Robust RVM Regression Using Sparse Outliers Model

Kernel regression techniques like 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 make the estimate 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 an (sparse) outlier noise term and a Gaussian noise term. We then estimate the outlier noise along with the model parameters. We explore two natural approaches for solving this estimation problem: 1) a Bayesian approach which follows the RVM framework, and 2) an optimization approach based on Basis Pursuit Denoising. The Bayesian approach has the advantage that it can be seamlessly incorporated into the RVM framework and thus inherits the subsequent advancement made towards faster computations of the RVM. Empirical evaluation of the robust algorithms show that the Bayesian approach performs better than the optimization approach. We further show the effectiveness of the bayesian approach in solving image denoising and age estimation problems.