Abstract

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.

摘要

在过去的几十年里，多任务学习（MTL）问题在人工智能和机器学习社区引起了广泛关注。但是，该领域的大多数已发表作品都侧重于点估计；也就是说，估计模型参数和/或进行预测。本文研究了 MTL 问题的另一个重要方面：模型选择和预测的不确定性量化。更具体地说，本文通过多元回归处理 MTL 问题，并开发了一种在所有潜在回归模型的空间上导出概率密度函数的新方法。有了这个密度函数，点估计，以及置信度和预测椭球，可以获得感兴趣的数量，比如未来的观察。所提出的方法，称为 GMTask，基于广义基准推理 (GFI) 框架，并显示出具有理想的理论特性。通过一系列数值实验和对两个真实数据集的应用说明了其有前途的经验特性。本文的补充材料可在线获取。