Regressão com instâncias corrompidas: Uma abordagem robusta e suas aplicações

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Multivariate Regression with Grossly Corrupted Observations: A Robust Approach and its Applications - Xiaowei Zhang, Chi Xu, Yu Zhang, Tingshao Zhu, Li Cheng Abstract: This paper studies 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. The implementation of our approach and comparison methods as well as the involved datasets are made publicly available in support of the open-source and reproducible research initiatives.

Conclusions: We consider a new approach dedicating to the multivariate regression problem where some output labels are either corrupted or missing. The gross error is explicitly addressed in our model, while it allows the adaptation of distinct regression elements or tasks according to their own noise levels. We further propose and analyze the convergence and runtime properties of the proposed proximal ADMM algorithm which is globally convergent and efficient. The model combined with the specifically designed solver enable our approach to tackle a diverse range of applications. This is practically demonstrated on two distinct applications, that is, to predict personalities based on behaviors at SNSs, as well as to estimation 3D hand pose from single depth images. Empirical experiments on synthetic and real datasets have showcased the applicability of our approach in the presence of label noises. For future work, we plan to integrate with more advanced deep learning techniques to better address more practical problems, including 3D hand pose estimation and beyond.