Iterative Learning in Support Vector Regression With Heterogeneous Variances

The presence of heterogeneous variances is the norm in practice, which makes machine learning predictions less reliable when noise variances are implicitly assumed to be equal. To this end, we extend support vector regression by allowing a range of variance functions in the model training. Specifically, we model the variance as a function of the mean and other variables as traditionally used in statistical modeling. This leads to iterative learning between support vector regression training and heterogeneous variance modeling. Extensive simulations are implemented to validate the effectiveness of the proposed framework in both linear and nonlinear regressions. Finally, two real data sets are used to demonstrate the superiority of the proposed algorithm in the presence of heterogeneity.