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.

Cluster analysis is a fundamental principle in exploratory data analysis, providing the user with a description of the group structure of given data. A key problem in this context is the interpretation and visualization of clustering solutions in high-dimensional or abstract data spaces. In particular, probabilistic descriptions of the group structure, essential to capture inter-cluster relationships, are hardly assessable by simple inspection ofthe probabilistic assignment variables. VVe present a novel approach to the visualization of group structure. It is based on a statistical model of the object assignments which have been observed or estimated by a probabilistic clustering procedure. The objects or data points are embedded in a low dimensional Euclidean space by approximating the observed data statistics with a Gaussian mixture model. The algorithm provides a new approach to the visualization of the inherent structure for a broad variety of data types, e.g.

A directed generative model for binary data using a small number of hidden continuous units is investigated. The relationships between the correlations of the underlying continuous Gaussian variables and the binary output variables are utilized to learn the appropriate weights of the network. The advantages of this approach are illustrated on a translationally invariant binary distribution and on handwritten digit images. Introduction Principal Components Analysis (PCA) is a widely used statistical technique for representing data with a large number of variables [1]. It is based upon the assumption that although the data is embedded in a high dimensional vector space, most of the variability in the data is captured by a much lower climensional manifold.

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.

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.

We present an unsupervised classification algorithm based on an ICA mixture model. The ICA mixture model assumes that the observed data can be categorized into several mutually exclusive data classes in which the components in each class are generated by a linear mixture of independent sources. The algorithm finds the independent sources, the mixing matrix for each class and also computes the class membership probability for each data point. This approach extends the Gaussian mixture model so that the classes can have non-Gaussian structure. We demonstrate that this method can learn efficient codes to represent images of natural scenes and text.

The difficulties lie in the Monte-Carlo E-step which consists of sampling from the posterior distribution of the hidden variables given the observations. The new idea presented in this paper is to generate samples from a Gaussian approximation to the true posterior from which it is easy to obtain independent samples. The parameters of the Gaussian approximation are either derived from the extended Kalman filter or the Fisher scoring algorithm. In case the posterior density is multimodal we propose to approximate the posterior by a sum of Gaussians (mixture of modes approach). We show that sampling from the approximate posterior densities obtained by the above algorithms leads to better models than using point estimates for the hidden states. In our experiment, the Fisher scoring algorithm obtained a better approximation of the posterior mode than the EKF. For a multimodal distribution, the mixture of modes approach gave superior results. 1 INTRODUCTION Nonlinear state space models (NSSM) are a general framework for representing nonlinear time series. In particular, any NARMAX model (nonlinear auto-regressive moving average model with external inputs) can be translated into an equivalent NSSM.

On the other hand, discriminative methods such as support vector machines enable us to construct flexible decision boundaries and often result in classification performance superior to that of the model based approaches. An ideal classifier should combine these two complementary approaches. In this paper, we develop a natural way of achieving this combination by deriving kernel functions for use in discriminative methods such as support vector machines from generative probability models.

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.

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