High-Dimensional Multi-Task Learning using Multivariate Regression and Generalized Fiducial Inference
针对多任务学习问题，提出一种基于广义置信推断的新方法GMTask，用于量化模型选择和预测的不确定性，并通过数值实验和真实数据验证其有效性。
Over the past decades, the Multi-Task Learning (MTL) problem has attracted much attention in the artificial intelligence and machine learning communities. However, most published work in this area focuses on point estimation; that is, estimating model parameters and/or making predictions. This article studies another important aspect of the MTL problem: uncertainty quantification for model choices and predictions. To be more specific, this article approaches the MTL problem with multivariate regression and develops a novel method for deriving a probability density function on the space of all potential regression models. With this density function, point estimates, as well as confidence and prediction ellipsoids, can be obtained for quantities of interest, such as future observations. The proposed method, termed GMTask, is based on the generalized fiducial inference (GFI) framework and is shown to enjoy desirable theoretical properties. Its promising empirical properties are illustrated via a sequence of numerical experiments and applications to two real datasets. Supplementary materials for this article are available online.