Double‐structured sparse multitask regression with application of statistical downscaling

Abstract

Statistical learning of high‐dimensional data often improves learning performance by taking advantage of structural information hidden in data. In this paper, we investigate the structured multitask learning problem and propose a generalized estimator to utilize the structural information simultaneously from the predictors and from the response variables. The key idea of our methodology is to apply flexible quadratic penalties to regularize the likelihood function that incorporates both types of structural information. We prove the theoretical statistical properties of the proposed estimator, which generalizes several state‐of‐the‐art sparse learning methods. Numerical examples are provided for the proposed estimator on synthetic data and on the statistical downscaling problem in climate research.

A hierarchical integrative group least absolute shrinkage and selection operator for analyzing environmental mixtures

“…Nelder (1977) and McCullagh and Nelder (1989) introduced the concepts of weak/strong heredity and marginality, respectively, as conceptual constraints to simplify model interpretation (McCullagh, 1984) and improve statistical power (Cox, 1984). Recent penalty-based methods that respect these heredity principles include the strong heredity interaction model (SHIM) (Choi et al, 2010), the LASSO for hierarchical interactions (hierNet) (Bien et al, 2013), and the group-LASSO interaction network (GLinternet) (Lim & Hastie, 2015). In addition to penalization-based methods, forward selection methods (Boos et al, 2009;Luo & Ghosal, 2015;Wasserman & Roeder, 2009) are also commonly used for variable selection in practice.…”

“…However, the number of candidate effects, including main effects and interaction effects, may be much larger than the number of observations (i.e., p >> n). To address this issue, one common approach is to introduce sparsity during estimation to shrink coefficient estimates towards a subset of variables that have stronger effects (Ashrap et al, 2020;Li & Ding, 2019;Liu et al, 2018;Roberts & Martin, 2005), although targeted selection of interaction effects have received less attention in environmental applications. This article proposes a variable selection framework to handle potential nonlinearity and interactions between a set of multiple exposures.…”

Statistics for climate informatics

“…Dash, Mishra, and Panigrahi () apply regression and artificial neural networks for improving predictions of northeast monsoon rainfall over the Indian peninsular. Li and Ding () propose a new form of penalized regression, which is an alternative to the existing methods of LASSO, ridge regression, and elastic net, and demonstrate its applicability in statistical downscaling of climate data.…”