41,653 research outputs found
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
Ridge Estimation of Inverse Covariance Matrices from High-Dimensional Data
We study ridge estimation of the precision matrix in the high-dimensional
setting where the number of variables is large relative to the sample size. We
first review two archetypal ridge estimators and note that their utilized
penalties do not coincide with common ridge penalties. Subsequently, starting
from a common ridge penalty, analytic expressions are derived for two
alternative ridge estimators of the precision matrix. The alternative
estimators are compared to the archetypes with regard to eigenvalue shrinkage
and risk. The alternatives are also compared to the graphical lasso within the
context of graphical modeling. The comparisons may give reason to prefer the
proposed alternative estimators
Differential expression analysis with global network adjustment
<p>Background: Large-scale chromosomal deletions or other non-specific perturbations of the transcriptome can alter the expression of hundreds or thousands of genes, and it is of biological interest to understand which genes are most profoundly affected. We present a method for predicting a gene’s expression as a function of other genes thereby accounting for the effect of transcriptional regulation that confounds the identification of genes differentially expressed relative to a regulatory network. The challenge in constructing such models is that the number of possible regulator transcripts within a global network is on the order of thousands, and the number of biological samples is typically on the order of 10. Nevertheless, there are large gene expression databases that can be used to construct networks that could be helpful in modeling transcriptional regulation in smaller experiments.</p>
<p>Results: We demonstrate a type of penalized regression model that can be estimated from large gene expression databases, and then applied to smaller experiments. The ridge parameter is selected by minimizing the cross-validation error of the predictions in the independent out-sample. This tends to increase the model stability and leads to a much greater degree of parameter shrinkage, but the resulting biased estimation is mitigated by a second round of regression. Nevertheless, the proposed computationally efficient “over-shrinkage” method outperforms previously used LASSO-based techniques. In two independent datasets, we find that the median proportion of explained variability in expression is approximately 25%, and this results in a substantial increase in the signal-to-noise ratio allowing more powerful inferences on differential gene expression leading to biologically intuitive findings. We also show that a large proportion of gene dependencies are conditional on the biological state, which would be impossible with standard differential expression methods.</p>
<p>Conclusions: By adjusting for the effects of the global network on individual genes, both the sensitivity and reliability of differential expression measures are greatly improved.</p>
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On Nonregularized Estimation of Psychological Networks.
An important goal for psychological science is developing methods to characterize relationships between variables. Customary approaches use structural equation models to connect latent factors to a number of observed measurements, or test causal hypotheses between observed variables. More recently, regularized partial correlation networks have been proposed as an alternative approach for characterizing relationships among variables through off-diagonal elements in the precision matrix. While the graphical Lasso (glasso) has emerged as the default network estimation method, it was optimized in fields outside of psychology with very different needs, such as high dimensional data where the number of variables (p) exceeds the number of observations (n). In this article, we describe the glasso method in the context of the fields where it was developed, and then we demonstrate that the advantages of regularization diminish in settings where psychological networks are often fitted ( p≪n ). We first show that improved properties of the precision matrix, such as eigenvalue estimation, and predictive accuracy with cross-validation are not always appreciable. We then introduce nonregularized methods based on multiple regression and a nonparametric bootstrap strategy, after which we characterize performance with extensive simulations. Our results demonstrate that the nonregularized methods can be used to reduce the false-positive rate, compared to glasso, and they appear to provide consistent performance across sparsity levels, sample composition (p/n), and partial correlation size. We end by reviewing recent findings in the statistics literature that suggest alternative methods often have superior performance than glasso, as well as suggesting areas for future research in psychology. The nonregularized methods have been implemented in the R package GGMnonreg
Feature selection guided by structural information
In generalized linear regression problems with an abundant number of
features, lasso-type regularization which imposes an -constraint on the
regression coefficients has become a widely established technique. Deficiencies
of the lasso in certain scenarios, notably strongly correlated design, were
unmasked when Zou and Hastie [J. Roy. Statist. Soc. Ser. B 67 (2005) 301--320]
introduced the elastic net. In this paper we propose to extend the elastic net
by admitting general nonnegative quadratic constraints as a second form of
regularization. The generalized ridge-type constraint will typically make use
of the known association structure of features, for example, by using temporal-
or spatial closeness. We study properties of the resulting "structured elastic
net" regression estimation procedure, including basic asymptotics and the issue
of model selection consistency. In this vein, we provide an analog to the
so-called "irrepresentable condition" which holds for the lasso. Moreover, we
outline algorithmic solutions for the structured elastic net within the
generalized linear model family. The rationale and the performance of our
approach is illustrated by means of simulated and real world data, with a focus
on signal regression.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS302 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the potential of Cherenkov Telescope Arrays and KM3 Neutrino Telescopes for the detection of extended sources
We discuss the discovery potential of extended very-high-energy (VHE)
neutrino sources by the future KM3 Neutrino Telescope (KM3NeT) in the context
of the constraining power of the Cherenkov Telescope Array (CTA), designed for
deep surveys of the sky in VHE gamma rays. The study is based on a comparative
analysis of sensitivities of KM3NeT and CTA. We show that a minimum gamma-ray
energy flux of E^2{\phi}_{\gamma}(10 TeV) > 1x10^{-12} TeV cm^{-2} s^{-1} is
required to identify a possible neutrino counterpart with a 3{\sigma}
significance and 10 years of KM3NeT observations with upgoing muons, if the
source has an angular size of R_{src} = 0.1 deg and emits gamma rays with an
E^{-2} energy spectrum through a full hadronic mechanism. This minimum
gamma-ray flux is increased to the level of E^2{\phi}_{\gamma}(10 TeV) >
2x10^{-11} TeV cm^{-2} s^{-1} in case of sources with radial extension of
R_{src} = 2.0 deg. The analysis methods are applied to the supernova remnant RX
J1713.7-3946 and the Galactic Center Ridge, as well as to the recent HAWC
catalog of multi-TeV gamma-ray sources.Comment: 15 pages, 7 figure
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