title: Classification via Bayesian Nonparametric Learning of Affine Subspaces.
abstract: It has become common for data sets to contain large numbers of variables in studies conducted in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric procedures tend to be non-robust because of insufficient data on these high dimensional spaces. This is particularly true when interest lies in building efficient classifiers in the presence of many predictor variables. When dealing with these types of data, it is often the case that most of the variability tends to lie along a few directions, or more generally along a much smaller dimensional submanifold of the data space. In this article, we propose a class of models that flexibly learn about this submanifold while simultaneously performing dimension reduction in classification. This methodology, allows the cell probabilities to vary nonparametrically based on a few coordinates expressed as linear combinations of the predictors. Also, as opposed to many black-box methods for dimensionality reduction, the proposed model is appealing in having clearly interpretable and identifiable parameters which provide insight into which predictors are important in determining accurate classification boundaries. Gibbs sampling methods are developed for posterior computation, and the methods are illustrated using simulated and real data applications.
authors.affiliation: Departamento de Estadística, Pontificia Universidad Católica de Chile, page@mat.puc.cl.
authors.forename: Garritt
authors.initials: G
authors.lastname: Page
authors.forename: Abhishek
authors.initials: A
authors.lastname: Bhattacharya
authors.forename: David
authors.initials: D
authors.lastname: Dunson
keywords: Classifier; Dimension reduction; Nonparametric Bayes; Variable selection
references.citation: BMC Bioinformatics. 2010 Nov 23;11:571
references.pmid: 21092268
references.citation: Ann Inst Stat Math. 2012 Aug 1;64(4):687-714
references.pmid: 22984295
references.citation: IEEE Trans Signal Process. 2010 Dec;58(12):6140-6155
references.pmid: 23894225
references.citation: J R Stat Soc Series B Stat Methodol. 2011 Jan 1;73(1):37-57
references.pmid: 21687778
references.citation: Biometrics. 2011 Sep;67(3):886-95
references.pmid: 21039398
references.citation: Biometrika. 2011 Jun;98(2):291-306
references.pmid: 23049129
references.citation: J Multivar Anal. 2012 Oct 1;111:1-19
references.pmid: 22754028