SHrinkage Covariance Estimation Incorporating Prior Biological Knowledge with Applications to High-Dimensional Data

In ``-omic data'' analysis, information on the structure of covariates are broadly available either from public databases describing gene regulation processes and functional groups such as the Kyoto encyclopedia of genes and genomes (KEGG), or from statistical analyses -- for example in form of partial correlation estimators. The analysis of transcriptomic data might benefit from the incorporation of such prior knowledge. In this paper we focus on the integration of structured information into statistical analyses in which at least one major step involves the estimation of a (high-dimensional) covariance matrix. More precisely, we revisit the recently proposed ``SHrinkage Incorporating Prior'' (SHIP) covariance estimation method which takes into account the group structure of the covariates, and suggest to integrate the SHIP covariance estimator into various multivariate methods such as linear discriminant analysis (LDA), global analysis of covariance (GlobalANCOVA), and regularized generalized canonical correlation analysis (RGCCA). We demonstrate the use of the resulting new methods based on simulations and discuss the benefit of the integration of prior information through the SHIP estimator. Reproducible R codes are available at http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/shipproject/index.html

SHrinkage Covariance Estimation Incorporating Prior Biological Knowledge with Applications to High-Dimensional Data

In ``-omic data'' analysis, information on the structure of covariates are broadly available either from public databases describing gene regulation processes and functional groups such as the Kyoto encyclopedia of genes and genomes (KEGG), or from statistical analyses -- for example in form of partial correlation estimators. The analysis of transcriptomic data might benefit from the incorporation of such prior knowledge. In this paper we focus on the integration of structured information into statistical analyses in which at least one major step involves the estimation of a (high-dimensional) covariance matrix. More precisely, we revisit the recently proposed ``SHrinkage Incorporating Prior'' (SHIP) covariance estimation method which takes into account the group structure of the covariates, and suggest to integrate the SHIP covariance estimator into various multivariate methods such as linear discriminant analysis (LDA), global analysis of covariance (GlobalANCOVA), and regularized generalized canonical correlation analysis (RGCCA). We demonstrate the use of the resulting new methods based on simulations and discuss the benefit of the integration of prior information through the SHIP estimator. Reproducible R codes are available at http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/shipproject/index.html

Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications

Food authenticity studies are concerned with determining if food samples have been correctly labelled or not. Discriminant analysis methods are an integral part of the methodology for food authentication. Motivated by food authenticity applications, a model-based discriminant analysis method that includes variable selection is presented. The discriminant analysis model is fitted in a semi-supervised manner using both labeled and unlabeled data. The method is shown to give excellent classification performance on several high-dimensional multiclass food authenticity datasets with more variables than observations. The variables selected by the proposed method provide information about which variables are meaningful for classification purposes. A headlong search strategy for variable selection is shown to be efficient in terms of computation and achieves excellent classification performance. In applications to several food authenticity datasets, our proposed method outperformed default implementations of Random Forests, AdaBoost, transductive SVMs and Bayesian Multinomial Regression by substantial margins

Functional Bipartite Ranking: a Wavelet-Based Filtering Approach

It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is randomly assigned, the objective is to learn a scoring function s with optimal ROC curve. Based on linear/nonlinear wavelet-based approximations, it is shown how to select compact finite dimensional representations of the input curves adaptively, in order to build accurate ranking rules, using recent advances in the ranking problem for multivariate data with binary feedback. Beyond theoretical considerations, the performance of the learning methods for functional bipartite ranking proposed in this paper are illustrated by numerical experiments

Deep Adaptive Feature Embedding with Local Sample Distributions for Person Re-identification

Person re-identification (re-id) aims to match pedestrians observed by disjoint camera views. It attracts increasing attention in computer vision due to its importance to surveillance system. To combat the major challenge of cross-view visual variations, deep embedding approaches are proposed by learning a compact feature space from images such that the Euclidean distances correspond to their cross-view similarity metric. However, the global Euclidean distance cannot faithfully characterize the ideal similarity in a complex visual feature space because features of pedestrian images exhibit unknown distributions due to large variations in poses, illumination and occlusion. Moreover, intra-personal training samples within a local range are robust to guide deep embedding against uncontrolled variations, which however, cannot be captured by a global Euclidean distance. In this paper, we study the problem of person re-id by proposing a novel sampling to mine suitable \textit{positives} (i.e. intra-class) within a local range to improve the deep embedding in the context of large intra-class variations. Our method is capable of learning a deep similarity metric adaptive to local sample structure by minimizing each sample's local distances while propagating through the relationship between samples to attain the whole intra-class minimization. To this end, a novel objective function is proposed to jointly optimize similarity metric learning, local positive mining and robust deep embedding. This yields local discriminations by selecting local-ranged positive samples, and the learned features are robust to dramatic intra-class variations. Experiments on benchmarks show state-of-the-art results achieved by our method.Comment: Published on Pattern Recognitio

A concave pairwise fusion approach to subgroup analysis

An important step in developing individualized treatment strategies is to correctly identify subgroups of a heterogeneous population, so that specific treatment can be given to each subgroup. In this paper, we consider the situation with samples drawn from a population consisting of subgroups with different means, along with certain covariates. We propose a penalized approach for subgroup analysis based on a regression model, in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject-specific intercepts. We apply concave penalty functions to pairwise differences of the intercepts. This procedure automatically divides the observations into subgroups. We develop an alternating direction method of multipliers algorithm with concave penalties to implement the proposed approach and demonstrate its convergence. We also establish the theoretical properties of our proposed estimator and determine the order requirement of the minimal difference of signals between groups in order to recover them. These results provide a sound basis for making statistical inference in subgroup analysis. Our proposed method is further illustrated by simulation studies and analysis of the Cleveland heart disease dataset

Latent protein trees

Unbiased, label-free proteomics is becoming a powerful technique for measuring protein expression in almost any biological sample. The output of these measurements after preprocessing is a collection of features and their associated intensities for each sample. Subsets of features within the data are from the same peptide, subsets of peptides are from the same protein, and subsets of proteins are in the same biological pathways, therefore, there is the potential for very complex and informative correlational structure inherent in these data. Recent attempts to utilize this data often focus on the identification of single features that are associated with a particular phenotype that is relevant to the experiment. However, to date, there have been no published approaches that directly model what we know to be multiple different levels of correlation structure. Here we present a hierarchical Bayesian model which is specifically designed to model such correlation structure in unbiased, label-free proteomics. This model utilizes partial identification information from peptide sequencing and database lookup as well as the observed correlation in the data to appropriately compress features into latent proteins and to estimate their correlation structure. We demonstrate the effectiveness of the model using artificial/benchmark data and in the context of a series of proteomics measurements of blood plasma from a collection of volunteers who were infected with two different strains of viral influenza.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS639 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org