Robust relevance vector machine with noise variance coefficient

Classical relevance vector machine is sensitive to outliers during training and has weak robustness. In order to solve this problem, a novel robust relevance vector machine is presented in this paper. The key idea of the proposed method is to introduce individual noise variance coefficient for each training sample. In the process of model training, the noise variance coefficients of outliers gradually decrease so as to automatically detect and eliminate outliers. In addition, the iterative formulae for the optimization of noise variance coefficients and hyperparameters are derived according to the Bayesian evidence framework. Simulation results on sinc function and some benchmark data sets demonstrate that the proposed robust relevance vector machine can resist the impact of outliers effectively and obtain better robustness in comparison with other methods.