20,779 research outputs found
Estimating False Discovery Proportion Under Arbitrary Covariance Dependence
Multiple hypothesis testing is a fundamental problem in high dimensional
inference, with wide applications in many scientific fields. In genome-wide
association studies, tens of thousands of tests are performed simultaneously to
find if any SNPs are associated with some traits and those tests are
correlated. When test statistics are correlated, false discovery control
becomes very challenging under arbitrary dependence. In the current paper, we
propose a novel method based on principal factor approximation, which
successfully subtracts the common dependence and weakens significantly the
correlation structure, to deal with an arbitrary dependence structure. We
derive an approximate expression for false discovery proportion (FDP) in large
scale multiple testing when a common threshold is used and provide a consistent
estimate of realized FDP. This result has important applications in controlling
FDR and FDP. Our estimate of realized FDP compares favorably with Efron
(2007)'s approach, as demonstrated in the simulated examples. Our approach is
further illustrated by some real data applications. We also propose a
dependence-adjusted procedure, which is more powerful than the fixed threshold
procedure.Comment: 51 pages, 7 figures. arXiv admin note: substantial text overlap with
arXiv:1012.439
A semi-proximal-based strictly contractive Peaceman-Rachford splitting method
The Peaceman-Rachford splitting method is very efficient for minimizing sum
of two functions each depends on its variable, and the constraint is a linear
equality. However, its convergence was not guaranteed without extra
requirements. Very recently, He et al. (SIAM J. Optim. 24: 1011 - 1040, 2014)
proved the convergence of a strictly contractive Peaceman-Rachford splitting
method by employing a suitable underdetermined relaxation factor. In this
paper, we further extend the so-called strictly contractive Peaceman-Rachford
splitting method by using two different relaxation factors, and to make the
method more flexible, we introduce semi-proximal terms to the subproblems. We
characterize the relation of these two factors, and show that one factor is
always underdetermined while the other one is allowed to be larger than 1. Such
a flexible conditions makes it possible to cover the Glowinski's ADMM whith
larger stepsize. We show that the proposed modified strictly contractive
Peaceman-Rachford splitting method is convergent and also prove
convergence rate in ergodic and nonergodic sense, respectively. The numerical
tests on an extensive collection of problems demonstrate the efficiency of the
proposed method
Matching Theory for Future Wireless Networks: Fundamentals and Applications
The emergence of novel wireless networking paradigms such as small cell and
cognitive radio networks has forever transformed the way in which wireless
systems are operated. In particular, the need for self-organizing solutions to
manage the scarce spectral resources has become a prevalent theme in many
emerging wireless systems. In this paper, the first comprehensive tutorial on
the use of matching theory, a Nobelprize winning framework, for resource
management in wireless networks is developed. To cater for the unique features
of emerging wireless networks, a novel, wireless-oriented classification of
matching theory is proposed. Then, the key solution concepts and algorithmic
implementations of this framework are exposed. Then, the developed concepts are
applied in three important wireless networking areas in order to demonstrate
the usefulness of this analytical tool. Results show how matching theory can
effectively improve the performance of resource allocation in all three
applications discussed
Relation Networks for Object Detection
Although it is well believed for years that modeling relations between
objects would help object recognition, there has not been evidence that the
idea is working in the deep learning era. All state-of-the-art object detection
systems still rely on recognizing object instances individually, without
exploiting their relations during learning.
This work proposes an object relation module. It processes a set of objects
simultaneously through interaction between their appearance feature and
geometry, thus allowing modeling of their relations. It is lightweight and
in-place. It does not require additional supervision and is easy to embed in
existing networks. It is shown effective on improving object recognition and
duplicate removal steps in the modern object detection pipeline. It verifies
the efficacy of modeling object relations in CNN based detection. It gives rise
to the first fully end-to-end object detector
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