Results 1  10
of
10
A Spectral Algorithm for Learning Mixtures of Distributions
 Journal of Computer and System Sciences
, 2002
"... 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 ..."
Abstract

Cited by 57 (4 self)
 Add to MetaCart
(Show Context)
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).
Modelling spatially correlated data via mixtures: a Bayesian approach
 Journal of the Royal Statistical Society, Series B
, 2002
"... 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 ..."
Abstract

Cited by 41 (2 self)
 Add to MetaCart
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 spatiallydependent 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.
Inference and Learning in Hybrid Bayesian Networks
, 1998
"... 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 ..."
Abstract

Cited by 39 (3 self)
 Add to MetaCart
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.
SimulationBased Methods for Blind MaximumLikelihood Filter Identification
, 1999
"... Blind linear system identication consists in estimating the parameters of a linear timeinvariant ..."
Abstract

Cited by 16 (10 self)
 Add to MetaCart
Blind linear system identication consists in estimating the parameters of a linear timeinvariant
Bayesian Clustering and Prediction in Heterogeneous Data Bases Using Multivariate Mixtures
, 2000
"... 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 pos ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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 MetropolisHastings 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...
Shared mixture distributions and shared mixture classifiers
 In Proc. Information, Decision and Control Conference
, 1999
"... 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 li ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
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, nondiscriminative 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.
Bayesian Clustering and Prediction in Genetic Data Bases Using Multivariate Mixtures
"... 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 continuo ..."
Abstract
 Add to MetaCart
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.
Stochastic Model Based Image Analysis
, 2000
"... 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 imagin ..."
Abstract
 Add to MetaCart
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 invivo as discussed in references [5]{ [11]. The major tasks of MR
Contents
"... II Signal conditioning and feature extraction 3 IIA Signals handling............... 3 IIB Steady state or transient information.... 3 ..."
Abstract
 Add to MetaCart
(Show Context)
II Signal conditioning and feature extraction 3 IIA Signals handling............... 3 IIB Steady state or transient information.... 3
Avoiding Spurious Local Maximizers in Mixture Modeling ∗ L.A. GarcaEscudero, A. Gordaliza,
"... The maximum likelihood estimation in the finite mixture of distributions setting is an illposed problem that is treatable, in practice, through the EM algorithm. However, the existence of spurious solutions (singularities and noninteresting local maximizers) makes difficult to find sensible mixtur ..."
Abstract
 Add to MetaCart
The maximum likelihood estimation in the finite mixture of distributions setting is an illposed problem that is treatable, in practice, through the EM algorithm. However, the existence of spurious solutions (singularities and noninteresting local maximizers) makes difficult to find sensible mixture fits for nonexpert practitioners. In this work, a constrained mixture fitting approach is presented with the aim of overcoming the troubles introduced by spurious solutions. Sound mathematical support is provided and, which is more relevant in practice, a feasible algorithm is also given. This algorithm allows for monitoring solutions in terms of the constant involved in the restrictions, which yields a natural way to discard spurious solutions and a valuable tool for data analysts.