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1.
An overview on the shrinkage properties of partial least squares regression
Title:
An overview on the shrinkage properties of partial least squares regression
Author:
Nicole Krämer
Nicole Krämer
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Description:
Linear regression, Biased estimators, Mean squared error
Linear regression, Biased estimators, Mean squared error
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Document Type:
article
URL:
http://hdl.handle.net/10.1007/s001800070038z
http://hdl.handle.net/10.1007/s001800070038z
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RePEc: Research Papers in Economics
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2.
The degrees of freedom of partial least squares regression
Title:
The degrees of freedom of partial least squares regression
Author:
Nicole Krämer; Masashi Sugiyama
Nicole Krämer; Masashi Sugiyama
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Description:
The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it makes the statistical analysi...
The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it makes the statistical analysis more involved. In this work, we study the intrinsic complexity of Partial Least Squares Regression. Our contribution is an unbiased estimate of its Degrees of Freedom. It is defined as the trace of the first derivative of the fitted values, seen as a function of the response. We establish two equivalent representations that rely on the close connection of Partial Least Squares to matrix decompositions and Krylov subspace techniques. We show that the Degrees of Freedom depend on the collinearity of the predictor variables: The lower the collinearity is, the higher the Degrees of Freedom are. In particular, they are typically higher than the naive approach that defines the Degrees of Freedom as the number of components. Further, we illustrate that the Degrees of Freedom are useful for model selection. Our experiments indicate that the model complexity based on the Degrees of Freedom estimate is lower than the model complexity of the naive approach. In terms of prediction accuracy, both methods obtain the same accuracy as crossvalidation
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Publisher:
Berlin : WIAS ; Göttingen : Niedersächsische Staats und Universitätsbibliothek ; Hannover : Technische Informationsbibliothek u. Universitätsbibliothek
Year of Publication:
2010
Subjects:
31.00
31.00
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DDC:
519 Probabilities & applied mathematics
(computed)
;
310 Collections of general statistics
(computed)
URL:
http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2012/wias_preprints_1487.pdf
http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2012/wias_preprints_1487.pdf
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GeorgAugustUniversität Göttingen: GOEDOC
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3.
Comments on: Augmenting the bootstrap to analyze high dimensional genomic data
Title:
Comments on: Augmenting the bootstrap to analyze high dimensional genomic data
Author:
AnneLaure Boulesteix
;
Athanassios Kondylis
;
Nicole Krämer
AnneLaure Boulesteix
;
Athanassios Kondylis
;
Nicole Krämer
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Document Type:
article
URL:
http://hdl.handle.net/10.1007/s1174900801030
http://hdl.handle.net/10.1007/s1174900801030
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RePEc: Research Papers in Economics
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4.
ASAP
Title:
ASAP
Author:
Tammo Krueger; Nicole Krämer; Konrad Rieck
Tammo Krueger; Nicole Krämer; Konrad Rieck
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Description:
Automatic inspection of network payloads is a prerequisite for effective analysis of network communication. Security research has largely focused on network analysis using protocol specifications, for example for intrusion detection, fuzz testing and forensic analysis. The specification of a protocol alone, however, is often not sufficient for a...
Automatic inspection of network payloads is a prerequisite for effective analysis of network communication. Security research has largely focused on network analysis using protocol specifications, for example for intrusion detection, fuzz testing and forensic analysis. The specification of a protocol alone, however, is often not sufficient for accurate analysis of communication, as it fails to reflect individual semantics of network applications. We propose a framework for semanticsaware analysis of network payloads which automaticylly extracts semantic components from recorded network traffic. Our method proceeds by mapping network payloads to a vector space and identifying semantic templates corresponding to base directions in the vector space. We demonstrate the efficacy of semanticsaware analysis in different security applications: automatic discovery of patterns in honeypot data, analysis of malware communication and network intrusion detection.
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Publisher:
Berlin : WIAS ; Göttingen : Niedersächsische Staats und Universitätsbibliothek ; Hannover : Technische Informationsbibliothek u. Universitätsbibliothek
Year of Publication:
2010
Subjects:
31.00
31.00
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URL:
http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2012/wias_preprints_1502.pdf
http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2012/wias_preprints_1502.pdf
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5.
Kernel Partial Least Squares is Universally Consistent
Open Access
Title:
Kernel Partial Least Squares is Universally Consistent
Author:
Gilles Blanchard
;
Nicole Krämer
Gilles Blanchard
;
Nicole Krämer
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Description:
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of wellknown classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as the solution of a global c...
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of wellknown classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as the solution of a global cost minimization procedure over a fixed model nor is it a linear estimator. Instead, approximate solutions are constructed by projections onto a nested set of datadependent subspaces. To prove consistency, we exploit the known fact that Partial Least Squares is equivalent to the conjugate gradient algorithm in combination with early stopping. The choice of the stopping rule (number of iterations) is a crucial point. We study two empirical stopping rules. The first one monitors the estimation error in each iteration step of Partial Least Squares, and the second one estimates the empirical complexity in terms of a condition number. Both stopping rules lead to universally consistent estimators provided the kernel is universal. 1
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20111213
Source:
http://jmlr.csail.mit.edu/proceedings/papers/v9/blanchard10a/blanchard10a.pdf
http://jmlr.csail.mit.edu/proceedings/papers/v9/blanchard10a/blanchard10a.pdf
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Document Type:
text
Language:
en
DDC:
519 Probabilities & applied mathematics
(computed)
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.241
http://jmlr.csail.mit.edu/proceedings/papers/v9/blanchard10a/blanchard10a.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.241
http://jmlr.csail.mit.edu/proceedings/papers/v9/blanchard10a/blanchard10a.pdf
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6.
On the Peaking Phenomenon of the Lasso in Model Selection”, (unpublished). Available at http://arxiv.org/abs/0904.4416
Open Access
Title:
On the Peaking Phenomenon of the Lasso in Model Selection”, (unpublished). Available at http://arxiv.org/abs/0904.4416
Author:
Nicole Krämer
Nicole Krämer
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Description:
I briefly report on some unexpected results that I obtained when optimizing the model parameters of the Lasso. In simulations with varying observationstovariables ratio n/p, I typically observe a strong peak in the test error curve at the transition point n/p = 1. This peaking phenomenon is welldocumented in scenarios that involve the inversi...
I briefly report on some unexpected results that I obtained when optimizing the model parameters of the Lasso. In simulations with varying observationstovariables ratio n/p, I typically observe a strong peak in the test error curve at the transition point n/p = 1. This peaking phenomenon is welldocumented in scenarios that involve the inversion of the sample covariance matrix, and as I illustrate in this note, it is also the source of the peak for the Lasso. The key problem is the parametrization of the Lasso penalty – as e.g. in the current R package lars – and I present a solution in terms of a normalized Lasso parameter. 1
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130805
Source:
http://arxiv.org/pdf/0904.4416v1.pdf
http://arxiv.org/pdf/0904.4416v1.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.7244
http://arxiv.org/pdf/0904.4416v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.7244
http://arxiv.org/pdf/0904.4416v1.pdf
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7.
Kernel Conjugate Gradient is Universally Consistent
Open Access
Title:
Kernel Conjugate Gradient is Universally Consistent
Author:
Gilles Blanchard
;
Nicole Krämer
Gilles Blanchard
;
Nicole Krämer
Minimize authors
Description:
We study the statistical consistency of conjugate gradient applied to a bounded regression learning problem seen as an inverse problem defined in a reproducing kernel Hilbert space. This approach leads to an estimator that stands out of the wellknown classical approaches, as it is not defined as the solution of a global cost minimization proced...
We study the statistical consistency of conjugate gradient applied to a bounded regression learning problem seen as an inverse problem defined in a reproducing kernel Hilbert space. This approach leads to an estimator that stands out of the wellknown classical approaches, as it is not defined as the solution of a global cost minimization procedure over a fixed model nor is it a linear estimator. Instead, approximate solutions are constructed by projections onto a nested set of datadependent subspaces. We study two empirical stopping rules that lead to universally consistent estimators provided the kernel is universal. As conjugate gradient is equivalent to Partial Least Squares, we therefore obtain consistency results for Kernel Partial Least Squares Regression.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20141008
Source:
http://ml.cs.tuberlin.de/~nkraemer/papers/preprint_cg.pdf
http://ml.cs.tuberlin.de/~nkraemer/papers/preprint_cg.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.9893
http://ml.cs.tuberlin.de/~nkraemer/papers/preprint_cg.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.9893
http://ml.cs.tuberlin.de/~nkraemer/papers/preprint_cg.pdf
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8.
Kernel Conjugate Gradient is Universally Consistent
Open Access
Title:
Kernel Conjugate Gradient is Universally Consistent
Author:
Gilles Blanchard
;
Nicole Krämer
Gilles Blanchard
;
Nicole Krämer
Minimize authors
Description:
We study the statistical consistency of conjugate gradient applied to a bounded regression learning problem seen as an inverse problem defined in a reproducing kernel Hilbert space. This approach leads to an estimator that stands out of the wellknown classical approaches, as it is not defined as the solution of a global cost minimization proced...
We study the statistical consistency of conjugate gradient applied to a bounded regression learning problem seen as an inverse problem defined in a reproducing kernel Hilbert space. This approach leads to an estimator that stands out of the wellknown classical approaches, as it is not defined as the solution of a global cost minimization procedure over a fixed model nor is it a linear estimator. Instead, approximate solutions are constructed by projections onto a nested set of datadependent subspaces. We study two empirical stopping rules that lead to universally consistent estimators provided the kernel is universal. As conjugate gradient is equivalent to Partial Least Squares, we therefore obtain consistency results for Kernel Partial Least Squares Regression.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20141008
Source:
http://arxiv.org/pdf/0902.4380v1.pdf
http://arxiv.org/pdf/0902.4380v1.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.4558
http://arxiv.org/pdf/0902.4380v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.4558
http://arxiv.org/pdf/0902.4380v1.pdf
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9.
Kernel Partial Least Squares is Universally Consistent
Open Access
Title:
Kernel Partial Least Squares is Universally Consistent
Author:
Gilles Blanchard
;
Nicole Krämer
Gilles Blanchard
;
Nicole Krämer
Minimize authors
Description:
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of wellknown classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as the solution of a global c...
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of wellknown classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as the solution of a global cost minimization procedure over a fixed model nor is it a linear estimator. Instead, approximate solutions are constructed by projections onto a nested set of datadependent subspaces. To prove consistency, we exploit the known fact that Partial Least Squares is equivalent to the conjugate gradient algorithm in combination with early stopping. The choice of the stopping rule (number of iterations) is a crucial point. We study two empirical stopping rules. The first one monitors the estimation error in each iteration step of Partial Least Squares, and the second one estimates the empirical complexity in terms of a condition number. Both stopping rules lead to universally consistent estimators provided the kernel is universal.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121130
Source:
http://ml.cs.tuberlin.de/~nkraemer/papers/pls_consistency.pdf
http://ml.cs.tuberlin.de/~nkraemer/papers/pls_consistency.pdf
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Document Type:
text
Language:
en
DDC:
519 Probabilities & applied mathematics
(computed)
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2716
http://ml.cs.tuberlin.de/~nkraemer/papers/pls_consistency.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2716
http://ml.cs.tuberlin.de/~nkraemer/papers/pls_consistency.pdf
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10.
Local models for ramified unitary groups
Open Access
Title:
Local models for ramified unitary groups
Author:
Nicole Krämer
Nicole Krämer
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121114
Source:
http://arxiv.org/pdf/math/0302025v1.pdf
http://arxiv.org/pdf/math/0302025v1.pdf
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text
Language:
en
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.241.4201
http://arxiv.org/pdf/math/0302025v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.241.4201
http://arxiv.org/pdf/math/0302025v1.pdf
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(1) allgemeines system der präferenzen
(1) although some were restricted to one sex only...
(1) an analysis of 22 european cohorts
(1) an analysis of 22 european cohorts within the...
(1) and 10 µm to 2 5 µm pmcoarse pm2 5 absorbance...
(1) and 2484 from cerebrovascular disease all...
(1) and annual average concentrations of nitrogen...
(1) and between 10 μm and 2·5 μm pmcoarse
Subject:
Dewey Decimal Classification (DDC)
(23) Economics [33*]
(19) Computer science, knowledge & systems [00*]
(15) Statistics [31*]
(15) Mathematics [51*]
(15) Medicine & health [61*]
(8) Psychology [15*]
(5) Social sciences, sociology & anthropology...
(5) Life sciences; biology [57*]
(3) Education [37*]
(2) Science [50*]
(2) Literature, rhetoric & criticism [80*]
(1) Library & information sciences [02*]
(1) Philosophy [10*]
(1) Political science [32*]
(1) Engineering [62*]
(1) Agriculture [63*]
(1) Arts [70*]
Dewey Decimal Classification (DDC):
Year of Publication
(49) 2014
(46) 2012
(27) 2013
(21) 2010
(20) 2009
(13) 2008
(13) 2011
(11) 2015
(9) 2007
(5) 2006
(2) 2005
(1) 2003
Year of Publication:
Content Provider
(48) CiteSeerX
(25) PASCAL EPrints
(20) PubMed Central
(14) ArXiv.org
(11) Basel Univ.: edoc
(9) Jülich Forschungszentrum: JuSER
(6) DuisburgEssen Univ.: DuEPublico
(6) Utrecht Univ.: Repository
(5) Finland National Inst. for Health and Welfare...
(5) Bielefeld Univ.: Publications
(5) Bochum Univ. (RUB): Campus Research Bibliography
(4) CogPrints (United Kingdom)
(4) London King's College: Research Portal
(4) Dundee Univ.: Online Publications
(3) BioMed Central
(3) DataCite Metadata Store
(3) HighWire Press
(3) Aarhus Univ.: Pure
(3) Zurich Univ.: ZORA
(2) Aalborg Univ. (AAU): VBN
(2) Göttingen Univ.: GOEDOC
(2) Harvard Univ.: DASH
(2) LeibnizOpen
(2) RePEc.org
(2) Dresden Univ. Tech.: Qucosa
(2) Lincoln Univ.: Lincoln Repository
(2) Umeå Univ.: Publications
(1) WRLC: Aladin Research Commons
(1) CSIC (Spanish National Research Council)
(1) DOAJ Articles
(1) Hagen Fernuniv.
(1) Gotland Univ.: Publications
(1) Hindawi Publishing Corporation
(1) Monash Univ.: Research Repository
(1) Munich LMU: Open Access
(1) Taiwan National Univ.: Repository
(1) PsyDok (Virtuelle Fachbibliothek Psychologie)
(1) Aachen RWTH: Publications
(1) Berlin TU: Digital Repository
(1) Giessen Univ.: Publicatoin Server
(1) EichstättIngolstadt Katholische Univ.
(1) Groningen Univ.
(1) Frankfurt/Main Univ.: Publications
(1) Hertfordshire Univ.
(1) Luxembourg Univ.: ORBilu
(1) Mannheim Univ.: MADOC
(1) Rotterdam Erasmus Univ.: RePub
(1) Uppsala Univ.: Publications
(1) EconStor
Content Provider:
Language
(132) English
(78) Unknown
(9) German
Language:
Document Type
(92) Text
(72) Article, Journals
(23) Reports, Papers, Lectures
(22) Unknown
(8) Theses
(2) Books
Document Type:
Access
(122) Unknown
(97) Open Access
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