A Review of Heteroscedasticity Treatment with Gaussian Processes and Quantile Regression Meta-models

For regression problems, the general practice is to consider a constant variance of the error term across all data. This aims to simplify an often complicated model and relies on the assumption that this error is independent of the input variables. This property is known as homoscedasticity. On the other hand, in the real world, this is often a naive assumption, as we are rarely able to exhaustively include all true explanatory variables for a regression. While Big Data is bringing new opportunities for regression applications, ignoring this limitation may lead to biased estimators and inaccurate confidence and prediction intervals.