Multi-task learning with application to water quality monitoring

Multi-task learning (MTL) exhibits improved performance in many problems in reality by utilizing the intrinsic features among multiple related tasks. In this paper, the problem of water quality monitoring is considered as multi-task learning, in which different tasks correspond to changes caused by new environment or different spectrometers. An improved learning model is presented describing the relationship between wavelengths and pollutant concentration as well as capturing the task relationships with a low-rank shared structure. Under the assumption that different tasks share some common wavelengths, an optimization problem is proposed with the predictors affected by these features and their corresponding coefficients that vary in different tasks. An alternating minimization algorithm is proposed to solve this problem. Experimental results demonstrate the effectiveness of the proposed algorithm in application.