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.

The Expectation-Maximization (EM) algorithm is an iterative procedure for maximum likelihood parameter estimation from data sets with missing or hidden variables [2]. It has been applied to system identification in linear stochastic state-space models, where the state variables are hidden from the observer and both the state and the parameters of the model have to be estimated simultaneously [9]. We present a generalization of the EM algorithm for parameter estimation in nonlinear dynamical systems. The "expectation" step makes use of Extended Kalman Smoothing to estimate the state, while the "maximization" step re-estimates the parameters using these uncertain state estimates. In general, the nonlinear maximization step is difficult because it requires integrating out the uncertainty in the states.

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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.

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 introduce a semi-supervised support vector machine (S3yM) method. Given a training set of labeled data and a working set of unlabeled data, S3YM constructs a support vector machine using both the training and working sets. We use S3 YM to solve the transduction problem using overall risk minimization (ORM) posed by Yapnik. The transduction problem is to estimate the value of a classification function at the given points in the working set. This contrasts with the standard inductive learning problem of estimating the classification function at all possible values and then using the fixed function to deduce the classes of the working set data.

A new algorithm for Support Vector regression is described.

AR-NNs are a natural generalization of the classic linear autoregressive AR(p) process (2) See, e.g., Brockwell & Davis (1987) for a comprehensive introduction into AR and ARMA (autoregressive moving average) models.

Following recent results [9, 8] showing the importance of the fatshattering dimension in explaining the beneficial effect of a large margin on generalization performance, the current paper investigates the implications of these results for the case of imbalanced datasets and develops two approaches to setting the threshold. The approaches are incorporated into ThetaBoost, a boosting algorithm for dealing with unequal loss functions. The performance of ThetaBoost and the two approaches are tested experimentally.