Hessian corrected input noise models

Abstract

When the inputs of a regression problem are corrupted with noise, integrating out the noise process leads to biased estimates. We present a method that corrects the bias caused by the integration. The correction is proportional to the Hessian of the learned model and to the variance of the input noise. The method works for arbitrary regression models, the only requirement is two times differentiability of the respective model. The conducted experiments suggest that significant improvement can be gained using the proposed method. Nevertheless, experiments on high dimensional data highlight the limitations of the algorithm. © 2013 Springer-Verlag Berlin Heidelberg.