Sparse Regression by Projection and Sparse Discriminant Analysis

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
Xin QiHongyu Zhao

Abstract

Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths and the tuning parameters are determined by a cross validation procedure to achieve the largest prediction accuracy. We provide a theoretical result for simultaneous model selection consistency and parameter estimation consistency of our method in high dimension. This new framework is then generalized such that it can be applied to principal components analysis, partial least squares and canonical correlation analysis. We also adapt this framework for discriminant analysis. Compared to the existing methods, where there is relatively little control of the dependency among the sparse components, our method can control the r...Continue Reading

References

Feb 2, 2002·Nature·Laura J van 't VeerStephen H Friend
May 16, 2002·Proceedings of the National Academy of Sciences of the United States of America·Robert TibshiraniGilbert Chu
Sep 6, 2005·Proceedings of the National Academy of Sciences of the United States of America·Lance D MillerJonas Bergh
Apr 11, 2006·Biostatistics·Yaqian GuoRobert Tibshirani
Jan 29, 2010·Journal of the Royal Statistical Society. Series B, Statistical Methodology·Hyonho Chun, Sündüz Keleş
Feb 11, 2012·Journal of the Royal Statistical Society. Series B, Statistical Methodology·Daniela M Witten, Robert Tibshirani

❮ Previous
Next ❯

Software Mentioned

of
spls
Bioconductor
sparseLDA
LARS
R package glmnet
LASSO
breastCancerNKI
breastCancerUPP
SCAD

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Statistical Applications in Genetics and Molecular Biology
Dongjun Chung, Sündüz Keleş
Journal of the Royal Statistical Society. Series B, Statistical Methodology
Hyonho Chun, Sündüz Keleş
Statistical Applications in Genetics and Molecular Biology
Anne-Laure Boulesteix
© 2021 Meta ULC. All rights reserved