We show that a simple spectral algorithm for learning a mixture of k spherical Gaussians in R works remarkably well --- it succeeds in identifying the Gaussians assuming essentially the minimum possible separation between their centers that keeps them unique (solving an open problem of [1]). The sample complexity and running time are polynomial in both n and k. The algorithm also works for the more general problem of learning a mixture of "weakly isotropic" distributions (e.g. a mixture of uniform distributions on cubes).

We survey the literature on methods for inference and learning in Bayesian Networks composed of discrete and continuous nodes, in which the continuous nodes have a multivariate Gaussian distribution, whose mean and variance depends on the values of the discrete nodes. We also briefly consider hybrid Dynamic Bayesian Networks, an extension of switching Kalman filters. This report is meant to summarize what is known at a sufficient level of detail to enable someone to implement the algorithms, but without dwelling on formalities.

This paper develops mixture models for spatially indexed data. We confine attention to the case of finite, typically irregular, patterns of points or regions with prescribed spatial relationships, and to problems where it is only the weights in the mixture that vary from one location to another. Our specific focus is on Poisson distributed data, and applications in disease mapping. We work in a Bayesian framework, with the Poisson parameters drawn from gamma priors, and an unknown number of components. We propose two alternative models for spatially-dependent weights, based on transformations of autoregressive gaussian processes: in one (the Logistic normal model), the mixture component labels are exchangeable, in the other (the Grouped continuous model), they are ordered. Reversible jump Markov chain Monte Carlo algorithms for posterior inference are developed. Finally, the performance of both of these formulations is examined on synthetic data and real data on mortality from rare disease.

Blind linear system identication consists in estimating the parameters of a linear timeinvariant

Based on multivariate mixture models we develop a general approach for clustering and classication. Using various distributions for the variables in the data base to be analyzed, an automatic classication is possible where discrete, categorical and continuos attributes are involved. A set of possibly quite heterogeneous variables is transformed into a purely homogeneous set of \attributes" represented by the posterior probabilities of each entry to belong to the groups. Using a simple technique to control \alive" or \dormant" components, we control the number of components in the mixture. Standard Metropolis-Hastings is used to approximate posterior moments and grouping probabilities. This work has special relevance in data mining of genetic data bases and applications are presented in this eld. Keywords: MCMC, AutoClass, Clustering, Data Mining, Genetics. Submitted to the Journal of Classication y Corresponding author. email: jac@matem.unam.mx . z email: amedra...

The shared mixture classifier extends the conditional mixture classifier by allowing all the mixture components to contribute to the feature density model. We consider mixtures of elliptically symmetrical densities, and provide gradient ascent and expectation maximisation algorithms for maximum likelihood estimation. Three criteria are examined: the joint, non-discriminative and discriminative likelihoods. The relationships between these criteria are discussed, and we compare the performance of shared and conditional mixture classifiers. Results are presented for an application of a shared mixture classifier to the problem of detecting buried land mines using infrared and visual imagery. They show consistently better performance from the shared model.

Introduction Quantitative analysis of magnetic resonance (MR) images deals with the problem of estimating tissue quantities and segmenting the anatomy into contiguous regions of interest. The problem has recently received much attention largely due to the improved delity and resolution of MR imaging systems, and the eective clinical utility of image analysis and understanding in diagnosis, monitoring, and intervention (e.g. see references [1]{ [4]). For example, pathological studies show that many neurological diseases are accompanied by subtle abnormal changes in brain tissue quantities and volumes as shown in reference [2]. Because of the virtual impossibility for clinicians to quantitatively analyze these pathological changes associated with a specic disease directly from MR images, considerable eort is required to develop accurate image analysis algorithms for identifying and quantifying these changes in-vivo as discussed in references [5]{ [11]. The major tasks of MR

Based on multivariate mixture models we develop a general approach for clustering and classi cation in data mining of genetic data bases. Using various distributions for the variables in the data base to be analyzed, an automatic classi cation is possible where discrete, categorical and continuous attributes are involved. A set of possibly quite heterogeneous variables is transformed into a purely homogeneous set of \attributes" represented by the posterior probabilities of each entry to belong to the groups. Using a simple technique to control \alive" or \dormant" components, we control the number of components in the mixture. Numerical techniques are used to approximate posterior moments and grouping probabilities. A simple graphical method is proposed to analyze the results.