Robust Support Vector Regression in Primal with Asymmetric Huber Loss

摘要

As real world data sets in general contain noise, construction of robust regression learning models to fit data with noise is an important and challenging research problem. It is all the more difficult to learn regression function with good generalization performance for input samples corrupted by asymmetric noise and outliers. In this work, we propose novel robust regularized support vector regression models with asymmetric Huber and ε-insensitive Huber loss functions leading to strongly convex minimization problems in simpler form whose solutions are obtained by simple functional iterative method. Numerical experiments performed on (1) synthetic data sets with different noise models and having outliers; (2) real world data sets, clearly show the effectiveness and applicability of the proposed support vector regression models with asymmetric Huber loss.