Sparse Variational Contaminated Noise Gaussian Process Regression with Applications in Geomagnetic Perturbations Forecasting

GPR models can also incorporate prior knowledge through selecting an appropriate kernel function. GPR commonly assumes a homoscedastic Gaussian distribution for observation noise because this yields an analytical form for the posterior predictive prediction. However, Bayesian inference based on Gaussian noise distributions is known to be sensitive to outliers which are defined as observations that strongly deviate from model assumptions. In regression, outliers can arise from relevant inputs being absent from the model, measurement error, and other unknown sources. These outliers are associated with unconsidered sources of variation that affect the target variable sporadically. In this case, the observation model is unable to distinguish between random noise and systematic effects not captured by the model. In the context of GPR under Gaussian noise, outliers can heavily influence the posterior predictive distribution, resulting in a biased estimate of the mean function and overly confident prediction intervals. Therefore, robust observation models are desired in the presence of potential outliers.