3,222 research outputs found
Rejoinder: One-step sparse estimates in nonconcave penalized likelihood models
We would like to take this opportunity to thank the discussants for their
thoughtful comments and encouragements on our work [arXiv:0808.1012]. The
discussants raised a number of issues from theoretical as well as computational
perspectives. Our rejoinder will try to provide some insights into these issues
and address specific questions asked by the discussants.Comment: Published in at http://dx.doi.org/10.1214/07-AOS0316REJ the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A new image thresholding method based on Gaussian mixture model
2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
Global and Quadratic Convergence of Newton Hard-Thresholding Pursuit
Algorithms based on the hard thresholding principle have been well studied
with sounding theoretical guarantees in the compressed sensing and more general
sparsity-constrained optimization. It is widely observed in existing empirical
studies that when a restricted Newton step was used (as the debiasing step),
the hard-thresholding algorithms tend to meet halting conditions in a
significantly low number of iterations and are very efficient. Hence, the thus
obtained Newton hard-thresholding algorithms call for stronger theoretical
guarantees than for their simple hard-thresholding counterparts. This paper
provides a theoretical justification for the use of the restricted Newton step.
We build our theory and algorithm, Newton Hard-Thresholding Pursuit (NHTP), for
the sparsity-constrained optimization. Our main result shows that NHTP is
quadratically convergent under the standard assumption of restricted strong
convexity and smoothness. We also establish its global convergence to a
stationary point under a weaker assumption. In the special case of the
compressive sensing, NHTP effectively reduces to some of the existing
hard-thresholding algorithms with a Newton step. Consequently, our fast
convergence result justifies why those algorithms perform better than without
the Newton step. The efficiency of NHTP was demonstrated on both synthetic and
real data in compressed sensing and sparse logistic regression
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
VISUAL CRYPTOGRAPHY FOR COLOR IMAGES
Visual cryptography is a secret sharing scheme for encrypting a secret image, it is a perfectly secure way that allows secret sharing without any cryptographic computation, which is termed as Visual Cryptography Scheme (VCS). In this paper secret image is divided into shares (printed on transparencies), and each share holds some information. At the receiver this shares are merged to obtain the secret information which is revealed without any complex computation. The proposed algorithm is for color host image, divided into three color planes Red, Green, Blue and merged with secret image which is binarized and divided into shares. The decoding requires aligning the result obtained by merging color host image and shares, so as to obtain the secret image
The Impact of Different Image Thresholding based Mammogram Image Segmentation- A Review
Images are examined and discretized numerical capacities. The goal of computerized image processing is to enhance the nature of pictorial data and to encourage programmed machine elucidation. A computerized imaging framework ought to have fundamental segments for picture procurement, exceptional equipment for encouraging picture applications, and a tremendous measure of memory for capacity and info/yield gadgets. Picture segmentation is the field broadly scrutinized particularly in numerous restorative applications and still offers different difficulties for the specialists. Segmentation is a critical errand to recognize districts suspicious of tumor in computerized mammograms. Every last picture have distinctive sorts of edges and diverse levels of limits. In picture transforming, the most regularly utilized strategy as a part of extricating articles from a picture is "thresholding". Thresholding is a prevalent device for picture segmentation for its straightforwardness, particularly in the fields where ongoing handling is required
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