of local approximation and lazy learning. Furthermore, beside the winner-takes-all strategy for model selection, a local combination of the most promising models is explored. The method proposed is tested on six different datasets and compared with a state-of-the-art approach.

One of the simplest methods is to use linear transformations of the observed data.

We present a method for automatically constructing macro-actions from scratch from primitive actions during the reinforcement learning process. The overall idea is to reinforce the tendency to perform action b after action a if such a pattern of actions has been rewarded. We test the method on a bicycle task, the car-on-the-hill task, the racetrack task and some grid-world tasks. For the bicycle and racetrack tasks the use of macro-actions approximately halves the learning time, while for one of the grid-world tasks the learning time is reduced by a factor of 5. The method did not work for the car-on-the-hill task for reasons we discuss in the conclusion.

In supervised learning, we have a set of explicative variables x from which we wish to predict a response variable y.

We propose a novel strategy for training neural networks using sequential sampling-importance resampling algorithms. This global optimisation strategy allows us to learn the probability distribution of the network weights in a sequential framework. It is well suited to applications involving online, nonlinear, non-Gaussian or non-stationary signal processing. 1 INTRODUCTION This paper addresses sequential training of neural networks using powerful sampling techniques. Sequential techniques are important in many applications of neural networks involving real-time signal processing, where data arrival is inherently sequential. Furthermore, one might wish to adopt a sequential training strategy to deal with non-stationarity in signals, so that information from the recent past is lent more credence than information from the distant past. One way to sequentially estimate neural network models is to use a state space formulation and the extended Kalman filter (Singhal and Wu 1988, de Freitas, Niranjan and Gee 1998).