Mixtures of Common Skew-t Factor Analyzers

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well-modelled by the mixtures of factor analyzers model or a variant thereof. Furthermore, assuming that the component densities follow a skew-t distribution allows robust clustering of skewed data. The alternating expectation-conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our model is applied to real and simulated data.This paper marks the first time that skewed common factors have been used

Bayesian inference for the multivariate skew-normal model: a Population Monte Carlo approach

Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory solutions for estimation and testing problems. A general population Monte Carlo algorithm is proposed which: 1) exploits the latent structure stochastic representation of skew-normal random variables to provide a full Bayesian analysis of the model and 2) accounts for the presence of constraints in the parameter space. The proposed approach can be defined as weakly informative, since the prior distribution approximates the actual reference prior for the shape parameter vector. Results are compared with the existing classical solutions and the practical implementation of the algorithm is illustrated via a simulation study and a real data example. A generalization to the matrix variate regression model with skew-normal error is also presented

Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions

The classical mixture of linear experts (MoE) model is one of the widespread statistical frameworks for modeling, classification, and clustering of data. Built on the normality assumption of the error terms for mathematical and computational convenience, the classical MoE model has two challenges: 1) it is sensitive to atypical observations and outliers, and 2) it might produce misleading inferential results for censored data. The paper is then aimed to resolve these two challenges, simultaneously, by proposing a novel robust MoE model for model-based clustering and discriminant censored data with the scale-mixture of normal class of distributions for the unobserved error terms. Based on this novel model, we develop an analytical expectation-maximization (EM) type algorithm to obtain the maximum likelihood parameter estimates. Simulation studies are carried out to examine the performance, effectiveness, and robustness of the proposed methodology. Finally, real data is used to illustrate the superiority of the new model.Comment: 21 pages

Parametric modeling of cellular state transitions as measured with flow cytometry

<p>Abstract</p> <p>Background</p> <p>Gradual or sudden transitions among different states as exhibited by cell populations in a biological sample under particular conditions or stimuli can be detected and profiled by flow cytometric time course data. Often such temporal profiles contain features due to transient states that present unique modeling challenges. These could range from asymmetric non-Gaussian distributions to outliers and tail subpopulations, which need to be modeled with precision and rigor.</p> <p>Results</p> <p>To ensure precision and rigor, we propose a parametric modeling framework StateProfiler based on finite mixtures of skew <it>t</it>-Normal distributions that are robust against non-Gaussian features caused by asymmetry and outliers in data. Further, we present in StateProfiler a new greedy EM algorithm for fast and optimal model selection. The parsimonious approach of our greedy algorithm allows us to detect the genuine dynamic variation in the key features as and when they appear in time course data. We also present a procedure to construct a well-fitted profile by merging any redundant model components in a way that minimizes change in entropy of the resulting model. This allows precise profiling of unusually shaped distributions and less well-separated features that may appear due to cellular heterogeneity even within clonal populations.</p> <p>Conclusions</p> <p>By modeling flow cytometric data measured over time course and marker space with StateProfiler, specific parametric characteristics of cellular states can be identified. The parameters are then tested statistically for learning global and local patterns of spatio-temporal change. We applied StateProfiler to identify the temporal features of yeast cell cycle progression based on knockout of S-phase triggering cyclins Clb5 and Clb6, and then compared the S-phase delay phenotypes due to differential regulation of the two cyclins. We also used StateProfiler to construct the temporal profile of clonal divergence underlying lineage selection in mammalian hematopoietic progenitor cells.</p

Flexible Mixture Modeling with the Polynomial Gaussian Cluster-Weighted Model

In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the mixture components by considering a polynomial regression. Secondly, it is not restricted to be used for model-based clustering only being contextualized in the most general model-based classification framework. Maximum likelihood parameter estimates are derived using the EM algorithm and model selection is carried out using the Bayesian information criterion (BIC) and the integrated completed likelihood (ICL). The paper also investigates the conditions under which the posterior probabilities of component-membership from a polynomial Gaussian CWM coincide with those of other well-established mixture-models which are related to it. With respect to these models, the polynomial Gaussian CWM has shown to give excellent clustering and classification results when applied to the artificial and real data considered in the paper