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This paper studies the problem of multivariate linear regression where aportion of the observations is grossly corrupted or is missing, and themagnitudes and locations of such occurrences are unknown in priori. To dealwith this problem, we propose a new approach by explicitly consider the errorsource as well as its sparseness nature. An interesting property of ourapproach lies in its ability of allowing individual regression output elementsor tasks to possess their unique noise levels. Moreover, despite working with anon-smooth optimization problem, our approach still guarantees to converge toits optimal solution. Experiments on synthetic data demonstrate thecompetitiveness of our approach compared with existing multivariate regressionmodels. In addition, empirically our approach has been validated with verypromising results on two exemplar real-world applications: The first concernsthe prediction of \textit{Big-Five} personality based on user behaviors atsocial network sites (SNSs), while the second is 3D human hand pose estimationfrom depth images. The implementation of our approach and comparison methods aswell as the involved datasets are made publicly available in support of theopen-source and reproducible research initiatives.

Multivariate Regression with Grossly Corrupted Observations: A Robust Approach and its Applications