15,036 research outputs found
Sure Screening for Gaussian Graphical Models
We propose {graphical sure screening}, or GRASS, a very simple and
computationally-efficient screening procedure for recovering the structure of a
Gaussian graphical model in the high-dimensional setting. The GRASS estimate of
the conditional dependence graph is obtained by thresholding the elements of
the sample covariance matrix. The proposed approach possesses the sure
screening property: with very high probability, the GRASS estimated edge set
contains the true edge set. Furthermore, with high probability, the size of the
estimated edge set is controlled. We provide a choice of threshold for GRASS
that can control the expected false positive rate. We illustrate the
performance of GRASS in a simulation study and on a gene expression data set,
and show that in practice it performs quite competitively with more complex and
computationally-demanding techniques for graph estimation
A fast algorithm for detecting gene-gene interactions in genome-wide association studies
With the recent advent of high-throughput genotyping techniques, genetic data
for genome-wide association studies (GWAS) have become increasingly available,
which entails the development of efficient and effective statistical
approaches. Although many such approaches have been developed and used to
identify single-nucleotide polymorphisms (SNPs) that are associated with
complex traits or diseases, few are able to detect gene-gene interactions among
different SNPs. Genetic interactions, also known as epistasis, have been
recognized to play a pivotal role in contributing to the genetic variation of
phenotypic traits. However, because of an extremely large number of SNP-SNP
combinations in GWAS, the model dimensionality can quickly become so
overwhelming that no prevailing variable selection methods are capable of
handling this problem. In this paper, we present a statistical framework for
characterizing main genetic effects and epistatic interactions in a GWAS study.
Specifically, we first propose a two-stage sure independence screening (TS-SIS)
procedure and generate a pool of candidate SNPs and interactions, which serve
as predictors to explain and predict the phenotypes of a complex trait. We also
propose a rates adjusted thresholding estimation (RATE) approach to determine
the size of the reduced model selected by an independence screening.
Regularization regression methods, such as LASSO or SCAD, are then applied to
further identify important genetic effects. Simulation studies show that the
TS-SIS procedure is computationally efficient and has an outstanding finite
sample performance in selecting potential SNPs as well as gene-gene
interactions. We apply the proposed framework to analyze an
ultrahigh-dimensional GWAS data set from the Framingham Heart Study, and select
23 active SNPs and 24 active epistatic interactions for the body mass index
variation. It shows the capability of our procedure to resolve the complexity
of genetic control.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS771 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Beyond Support in Two-Stage Variable Selection
Numerous variable selection methods rely on a two-stage procedure, where a
sparsity-inducing penalty is used in the first stage to predict the support,
which is then conveyed to the second stage for estimation or inference
purposes. In this framework, the first stage screens variables to find a set of
possibly relevant variables and the second stage operates on this set of
candidate variables, to improve estimation accuracy or to assess the
uncertainty associated to the selection of variables. We advocate that more
information can be conveyed from the first stage to the second one: we use the
magnitude of the coefficients estimated in the first stage to define an
adaptive penalty that is applied at the second stage. We give two examples of
procedures that can benefit from the proposed transfer of information, in
estimation and inference problems respectively. Extensive simulations
demonstrate that this transfer is particularly efficient when each stage
operates on distinct subsamples. This separation plays a crucial role for the
computation of calibrated p-values, allowing to control the False Discovery
Rate. In this setup, the proposed transfer results in sensitivity gains ranging
from 50% to 100% compared to state-of-the-art
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