A novel framework for parsimonious multivariate analysis

This paper proposes a framework in which a multivariate analysis method (MVA) guides a selection of input variables that leads to a sparse feature extraction. This framework, called parsimonious MVA, is specially suited for high dimensional data such as gene arrays, digital pictures, etc. The feature selection relies on the analysis of consistency in the behaviour of the input variables through the elements of an ensemble of MVA projection matrices. The ensemble is constructed following a bootstrap that builds on an efficient and generalized MVA formulation that covers PCA, CCA and OPLS. Moreover, it allows the estimation of the relative relevance of each selected input variable. Experimental results point out that the features extracted by the parsimonious MVA have excellent discrimination power, comparing favorably with state-of-the-art methods, and are potentially useful to build interpretable features. Besides, the parsimonious feature extractor is shown to be robust against to parameter selection, as we all computationally efficient.This work has been partly funded by the Spanish MINECO grant TEC2014-52289R and TEC2013-48439-C4-1-R. The authors want to thank the action editor and the reviewers for their valuable feedback

Restricted Covariance Priors with Applications in Spatial Statistics

We present a Bayesian model for area-level count data that uses Gaussian random effects with a novel type of G-Wishart prior on the inverse variance--covariance matrix. Specifically, we introduce a new distribution called the truncated G-Wishart distribution that has support over precision matrices that lead to positive associations between the random effects of neighboring regions while preserving conditional independence of non-neighboring regions. We describe Markov chain Monte Carlo sampling algorithms for the truncated G-Wishart prior in a disease mapping context and compare our results to Bayesian hierarchical models based on intrinsic autoregression priors. A simulation study illustrates that using the truncated G-Wishart prior improves over the intrinsic autoregressive priors when there are discontinuities in the disease risk surface. The new model is applied to an analysis of cancer incidence data in Washington State.Comment: Published at http://dx.doi.org/10.1214/14-BA927 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Model-based clustering via linear cluster-weighted models

A novel family of twelve mixture models with random covariates, nested in the linear $t$ cluster-weighted model (CWM), is introduced for model-based clustering. The linear $t$ CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented