Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

The task in text retrieval is to find the subset of a collection of documents relevant to a user's information request, usually expressed as a set of words. Classically, documents and queries are represented as vectors of word counts. In its simplest form, relevance is defined to be the dot product between a document and a query vector-a measure of the number of common terms. A central difficulty in text retrieval is that the presence or absence of a word is not sufficient to determine relevance to a query. Linear dimensionality reduction has been proposed as a technique for extracting underlying structure from the document collection.

Face recognition is different from classical pattern-recognition problems such as character recognition.

SVMs have empirically been shown to give good generalization performance on a wide variety of problems. However, the use of SVMs is stilI limited to a small group of researchers. One possible reason is that training algorithms for SVMs are slow, especially for large problems. Another explanation is that SVM training algorithms are complex, subtle, and sometimes difficult to implement. This paper describes a new SVM learning algorithm that is easy to implement, often faster, and has better scaling properties than the standard SVM training algorithm. The new SVM learning algorithm is called Sequential Minimal Optimization (or SMO).

Gaussian process (GP) prediction suffers from O(n3) scaling with the data set size n. By using a finite-dimensional basis to approximate the GP predictor, the computational complexity can be reduced. We derive optimal finite-dimensional predictors under a number of assumptions, and show the superiority of these predictors over the Projected Bayes Regression method (which is asymptotically optimal). We also show how to calculate the minimal model size for a given n. The calculations are backed up by numerical experiments.

Dyadzc data refers to a domain with two finite sets of objects in which observations are made for dyads, i.e., pairs with one element from either set. This type of data arises naturally in many application ranging from computational linguistics and information retrieval to preference analysis and computer vision. In this paper, we present a systematic, domain-independent framework of learning from dyadic data by statistical mixture models. Our approach covers different models with fiat and hierarchical latent class structures. We propose an annealed version of the standard EM algorithm for model fitting which is empirically evaluated on a variety of data sets from different domains. 1 Introduction Over the past decade learning from data has become a highly active field of research distributed over many disciplines like pattern recognition, neural computation, statistics, machine learning, and data mining.

We propose a new in-sample cross validation based method (randomized GACV) for choosing smoothing or bandwidth parameters that govern the bias-variance or fit-complexity tradeoff in'soft' classification. Soft classification refers to a learning procedure which estimates the probability that an example with a given attribute vector is in class 1 vs class O. The target for optimizing the the tradeoff is the Kullback-Liebler distance between the estimated probability distribution and the'true' probability distribution, representing knowledge of an infinite population. The method uses a randomized estimate of the trace of a Hessian and mimics cross validation at the cost of a single relearning with perturbed outcome data.

Even if the underlying phenomena are inherently deterministic, the complexity of these phenomena often makes a probabilistic formulation the only feasible approach from the computational point of view. Although quantities such as the mean, the variance, and possibly higher order moments of a random variable have often been sufficient to characterize a particular problem, the quest for higher modeling accuracy, and for more realistic assumptions drives us towards modeling the available random variables using their probability density. This of course leads us to the problem of density estimation (see [6]). The most common approach for density estimation is the nonparametric approach, where the density is determined according to a formula involving the data points available. The most common non parametric methods are the kernel density estimator, also known as the Parzen window estimator [4] and the k-nearest neighbor technique [1].

In fact, for many of the kernels used (not the polynomial kernels) like Gaussian rbf-kernels it can be shown [6] that SV machines are universal approximators. While this is advantageous in general, parametric models are useful techniques in their own right. Especially if one happens to have additional knowledge about the problem, it would be unwise not to take advantage of it. For instance it might be the case that the major properties of the data are described by a combination of a small set of linear independent basis functions {¢Jt (.),..., ¢n (.)}. Or one may want to correct the data for some (e.g.

We present a split and merge EM (SMEM) algorithm to overcome the local maximum problem in parameter estimation of finite mixture models. In the case of mixture models, non-global maxima often involve having too many components of a mixture model in one part of the space and too few in another, widely separated part of the space. To escape from such configurations we repeatedly perform simultaneous split and merge operations using a new criterion for efficiently selecting the split and merge candidates. We apply the proposed algorithm to the training of Gaussian mixtures and mixtures of factor analyzers using synthetic and real data and show the effectiveness of using the split and merge operations to improve the likelihood of both the training data and of held-out test data. 1 INTRODUCTION Mixture density models, in particular normal mixtures, have been extensively used in the field of statistical pattern recognition [1]. Recently, more sophisticated mixture density models such as mixtures of latent variable models (e.g., probabilistic PCA or factor analysis) have been proposed to approximate the underlying data manifold [2]-[4].