Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Gaussian ProcessesSimilar Papers 제목 키워드 기반
Posterior Covariance Structures in Gaussian Processes
In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but…
Gaussian ProcessesMulti-Response Heteroscedastic Gaussian Process Models and Their Inference
Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships …
regressionState Space ModelsVariational InferenceUncertainty Disentanglement with Non-stationary Heteroscedastic Gaussian Processes for Active Learning
Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstra…
Active LearningDisentanglementGaussian ProcessesA Tutorial on Sparse Gaussian Processes and Variational Inference
Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods…
Bayesian InferenceGaussian ProcessesregressionVariational InferenceGGMPs: Generalized Gaussian Mixture Processes
Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but stand…
Density EstimationGaussian Processes