983 research outputs found
The bootstrap -A review
The bootstrap, extensively studied during the last decade, has become a powerful tool in different areas of Statistical Inference. In this work, we present the main ideas of bootstrap methodology in several contexts, citing the most relevant contributions and illustrating with examples and simulation studies some interesting aspects
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
Testing Conditional Independence in Supervised Learning Algorithms
We propose the conditional predictive impact (CPI), a consistent and unbiased
estimator of the association between one or several features and a given
outcome, conditional on a reduced feature set. Building on the knockoff
framework of Cand\`es et al. (2018), we develop a novel testing procedure that
works in conjunction with any valid knockoff sampler, supervised learning
algorithm, and loss function. The CPI can be efficiently computed for
high-dimensional data without any sparsity constraints. We demonstrate
convergence criteria for the CPI and develop statistical inference procedures
for evaluating its magnitude, significance, and precision. These tests aid in
feature and model selection, extending traditional frequentist and Bayesian
techniques to general supervised learning tasks. The CPI may also be applied in
causal discovery to identify underlying multivariate graph structures. We test
our method using various algorithms, including linear regression, neural
networks, random forests, and support vector machines. Empirical results show
that the CPI compares favorably to alternative variable importance measures and
other nonparametric tests of conditional independence on a diverse array of
real and simulated datasets. Simulations confirm that our inference procedures
successfully control Type I error and achieve nominal coverage probability. Our
method has been implemented in an R package, cpi, which can be downloaded from
https://github.com/dswatson/cpi
Model-Based Clustering and Classification of Functional Data
The problem of complex data analysis is a central topic of modern statistical
science and learning systems and is becoming of broader interest with the
increasing prevalence of high-dimensional data. The challenge is to develop
statistical models and autonomous algorithms that are able to acquire knowledge
from raw data for exploratory analysis, which can be achieved through
clustering techniques or to make predictions of future data via classification
(i.e., discriminant analysis) techniques. Latent data models, including mixture
model-based approaches are one of the most popular and successful approaches in
both the unsupervised context (i.e., clustering) and the supervised one (i.e,
classification or discrimination). Although traditionally tools of multivariate
analysis, they are growing in popularity when considered in the framework of
functional data analysis (FDA). FDA is the data analysis paradigm in which the
individual data units are functions (e.g., curves, surfaces), rather than
simple vectors. In many areas of application, the analyzed data are indeed
often available in the form of discretized values of functions or curves (e.g.,
time series, waveforms) and surfaces (e.g., 2d-images, spatio-temporal data).
This functional aspect of the data adds additional difficulties compared to the
case of a classical multivariate (non-functional) data analysis. We review and
present approaches for model-based clustering and classification of functional
data. We derive well-established statistical models along with efficient
algorithmic tools to address problems regarding the clustering and the
classification of these high-dimensional data, including their heterogeneity,
missing information, and dynamical hidden structure. The presented models and
algorithms are illustrated on real-world functional data analysis problems from
several application area
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