We propose an extension of a result by Repetowicz et al. (Repetowicz 2004) about Wick’s theorem and its applications: we first show that Wick’s theorem can be extended to the uniform distribution on the sphere and then to the whole class of elliptical distributions. Then, as a special case, we detail this result for distributions that are scale mixtures of Gaussians. Finally, we show that these...

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the mult...

Nowadays, geographic information related to Twitter is crucially important for fine-grained applications. However, the amount of geographic information available on Twitter is low, which makes the pursuit of many applications challenging. Under such circumstances, estimating the location of a tweet is an important goal of the study. Unlike most previous studies that estimate the pre-defined dis...

We present a novel algorithm called PG-means which is able to learn the number of clusters in a classical Gaussian mixture model. Our method is robust and efficient; it uses statistical hypothesis tests on one-dimensional projections of the data and model to determine if the examples are well represented by the model. In so doing, we are applying a statistical test for the entire model at once,...

The mixtures of experts (ME) model ooers a modular structure suitable for a divide-and-conquer approach to pattern recognition. It has a probabilistic interpretation in terms of a mixture model, which forms the basis for the error function associated with MEs. In this paper, it is shown that for classiication problems the minimization of this ME error function leads to ME outputs estimating the...

This paper addresses the problem of the adaptation of a Gaussian Mixture Regression (GMR) to a new input distribution, using a limited amount of input-only examples. We propose a new model for GMR adaptation, called Joint GMR (J-GMR), that extends the previously published framework of Cascaded GMR (C-GMR). We provide an exact EM training algorithm for the J-GMR. We discuss the merits of the J-G...

Empirical evidence, obtained from nonparametric estimation of the income distribution, exhibits strong heterogeneity in most populations of interest. It is common, therefore, to suspect that the population is composed of several homogeneous subpopulations. Such an assumption leads us to consider mixed income distributions whose components feature the distributions of the incomes of a particular...

Random vectors on the positive orthant whose distributions possess hidden regular variation are a subclass of those whose distributions are multivariate regularly varying. The concept is an elaboration of the coefficient of tail dependence of Ledford and Tawn(1996, 1997). We provide characterizations and examples of such distribution in terms of mixture models and product models.

In data sets that consist of a large number of clusters, a frequent goal of the analysis is to detect whether heterogeneity exists between clusters. A standard approach taken in the statistical literature is to model the heterogeneity in the framework of a mixture model and to derive a score test to detect heterogeneity. The likelihood function, from which the score test derives, depends heavil...

This1 chapter addresses the problems of minimum mean square error (MMSE) estimation in non-Gaussian linear and nonlinear systems. In many scientific and practical problems (such as control, astronomy, economic data analysis, communication and radar surveillance), estimation of time-varying system state using a sequence of noisy measurements is performed using the dynamic state-space (DSS) model...