Robust Regression

Abstract

Discriminative methods (e.g., kernel regression, SVM) have been extensively used to solve problems such as object recognition, image alignment and pose estimation from images. These methods typically map image features ( X) to continuous (e.g., pose) or discrete (e.g., object category) values. A major drawback of existing discriminative methods is that samples are directly projected onto a subspace and hence fail to account for outliers common in realistic training sets due to occlusion, specular reflections or noise. It is important to notice that existing discriminative approaches assume the input variables X to be noise free. Thus, discriminative methods experience significant performance degradation when gross outliers are present. Despite its obvious importance, the problem of robust discriminative learning has been relatively unexplored in computer vision. This paper develops the theory of robust regression (RR) and presents an effective convex approach that uses recent advances on rank minimization. The framework applies to a variety of problems in computer vision including robust linear discriminant analysis, regression with missing data, and multi-label classification. Several synthetic and real examples with applications to head pose estimation from images, image and video classification and facial attribute classification with missing data are used to illustrate the benefits of RR.

Joint feature-sample selection and robust diagnosis of Parkinson's disease from MRI data

“…To clean the testing data, one can use RPCA (Candès et al, 2011; Huang et al, 2016), but as discussed before, it is an unsupervised approach. To this end, we utilize the samples cleaned in the training stage, D , in a supervised manner.…”

Exploring diagnosis and imaging biomarkers of Parkinson’s disease via iterative canonical correlation analysis based feature selection

“…RLDA can be seen as a special case of robust regression (RR) method (Huang et al, 2016), since binary classification can be treated as a special case of regression.…”

“…The above RLDA formulation can be easily solved by augmented Lagrangian multipliers method. For more details, please refer to (Huang et al, 2016). …”

“…As also confirmed in the literature, regression methods can be extended for the challenging classification tasks (Naghibi et al, 2015; Wang et al, 2010; Huang et al, 2011). Nevertheless, the lack of robustness against noise is one of the major drawbacks of most existing regression approaches, especially when the outliers affect the normal distribution of subjects within high-dimensional feature space (Huang et al, 2016). Therefore, robust regression methods (Rousseeuw and Leroy, 2005; Van Huffel and Vandewalle, 1991) have developed during the past decades.…”

“…They have indicated that their method is also robust to some levels of noises. Of note, the robust LDA (Huang et al, 2016) used in this study is an extension of the robust regression study, which is inspired by existing work on robust PCA (De La Torre and Black, 2003). It enjoys the following advantages compared to the aforementioned methods: 1) it is a convex approach; 2) except for sparsity, there is no assumption imposed on the noise in the data; 3) it automatically cleans the noise in the features when learning a classifier.…”