Robust Multivariate Regression with Grossly Corrupted Observations and Its Application to Personality Prediction

Abstract

We consider the problem of multivariate linear regression with a small fraction of the responses being missing and grossly corrupted, where the magnitudes and locations of such occurrences are not known in priori. This is addressed in our approach by explicitly taking into account the error source and its sparseness nature. Moreover, our approach allows each regression task to possess its distinct noise level. We also propose a new algorithm that is theoretically shown to always converge to the optimal solution of its induced non-smooth optimization problem. Experiments on controlled simulations suggest the competitiveness of our algorithm comparing to existing multivariate regression models. In particular, we apply our model to predict the \textit{Big-Five} personality from user behaviors at Social Network Sites (SNSs) and microblogs, an important yet difficult problem in psychology, where empirical results demonstrate its superior performance with respect to related learning methods.