Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions
This work addresses a theoretical bottleneck in HGPs for researchers in machine learning and control systems, but it appears incremental as it builds on existing HGP methods.
The study tackled the challenge of calculating exact posterior distributions for heteroscedastic Gaussian processes (HGPs), which are not multivariate normal, by deriving their exact means, variances, and cumulative distributions, and applied these findings to a chance-constrained tracking controller that handles disturbances in a plant system.
This study introduces a novel theoretical framework for analyzing heteroscedastic Gaussian processes (HGPs) that identify unknown systems in a data-driven manner. Although HGPs effectively address the heteroscedasticity of noise in complex training datasets, calculating the exact posterior distributions of the HGPs is challenging, as these distributions are no longer multivariate normal. This study derives the exact means, variances, and cumulative distributions of the posterior distributions. Furthermore, the derived theoretical findings are applied to a chance-constrained tracking controller. After an HGP identifies an unknown disturbance in a plant system, the controller can handle chance constraints regarding the system despite the presence of the disturbance.