Double‐structured sparse multitask regression with application of statistical downscaling

Abstract

AbstractStatistical 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.