A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allows us to summarize the properties of the high-dimensional clusters (or density...

In the mixture distribution model (for continuous and discrete cases) the density function, f̃ (t) is given by a linear combination of k density functions, fi(t), i= 1, · · · ,k, with non-negative weights pi which must sum to 1.0. We propose a generalization of the mixture model where the weights are not restricted to being constant. The specification of the weight functions is not easy because ...

We explore a recently proposed mixture model approach to understanding interactions between conflicting sensory cues. Alternative model formulations, differing in their sensory noise models and inference methods, are compared based on their fit to experimental data. Heavy-tailed sensory likelihoods yield a better description of the subjects’ response behavior than standard Gaussian noise models...

revision date: May 2008 This abstract was prepared by the principal investigator for the project. Please see www.americanchemistry.com/lri for more information about the LRI.

We introduce a one-parameter family of massive Laplacian operators (∆)k∈[0,1) defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for minus the inverse of ∆, the massive Green function, which has the remarkable property of only depending on the local geometry of the graph, and compute its asymptotics. We study the corresponding statistical mechanics model of ...

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...