Robust Multivariate Lasso Regression with Covariance Estimation

Multivariate regression with covariance estimation (MRCE) is a method that performs sparse estimation of multivariate regression coefficients, while taking account the covariance structure of the response variables. MRCE uses a penalized likelihood approach to simultaneously estimate the regression...

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Bibliographic Details
Published in:Journal of computational and graphical statistics Vol. 32; no. 3; pp. 961 - 973
Main Authors: Chang, Le, Welsh, A. H.
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.07.2023
Taylor & Francis Ltd
Subjects:
Algorithms
Covariance matrix
Graphical lasso
Lasso
Multivariate analysis
Multivariate regression
Optimization
Oracal property
Outliers (statistics)
Proximal gradient algorithm
Regression coefficients
Robust estimation
Robustness (mathematics)
ISSN:1061-8600, 1537-2715
Online Access:Get full text
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Summary:Multivariate regression with covariance estimation (MRCE) is a method that performs sparse estimation of multivariate regression coefficients, while taking account the covariance structure of the response variables. MRCE uses a penalized likelihood approach to simultaneously estimate the regression coefficients and the inverse covariance matrix so that prediction accuracy can be significantly improved. However, traditional likelihood-based methods such as MRCE can produce very misleading results in the presence of outliers. In this work, we propose an extension of MRCE, namely, a robust multivariate lasso regression with covariance estimation (RMLC) to handle potential outliers within the data. By using Huber's loss or Tukey's biweight loss, RMLC can be resistant to outliers in the responses or in both the responses and the covariates. A novel optimization algorithm that incorporates a 2-fold accelerated proximal gradient (APG) algorithm is developed to solve RMLC efficiently. We also demonstrate that our proposed RMLC enjoys the oracle property. Our simulation study shows that RMLC produces very reliable results for both the regression coefficients and the correlation structure of the responses, even if the data are contaminated. A real analysis on hyperspectral data further demonstrates the utility of RMLC. Supplementary materials for this article are available online.
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ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2022.2118752