Robust multitask Elliptical Regression (ROMER)

Multitask regression, and in particular the setting where each task is data starved, is a common challenge in machine learning and signal processing. The goal in such cases is to leverage the correlation or joint structure between the tasks in order to gain higher accuracy. In realistic settings the underlying distribution is often heavy-tailed or contaminated and requires the use of robust statistics. To enjoy the benefits of both, we interpret multitask regression as estimation of the parameters of a multivariate conditional distribution. This naturally leads to RObust Multitask Elliptical Regression (ROMER), and allows for robust estimation in the predictive or conditional multitask setting. Following the introduction of the model, we characterize the optimization landscape, and demonstrate its efficacy in a real-world problem of river discharge estimation across multiple river sites.