Principal support vector machines for linear and nonlinear sufficient dimension reduction

DOI10.1214/11-AOS932zbMath1246.62153arXiv1203.2790OpenAlexW2035140935WikidataQ57434300 ScholiaQ57434300MaRDI QIDQ449992

Andreas Artemiou, Bing Li, Lexin Li

Publication date: 3 September 2012

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.2790

zbMATH Keywords

principal componentsreproducing kernel Hilbert spaceinverse regressioncontour regressioninvariant kernel

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Learning and adaptive systems in artificial intelligence (68T05) Applications of functional analysis in probability theory and statistics (46N30) Graphical methods in statistics (62A09)

Related Items (40)

Dimension reduction for functional data based on weak conditional moments ⋮ Sufficient dimension reduction via principal L\(q\) support vector machine ⋮ A brief review of linear sufficient dimension reduction through optimization ⋮ Sliced Inverse Regression in Metric Spaces ⋮ Dimension reduction in binary response regression: a joint modeling approach ⋮ On expectile-assisted inverse regression estimation for sufficient dimension reduction ⋮ High-dimensional sufficient dimension reduction through principal projections ⋮ Quantile-slicing estimation for dimension reduction in regression ⋮ Nonlinear predictive directions in clinical trials ⋮ Penalized principal logistic regression for sparse sufficient dimension reduction ⋮ Principal quantile regression for sufficient dimension reduction with heteroscedasticity ⋮ Principal minimax support vector machine for sufficient dimension reduction with contaminated data ⋮ On the conditional distributions of low-dimensional projections from high-dimensional data ⋮ Unnamed Item ⋮ Nonlinear and additive principal component analysis for functional data ⋮ A robust proposal of estimation for the sufficient dimension reduction problem ⋮ Predictive power of principal components for single-index model and sufficient dimension reduction ⋮ Nonlinear dimension reduction for conditional quantiles ⋮ A new reproducing kernel‐based nonlinear dimension reduction method for survival data ⋮ Dimension reduction techniques for conditional expectiles ⋮ On post dimension reduction statistical inference ⋮ Using sliced inverse mean difference for sufficient dimension reduction ⋮ On a nonlinear extension of the principal fitted component model ⋮ A general theory for nonlinear sufficient dimension reduction: formulation and estimation ⋮ A study on imbalance support vector machine algorithms for sufficient dimension reduction ⋮ A comparative study of the use of large margin classifiers on seismic data ⋮ On efficient dimension reduction with respect to a statistical functional of interest ⋮ Sliced inverse median difference regression ⋮ Using DAGs to identify the sufficient dimension reduction in the principal fitted components model ⋮ Statistical learning on emerging economies ⋮ Principal weighted logistic regression for sufficient dimension reduction in binary classification ⋮ An ensemble of inverse moment estimators for sufficient dimension reduction ⋮ Graph informed sliced inverse regression ⋮ A Cost Based Reweighted Scheme of Principal Support Vector Machine ⋮ Inverse regression-based uncertainty quantification algorithms for high-dimensional models: theory and practice ⋮ On the predictive potential of kernel principal components ⋮ Gradient-Based Kernel Dimension Reduction for Regression ⋮ On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis ⋮ Using adaptively weighted large margin classifiers for robust sufficient dimension reduction ⋮ On sufficient dimension reduction via principal asymmetric least squares

Uses Software

• Kernlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fisher lecture: Dimension reduction in regression
• The commutation matrix: Some properties and applications
• On almost linearity of low dimensional projections from high dimensional data
• Principal fitted components for dimension reduction in regression
• Successive direction extraction for estimating the central subspace in a multiple-index regres\-sion
• On the distribution of the left singular vectors of a random matrix and its applications
• Asymptotics for sliced average variance estimation
• Dimension reduction for nonelliptically distributed predictors
• An RKHS formulation of the inverse regression dimension-reduction problem
• A nonlinear multi-dimensional variable selection method for high dimensional data: sparse MAVE
• A characterization of spherical distributions
• Estimating the dimension of a model
• Convex functional analysis
• Regression analysis under link violation
• Dimension reduction for conditional mean in regression
• Kernel dimension reduction in regression
• Contour regression: a general approach to dimension reduction
• On Directional Regression for Dimension Reduction
• Sliced Inverse Regression for Dimension Reduction
• On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma
• Asymptotic Statistics
• Graphics for Regressions With a Binary Response
• Nonparametric estimating equations based on a penalized information criterion
• An Adaptive Estimation of Dimension Reduction Space
• Dimension Reduction for the Conditionalkth Moment in Regression
• On Quasi Likelihood Equations with Non-parametric Weights
• Algorithmic Learning Theory
• Sufficient Dimension Reduction via Inverse Regression
• On Sliced Inverse Regression With High-Dimensional Covariates
• Theory of Reproducing Kernels
• Comment

This page was built for publication: Principal support vector machines for linear and nonlinear sufficient dimension reduction