In recent years variational methods have become a popular tool for approximate inference and learning in a wide variety of probabilistic models. For each new application, however, it is currently necessary first to derive the variational update equations, and then to implement them in application-specific code. Each of these steps is both time consuming and error prone. In this paper we describe a general purpose inference engine called VIBES ('Variational Inference for Bayesian Networks') which allows a wide variety of probabilistic models to be implemented and solved variationally without recourse to coding. New models are specified either through a simple script or via a graphical interface analogous to a drawing package. VIBES then automatically generates and solves the variational equations. We illustrate the power and flexibility of VIBES using examples from Bayesian mixture modelling.

Classification trees are one of the most popular types of classifiers, with ease of implementation and interpretation being among their attractive features. Despite the widespread use of classification trees, theoretical analysis of their performance is scarce. In this paper, we show that a new family of classification trees, called dyadic classification trees (DCTs), are near optimal (in a minimax sense) for a very broad range of classification problems. This demonstrates that other schemes (e.g., neural networks, support vector machines) cannot perform significantly better than DCTs in many cases. We also show that this near optimal performance is attained with linear (in the number of training data) complexity growing and pruning algorithms. Moreover, the performance of DCTs on benchmark datasets compares favorably to that of standard CART, which is generally more computationally intensive and which does not possess similar near optimality properties. Our analysis stems from theoretical results on structural risk minimization, on which the pruning rule for DCTs is based.

We consider the problem of choosing a kernel suitable for estimation using a Gaussian Process estimator or a Support Vector Machine. A novel solution is presented which involves defining a Reproducing Kernel Hilbert Space on the space of kernels itself. By utilizing an analog of the classical representer theorem, the problem of choosing a kernel from a parameterized family of kernels (e.g. of varying width) is reduced to a statistical estimation problem akin to the problem of minimizing a regularized risk functional. Various classical settings for model or kernel selection are special cases of our framework.

We consider the problem of illusory or artefactual structure from the visualisation of high-dimensional structureless data. In particular we examine the role of the distance metric in the use of topographic mappings based on the statistical field of multidimensional scaling. We show that the use of a squared Euclidean metric (i.e. the SS

Recent algorithms for sparse coding and independent component analysis (ICA) have demonstrated how localized features can be learned from natural images. However, these approaches do not take image transformations into account. As a result, they produce image codes that are redundant because the same feature is learned at multiple locations. We describe an algorithm for sparse coding based on a bilinear generative model of images. By explicitly modeling the interaction between image features and their transformations, the bilinear approach helps reduce redundancy in the image code and provides a basis for transformationinvariant vision.

If the cortex uses spike timing to compute, the timing of the spikes must be robust to perturbations. Based on a recent framework that provides a simple criterion to determine whether a spike sequence produced by a generic network is sensitive to initial conditions, and numerical simulations of a variety of network architectures, we argue within the limits set by our model of the neuron, that it is unlikely that precise sequences of spike timings are used for computation under conditions typically found in the cortex. 1 Introduction

Side-chain prediction is an important subtask in the protein-folding problem. We show that finding a minimal energy side-chain configuration is equivalent to performing inference in an undirected graphical model. The graphical model is relatively sparse yet has many cycles. We used this equivalence to assess the performance of approximate inference algorithms in a real-world setting. Specifically we compared belief propagation (BP), generalized BP (GBP) and naive mean field (MF).

Machine learning has reached a point where many probabilistic methods can be understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms customized for different models.

They are very well suited to handle discrete of continuous sequences of varying sizes. Moreover, an efficient training algorithm (EM) is available, as well as an efficient decoding algorithm (Viterbi), which provides the optimal sequence of states (and the corresponding sequence of high level events) associated with a given sequence of low-level data. On the other hand, multimodal information processing is currently a very challenging framework of applications including multimodal person authentication, multimodal speech recognition, multimodal event analyzers, etc. In that framework, the same sequence of events is represented not only by a single sequence of data but by a series of sequences of data, each of them coming eventually from a different modality: video streams with various viewpoints, audio stream(s), etc. One such task, which will be presented in this paper, is multimodal speech recognition using both a microphone and a camera recording a speaker simultaneously while he (she) speaks.

Echo state networks (ESN) are a novel approach to recurrent neural network training. An ESN consists of a large, fixed, recurrent "reservoir" network, from which the desired output is obtained by training suitable output connection weights. Determination of optimal output weights becomes a linear, uniquely solvable task of MSE minimization. This article reviews the basic ideas and describes an online adaptation scheme based on the RLS algorithm known from adaptive linear systems. As an example, a 10th order NARMA system is adaptively identified.