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Robust reduced-rank regression
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-r...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Oxford University Press
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5793675/ https://www.ncbi.nlm.nih.gov/pubmed/29430036 http://dx.doi.org/10.1093/biomet/asx032 |
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author | She, Y. Chen, K. |
author_facet | She, Y. Chen, K. |
author_sort | She, Y. |
collection | PubMed |
description | In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint modelling and outlier detection. The problem is formulated as a regularized multivariate regression with a sparse mean-shift parameterization, which generalizes and unifies some popular robust multivariate methods. An efficient thresholding-based iterative procedure is developed for optimization. We show that the algorithm is guaranteed to converge and that the coordinatewise minimum point produced is statistically accurate under regularity conditions. Our theoretical investigations focus on non-asymptotic robust analysis, demonstrating that joint rank reduction and outlier detection leads to improved prediction accuracy. In particular, we show that redescending [Formula: see text]-functions can essentially attain the minimax optimal error rate, and in some less challenging problems convex regularization guarantees the same low error rate. The performance of the proposed method is examined through simulation studies and real-data examples. |
format | Online Article Text |
id | pubmed-5793675 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Oxford University Press |
record_format | MEDLINE/PubMed |
spelling | pubmed-57936752018-09-01 Robust reduced-rank regression She, Y. Chen, K. Biometrika Articles In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint modelling and outlier detection. The problem is formulated as a regularized multivariate regression with a sparse mean-shift parameterization, which generalizes and unifies some popular robust multivariate methods. An efficient thresholding-based iterative procedure is developed for optimization. We show that the algorithm is guaranteed to converge and that the coordinatewise minimum point produced is statistically accurate under regularity conditions. Our theoretical investigations focus on non-asymptotic robust analysis, demonstrating that joint rank reduction and outlier detection leads to improved prediction accuracy. In particular, we show that redescending [Formula: see text]-functions can essentially attain the minimax optimal error rate, and in some less challenging problems convex regularization guarantees the same low error rate. The performance of the proposed method is examined through simulation studies and real-data examples. Oxford University Press 2017-09 2017-07-12 /pmc/articles/PMC5793675/ /pubmed/29430036 http://dx.doi.org/10.1093/biomet/asx032 Text en © 2017 Biometrika Trust |
spellingShingle | Articles She, Y. Chen, K. Robust reduced-rank regression |
title | Robust reduced-rank regression |
title_full | Robust reduced-rank regression |
title_fullStr | Robust reduced-rank regression |
title_full_unstemmed | Robust reduced-rank regression |
title_short | Robust reduced-rank regression |
title_sort | robust reduced-rank regression |
topic | Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5793675/ https://www.ncbi.nlm.nih.gov/pubmed/29430036 http://dx.doi.org/10.1093/biomet/asx032 |
work_keys_str_mv | AT shey robustreducedrankregression AT chenk robustreducedrankregression |