Robust RVM regression using sparse outlier model

Kernel regression techniques such as Relevance Vector Machine (RVM) regression, Support Vector Regression and Gaussian processes are widely used for solving many computer vision problems such as age, head pose, 3D human pose and lighting estimation. However, the presence of outliers in the training dataset makes the estimates from these regression techniques unreliable. In this paper, we propose robust versions of the RVM regression that can handle outliers in the training dataset. We decompose the noise term in the RVM formulation into a (sparse) outlier noise term and a Gaussian noise term. We then estimate the outlier noise along with the model parameters. We present two approaches for solving this estimation problem: (1) a Bayesian approach, which essentially follows the RVM framework and (2) an optimization approach based on Basis Pursuit Denoising. In the Bayesian approach, the robust RVM problem essentially becomes a bigger RVM problem with the advantage that it can be solved efficiently by a fast algorithm. Empirical evaluations, and real experiments on image de-noising and age estimation demonstrate the better performance of the robust RVM algorithms over that of the RVM reg ression.