We introduce a new learning algorithm for decision lists to allow features that are constructed from the data and to allow a tradeoff between accuracy and complexity. We bound its generalization error in terms of the number of errors and the size of the classifier it finds on the training data. We also compare its performance on some natural data sets with the set covering machine and the support vector machine.

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

We investigate the problem of learning a classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column objects may belong to different sets, and the entries in the matrix express the relationships between them. We interpret the matrix elements as being produced by an unknown kernel which operates on object pairs and we show that - under mild assumptions - these kernels correspond to dot products in some (unknown) feature space. Minimizing a bound for the generalization error of a linear classifier which has been obtained using covering numbers we derive an objective function for model selection according to the principle of structural risk minimization. The new objective function has the advantage that it allows the analysis of matrices which are not positive definite, and not even symmetric or square.

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.

Low rank approximation techniques are widespread in pattern recognition research -- they include Latent Semantic Analysis (LSA), Probabilistic LSA, Principal Components Analysus (PCA), the Generative Aspect Model, and many forms of bibliometric analysis. All make use of a low-dimensional manifold onto which data are projected. Such techniques are generally "unsupervised," which allows them to model data in the absence of labels or categories. With many practical problems, however, some prior knowledge is available in the form of context. In this paper, I describe a principled approach to incorporating such information, and demonstrate its application to PCA-based approximations of several data sets.

Pairwise data in empirical sciences typically violate metricity, either due to noise or due to fallible estimates, and therefore are hard to analyze by conventional machine learning technology. In this paper we therefore study ways to work around this problem. First, we present an alternative embedding to multidimensional scaling (MDS) that allows us to apply a variety of classical machine learning and signal processing algorithms. The class of pairwise grouping algorithms which share the shift-invariance property is statistically invariant under this embedding procedure, leading to identical assignments of objects to clusters. Based on this new vectorial representation, denoising methods are applied in a second step. Both steps provide a theoretically well controlled setup to translate from pairwise data to the respective denoised metric representation. We demonstrate the practical usefulness of our theoretical reasoning by discovering structure in protein sequence data bases, visibly improving performance upon existing automatic methods. 1 Introduction Unsupervised grouping or clustering aims at extracting hidden structure from data (see e.g.

The similarity between objects is a fundamental element of many learning algorithms. Most nonparametric methods take this similarity to be fixed, but much recent work has shown the advantages of learning it, in particular to exploit the local invariances in the data or to capture the possibly nonlinear manifold on which most of the data lies. We propose a new nonparametric kernel density estimation method which captures the local structure of an underlying manifold through the leading eigenvectors of regularized local covariance matrices.

We present a meta-algorithm for learning in this framework that learns via a single linear classifier in high dimension. We discuss distribution independent as well as margin-based generalization bounds and present empirical and theoretical evidence showing that constraint classification benefits over existing methods of multiclass classification.

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.

We propose in this paper a probabilistic approach for adaptive inference of generalized nonlinear classification that combines the computational advantage of a parametric solution with the flexibility of sequential sampling techniques. We regard the parameters of the classifier as latent states in a first order Markov process and propose an algorithm which can be regarded as variational generalization of standard Kalman filtering. The variational Kalman filter is based on two novel lower bounds that enable us to use a non-degenerate distribution over the adaptation rate. An extensive empirical evaluation demonstrates that the proposed method is capable of infering competitive classifiers both in stationary and non-stationary environments. Although we focus on classification, the algorithm is easily extended to other generalized nonlinear models.