Partial Least Squares: A Versatile Tool for the Analysis of High-Dimensional Genomic Data

Partial Least Squares (PLS) is a highly efficient statistical regression technique that is well suited for the analysis of high-dimensional genomic data. In this paper we review the theory and applications of PLS both under methodological and biological points of view. Focusing on microarray expression data we provide a systematic comparison of the PLS approaches currently employed, and discuss problems as different as tumor classification, identification of relevant genes, survival analysis and modeling of gene networks

Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.Comment: 30 pages, 2 figure

Optimal classifier selection and negative bias in error rate estimation: An empirical study on high-dimensional prediction

In biometric practice, researchers often apply a large number of different methods in a "trial-and-error" strategy to get as much as possible out of their data and, due to publication pressure or pressure from the consulting customer, present only the most favorable results. This strategy may induce a substantial optimistic bias in prediction error estimation, which is quantitatively assessed in the present manuscript. The focus of our work is on class prediction based on high-dimensional data (e.g. microarray data), since such analyses are particularly exposed to this kind of bias. In our study we consider a total of 124 variants of classifiers (possibly including variable selection or tuning steps) within a cross-validation evaluation scheme. The classifiers are applied to original and modified real microarray data sets, some of which are obtained by randomly permuting the class labels to mimic non-informative predictors while preserving their correlation structure. We then assess the minimal misclassification rate over the different variants of classifiers in order to quantify the bias arising when the optimal classifier is selected a posteriori in a data-driven manner. The bias resulting from the parameter tuning (including gene selection parameters as a special case) and the bias resulting from the choice of the classification method are examined both separately and jointly. We conclude that the strategy to present only the optimal result is not acceptable, and suggest alternative approaches for properly reporting classification accuracy

High Dimensional Classification with combined Adaptive Sparse PLS and Logistic Regression

Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection, which combined constitute a powerful framework for classification, as well as data visualization and interpretation. However, current proposed combinations lead to instable and non convergent methods due to inappropriate computational frameworks. We hereby propose a stable and convergent approach for classification in high dimensional based on sparse Partial Least Squares (sparse PLS). Results: We start by proposing a new solution for the sparse PLS problem that is based on proximal operators for the case of univariate responses. Then we develop an adaptive version of the sparse PLS for classification, which combines iterative optimization of logistic regression and sparse PLS to ensure convergence and stability. Our results are confirmed on synthetic and experimental data. In particular we show how crucial convergence and stability can be when cross-validation is involved for calibration purposes. Using gene expression data we explore the prediction of breast cancer relapse. We also propose a multicategorial version of our method on the prediction of cell-types based on single-cell expression data. Availability: Our approach is implemented in the plsgenomics R-package.Comment: 9 pages, 3 figures, 4 tables + Supplementary Materials 8 pages, 3 figures, 10 table

Classification of gene expression autism data based on adaptive penalized logistic regression

The common issues of high-dimensional gene expression data are that many of genes may not be relevant to their diseases. Gene selection has been proved to be an effective way to improve the result of many classification methods. In this paper, an adaptive penalized logistic regression is proposed, with the aim of identification relevant genes and provides high classification accuracy of autism data, by combining the logistic regression with the weighted L1-norm. Experimental results show that the proposed method significantly outperforms two competitor methods in terms of classification accuracy, G-mean, and area under the curve. Thus, the proposed method can be useful for other cancer classification using DNA gene expression data in the real clinical practice

An efficient gene selection method for high-dimensional microarray data based on sparse logistic regression

Gene selection in high-dimensional microarray data has become increasingly important in cancer classification. The high dimensionality of microarray data makes the application of many expert classifier systems difficult.To simultaneously perform gene selection and estimate the gene coefficientsin the model, sparse logistic regression using L1-norm was successfully applied in high-dimensional microarray data. However, when there are highcorrelation among genes, L1-norm cannot perform effectively. To addressthis issue, an efficient sparse logistic regression (ESLR) is proposed. Extensive applications using high-dimensional gene expression data show that ourproposed method can successfully select the highly correlated genes. Furthermore, ESLR is compared with other three methods and exhibits competitiveperformance in both classification accuracy and Youdens index. Thus, wecan conclude that ESLR has significant impact in sparse logistic regressionmethod and could be used in the field of high-dimensional microarray datacancer classification

Extreme Value Distribution Based Gene Selection Criteria for Discriminant Microarray Data Analysis Using Logistic Regression

One important issue commonly encountered in the analysis of microarray data is to decide which and how many genes should be selected for further studies. For discriminant microarray data analyses based on statistical models, such as the logistic regression models, gene selection can be accomplished by a comparison of the maximum likelihood of the model given the real data, $\hat{L}(D|M)$, and the expected maximum likelihood of the model given an ensemble of surrogate data with randomly permuted label, $\hat{L}(D_0|M)$. Typically, the computational burden for obtaining $\hat{L}(D_0|M)$ is immense, often exceeding the limits of computing available resources by orders of magnitude. Here, we propose an approach that circumvents such heavy computations by mapping the simulation problem to an extreme-value problem. We present the derivation of an asymptotic distribution of the extreme-value as well as its mean, median, and variance. Using this distribution, we propose two gene selection criteria, and we apply them to two microarray datasets and three classification tasks for illustration.Comment: to be published in Journal of Computational Biology (2004