123,690 research outputs found
Estimation for ultra-high dimensional factor model: a pivotal variable detection based approach
For factor model, the involved covariance matrix often has no row sparse
structure because the common factors may lead some variables to strongly
associate with many others. Under the ultra-high dimensional paradigm, this
feature causes existing methods for sparse covariance matrix in the literature
not directly applicable. In this paper, for general covariance matrix, a novel
approach to detect these variables that is called the pivotal variables is
suggested. Then, two-stage estimation procedures are proposed to handle
ultra-high dimensionality in factor model. In these procedures, pivotal
variable detection is performed as a screening step and then existing
approaches are applied to refine the working model. The estimation efficiency
can be promoted under weaker assumptions on the model structure. Simulations
are conducted to examine the performance of the new method and a real dataset
is analysed for illustration
Deep-gKnock: nonlinear group-feature selection with deep neural network
Feature selection is central to contemporary high-dimensional data analysis.
Grouping structure among features arises naturally in various scientific
problems. Many methods have been proposed to incorporate the grouping structure
information into feature selection. However, these methods are normally
restricted to a linear regression setting. To relax the linear constraint, we
combine the deep neural networks (DNNs) with the recent Knockoffs technique,
which has been successful in an individual feature selection context. We
propose Deep-gKnock (Deep group-feature selection using Knockoffs) as a
methodology for model interpretation and dimension reduction. Deep-gKnock
performs model-free group-feature selection by controlling group-wise False
Discovery Rate (gFDR). Our method improves the interpretability and
reproducibility of DNNs. Experimental results on both synthetic and real data
demonstrate that our method achieves superior power and accurate gFDR control
compared with state-of-the-art methods
Theory of Bergman Spaces in the Unit Ball of
There has been a great deal of work done in recent years on weighted Bergman
spaces \apa on the unit ball \bn of \cn, where and
. We extend this study in a very natural way to the case where
is {\em any} real number and . This unified treatment
covers all classical Bergman spaces, Besov spaces, Lipschitz spaces, the Bloch
space, the Hardy space , and the so-called Arveson space. Some of our
results about integral representations, complex interpolation, coefficient
multipliers, and Carleson measures are new even for the ordinary (unweighted)
Bergman spaces of the unit disk.Comment: 83 pages, revised from 2005 manuscrip
Pareto optimal multi-robot motion planning
This paper studies a class of multi-robot coordination problems where a team
of robots aim to reach their goal regions with minimum time and avoid
collisions with obstacles and other robots. A novel numerical algorithm is
proposed to identify the Pareto optimal solutions where no robot can
unilaterally reduce its traveling time without extending others'. The
consistent approximation of the algorithm in the epigraphical profile sense is
guaranteed using set-valued numerical analysis. Experiments on an indoor
multi-robot platform and computer simulations show the anytime property of the
proposed algorithm; i.e., it is able to quickly return a feasible control
policy that safely steers the robots to their goal regions and it keeps
improving policy optimality if more time is given
Stochastic Primal-Dual Coordinate Method with Large Step Size for Composite Optimization with Composite Cone-constraints
We introduce a stochastic coordinate extension of the first-order primal-dual
method studied by Cohen and Zhu (1984) and Zhao and Zhu (2018) to solve
Composite Optimization with Composite Cone-constraints (COCC). In this method,
we randomly choose a block of variables based on the uniform distribution. The
linearization and Bregman-like function (core function) to that randomly
selected block allow us to get simple parallel primal-dual decomposition for
COCC. We obtain almost surely convergence and O(1/t) expected convergence rate
in this work. The high probability complexity bound is also derived in this
paper.Comment: arXiv admin note: substantial text overlap with arXiv:1804.0080
On genetic correlation estimation with summary statistics from genome-wide association studies
Genome-wide association studies (GWAS) have been widely used to examine the
association between single nucleotide polymorphisms (SNPs) and complex traits,
where both the sample size n and the number of SNPs p can be very large.
Recently, cross-trait polygenic risk score (PRS) method has gained extremely
popular for assessing genetic correlation of complex traits based on GWAS
summary statistics (e.g., SNP effect size). However, empirical evidence has
shown a common bias phenomenon that even highly significant cross-trait PRS can
only account for a very small amount of genetic variance (R^2 often <1%). The
aim of this paper is to develop a novel and powerful method to address the bias
phenomenon of cross-trait PRS. We theoretically show that the estimated genetic
correlation is asymptotically biased towards zero when complex traits are
highly polygenic/omnigenic. When all p SNPs are used to construct PRS, we show
that the asymptotic bias of PRS estimator is independent of the unknown number
of causal SNPs m. We propose a consistent PRS estimator to correct such
asymptotic bias. We also develop a novel estimator of genetic correlation which
is solely based on two sets of GWAS summary statistics. In addition, we
investigate whether or not SNP screening by GWAS p-values can lead to improved
estimation and show the effect of overlapping samples among GWAS. Our results
may help demystify and tackle the puzzling "missing genetic overlap" phenomenon
of cross-trait PRS for dissecting the genetic similarity of closely related
heritable traits. We illustrate the finite sample performance of our
bias-corrected PRS estimator by using both numerical experiments and the UK
Biobank data, in which we assess the genetic correlation between brain white
matter tracts and neuropsychiatric disorders.Comment: 50 page
Stochastic Primal-Dual Coordinate Method for Nonlinear Convex Cone Programs
Block coordinate descent (BCD) methods and their variants have been widely
used in coping with large-scale nonconstrained optimization problems in many
fields such as imaging processing, machine learning, compress sensing and so
on. For problem with coupling constraints, Nonlinear convex cone programs
(NCCP) are important problems with many practical applications, but these
problems are hard to solve by using existing block coordinate type methods.
This paper introduces a stochastic primal-dual coordinate (SPDC) method for
solving large-scale NCCP. In this method, we randomly choose a block of
variables based on the uniform distribution. The linearization and Bregman-like
function (core function) to that randomly selected block allow us to get simple
parallel primal-dual decomposition for NCCP. The sequence generated by our
algorithm is proved almost surely converge to an optimal solution of primal
problem. Two types of convergence rate with different probability (almost
surely and expected) are also obtained. The probability complexity bound is
also derived in this paper
C-metric like vacuum with non-negative cosmological constant in five dimensions
We present and analyze an exact 5-dimensional vacuum solution of Einstein
equation with non-negative cosmological constant written in a C-metric like
coordinate. The metric does not contain any black hole horizons in it, but has
two acceleration horizons and a static patch in between. The coordinate system,
horizon geometry and global structures are analyzed in detail, and in the case
of vanishing cosmological constant, a simple exterior geometric interpretation
is given. The metric possesses a spacelike Killing coordinate besides
the timelike coordinate , along which the spacetime can be dimensionally
reduced via Kaluza-Klein mechanism and interpreted as Einstein gravity coupled
to a 4 dimensional Liouville field (and a Maxwell field as well if a boost
operation is performed before the Kaluza-Klein reduction).Comment: PDFLaTeX with 3 PDF figure
Three dimensional central configurations in H3 and S3
We show that each central configuration in the three-dimensional hyperbolic
sphere is equivalent to one central configuration on a particular two-
dimensional hyperbolic sphere. However, there exist both special and ordinary
central configurations in the three-dimensional sphere that are not confined to
any two-dimensional sphere.Comment: 10 pages, 2 figure
Half of an antipodal spherical design
We investigate several antipodal spherical designs on whether we can choose
half of the points, one from each antipodal pair, such that they are balanced
at the origin. In particular, root systems of type A, D and E, minimal points
of Leech lattice and the unique tight 7-design on are studied. We also
study a half of an antipodal spherical design from the viewpoint of association
schemes and spherical designs of harmonic index
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