This document is about the multi-document Von-Mises-Fisher mixture model with a Dirichlet prior, referred to as VMFMix. VMFMix is analogous to Latent Dirichlet Allocation (LDA) in that they can capture the co-occurrence patterns acorss multiple documents. The difference is that in VMFMix, the topic-word distribution is defined on a continuous n-dimensional hypersphere. Hence VMFMix is used to d...

The multiple testing procedure by Efron et al. (Efron et al., 2000; Efron et al., 2001) using mixture model in an Empirical Bayes setting has recently received a fair bit of attention. This procedure departs from most traditional approaches in that it attempts to borrow strength across variables to improve inference. The relative innovative nature of this technique warrants a careful study into...

This is where is the estimated posteriori probability that xj belongs to term i, is the estimated mixing coefficient, is the estimated mean, and is the estimated variance of the ith term. We have written our estimate as to explicitly draw attention to the dependence of it on the estimated parameter set . The reader is referred to the works of McLachlan, G.J., and Basford, K.E. (1988) and Titf̂ x...

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...