This paper aims to develop an optimality theory for linear discriminant
analysis in the high-dimensional setting. A data-driven and tuning free
classification rule, which is based on an adaptive constrained $\ell_1$
minimization approach, is proposed and analyzed. Minimax lower bounds are
obtained and this classification rule is shown to be simultaneously rate
optimal over a collection of parameter spaces. In addition, we consider
classification with incomplete data under the missing completely at random
(MCR) model. An adaptive classifier with theoretical guarantees is introduced
and optimal rate of convergence for high-dimensional linear discriminant
analysis under the MCR model is established. The technical analysis for the
case of missing data is much more challenging than that for the complete data.
We establish a large deviation result for the generalized sample covariance
matrix, which serves as a key technical tool and can be of independent
interest. An application to lung cancer and leukemia studies is also discussed.
Описание
High-dimensional Linear Discriminant Analysis: Optimality, Adaptive
Algorithm, and Missing Data
%0 Generic
%1 cai2018highdimensional
%A Cai, T. Tony
%A Zhang, Linjun
%D 2018
%K LDA high-dimensional
%T High-dimensional Linear Discriminant Analysis: Optimality, Adaptive
Algorithm, and Missing Data
%U http://arxiv.org/abs/1804.03018
%X This paper aims to develop an optimality theory for linear discriminant
analysis in the high-dimensional setting. A data-driven and tuning free
classification rule, which is based on an adaptive constrained $\ell_1$
minimization approach, is proposed and analyzed. Minimax lower bounds are
obtained and this classification rule is shown to be simultaneously rate
optimal over a collection of parameter spaces. In addition, we consider
classification with incomplete data under the missing completely at random
(MCR) model. An adaptive classifier with theoretical guarantees is introduced
and optimal rate of convergence for high-dimensional linear discriminant
analysis under the MCR model is established. The technical analysis for the
case of missing data is much more challenging than that for the complete data.
We establish a large deviation result for the generalized sample covariance
matrix, which serves as a key technical tool and can be of independent
interest. An application to lung cancer and leukemia studies is also discussed.
@misc{cai2018highdimensional,
abstract = {This paper aims to develop an optimality theory for linear discriminant
analysis in the high-dimensional setting. A data-driven and tuning free
classification rule, which is based on an adaptive constrained $\ell_1$
minimization approach, is proposed and analyzed. Minimax lower bounds are
obtained and this classification rule is shown to be simultaneously rate
optimal over a collection of parameter spaces. In addition, we consider
classification with incomplete data under the missing completely at random
(MCR) model. An adaptive classifier with theoretical guarantees is introduced
and optimal rate of convergence for high-dimensional linear discriminant
analysis under the MCR model is established. The technical analysis for the
case of missing data is much more challenging than that for the complete data.
We establish a large deviation result for the generalized sample covariance
matrix, which serves as a key technical tool and can be of independent
interest. An application to lung cancer and leukemia studies is also discussed.},
added-at = {2018-04-10T16:09:36.000+0200},
author = {Cai, T. Tony and Zhang, Linjun},
biburl = {https://www.bibsonomy.org/bibtex/26150834e1dc073572815ad89e4ac3aa2/minhtang},
description = {High-dimensional Linear Discriminant Analysis: Optimality, Adaptive
Algorithm, and Missing Data},
interhash = {7bb9273900429625e363231ad4a38559},
intrahash = {6150834e1dc073572815ad89e4ac3aa2},
keywords = {LDA high-dimensional},
note = {cite arxiv:1804.03018},
timestamp = {2018-04-10T16:09:36.000+0200},
title = {High-dimensional Linear Discriminant Analysis: Optimality, Adaptive
Algorithm, and Missing Data},
url = {http://arxiv.org/abs/1804.03018},
year = 2018
}