Uncertain Multi-Task Learning and Its Applications in Index Forecasting

When monitoring, controlling or optimizing complex processes, people try to forecast some concerned key indices, such as product quality. However, in practical applications, small sample size problem and data uncertainty affect the accuracy of forecasting. In this paper, a novel Index Forecasting algorithm is proposed called Uncertain Multi-Task Learning (UMTL), in which similar forecasting problems are modeled cooperatively so as to overcome the small sample size problem. Data uncertainty is estimated based on experiences or prior knowledge and is handled through chance constraints. Specifically, in UMTL, the differences among model parameters are limited to be sparse through the non-convex L_0 norm. For the purpose of computation, according to the Markov inequality, the designed chance constraints are converted into second order cone constraints. The entire non-convex constraint optimization problem of UMTL is solved through the Difference of Convex function Algorithm. The effectiveness of the proposed algorithm is demonstrated via numerical simulations.