Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries by such data mining approaches be spurious due to high dimensionality and limited sample size? Can our fundamental assumptions on exogeneity of covariates needed for such variable selection be validated with the data? To answer these questions, we need to derive the distributions of the maximum spurious correlations given certain number of predictors, namely, the distribution of the correlation of a response variable Y with the best s linear combinations of p covariates X, even when X and Y are independent. When the covariance matrix of X possesses the restricted eigenvalue property, we derive such distributions for both finite s and diverging s, using Gaussian approximation and empirical process

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

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting statistical inference. Principal component analysis, commonly referred to as PCA, has become an essential tool for multivariate data analysis and unsupervised dimension reduction, the goal of which is to find a lower dimensional subspace that captures most of the variation in the dataset. This article provides an overview of methodological and theoretical developments of PCA over the past decade, with focus on its applications to big data analytics. We first review the mathematical formulation of PCA and its theoretical development from the view point of perturbation analysis. We then briefly discuss the relationship between PCA and factor analysis as well as its applications to

<b>Motivation:</b> Normalization of microarray data is essential for multiple-array analyses. Several normalization protocols have been proposed based on different biological or statistical assumptions. A fundamental problem arises whether they have effectively normalized arrays. In addition, for a given array, the question arises how to choose a method to most effectively normalize the microarray data.

Macrophages play an important role in the inflammatory responses involved with spinal cord injury (SCI). We have previously demonstrated that infiltrated bone marrow-derived macrophages (BMDMs) engulf myelin debris, forming myelin-laden macrophages (mye-M). These mye-M promote disease progression through their pro-inflammatory phenotype, enhanced neurotoxicity, and impaired phagocytic capacity for apoptotic cells. We thus hypothesize that the excessive accumulation of mye-M is the root of secondary injury, and that targeting mye-M represents an efficient strategy to improve the local inflammatory microenvironment in injured spinal cords and to further motor neuron function recovery. In this study, we administer murine embryonic stem cell conditioned media (ESC-M) as a cell-free stem cell based therapy to treat a mouse model of SCI. We showed that BMDMs, but not microglial cells, engulf myelin debris generated at the injury site. Phagocytosis of myelin debris leads to the formation of mye-M in the injured spinal cord, which are surrounded by activated microglia cells. These mye-M are pro-inflammatory and lose the normal macrophage phagocytic capacity for apoptotic cells. We therefore focus on how to trigger lipid efflux from mye-M and thus restore their function. Using ESC-M as an immune modulating treatment for inflammatory damage after SCI, we rescued mye-M function and improved functional locomotor recovery. ESC-M treatment on mye-M resulted in improved exocytosis of internalized lipids and a normal capacity for apoptotic cell phagocytosis. Furthermore, when ESC-M was administered