Simultaneously Leveraging Output and Task Structures for Multiple-Output Regression

Multiple-output regression models require estimating multiple functions, one for each output. To improve parameter estimation in such models, methods based on structural regularization of the model parameters are usually needed. In this paper, we present a multiple-output regression model that leverages the covariance structure of the functions (i.e., how the multiple functions are related with each other) as well as the conditional covariance structure of the outputs. This is in contrast with existing methods that usually take into account only one of these structures. More importantly, unlike most of the other existing methods, none of these structures need be known a priori in our model, and are learned from the data.