Robust Multivariate Regression with Grossly Corrupted Observations

Robust Multivariate Regression with Grossly
Corrupted Observations: Algorithm and Applications



Xiaowei Zhang, Chi Xu, Yu Zhang, Li Cheng,
@Machine Learning For Bioimage Analysis Group, BII, A*STAR,Singapore
 and
Tingshao Zhu,
@Institute of Psychology, Chinese Academy of Sciences, China

  • Introduction

    • We consider the problem of multivariate linear regression where a portion of the observations is grossly corrupted or is missing, and the magnitudes and locations of such occurrences are unknown in priori. To deal with this problem, we propose a new approach by explicitly consider the error source as well as its sparseness nature. An interesting property of our approach lies in its ability of allowing individual regression output elements or tasks to possess their unique noise levels. Moreover, despite working with a non-smooth optimization problem, our approach still guarantees to converge to its optimal solution. Experiments on synthetic data demonstrate the competitiveness of our approach compared with existing multivariate regression models. In addition, empirically our approach has been validated with very promising results on two exemplar real-world applications: The first concerns the prediction of \textit{Big-Five} personality based on user behaviors at social network sites (SNSs), while the second is 3D human hand pose estimation from depth images.

  • Publications

  1. Xiaowei Zhang, Chi Xu, Yu Zhang, Tingshao Zhu, and Li Cheng. Multivariate Regression with Grossly Corrupted Observations: A Robust Approach and Its Applications. arXiv:1701.02892, 2017.

  2. Xiaowei Zhang, Li Cheng, and Tingshao Zhu. Robust Multivariate Regression with Grossly Corrupted Observations and Its Application to Personality Prediction. Proceedings of the 7th Asian Conference on Machine Learning (ACML), JMLR W&CP Vol. 45, pp. 112-126, 2015.

  • MATLAB codes

    To support of the open-source research activities, we have released our codes which can be used to reproduce most of the results in our paper. Codes can be downloaded here.