A study conducted by Yuji Ito was selected for presentation at The 2025 American Control Conference (ACC). This study was conducted with the cooperation of Toyota Motor Corporation's Frontier Research Center.
Real-world data often include noise whose magnitude varies depending on input conditions. Gaussian process regression is a probabilistic learning method that estimates unknown functions from data while quantifying predictive uncertainty, which is crucial in safety-critical applications such as control systems and robotics. Conventional Gaussian process regression assumes constant noise variance, making it difficult to handle heteroscedastic noise that changes across the input space. In such cases, the exact posterior distribution of predictions has remained theoretically intractable.
In this study, we develop a new theoretical framework for heteroscedastic Gaussian processes and derive exact expressions for the posterior mean, variance, and cumulative distribution. The key contribution is that these quantities are obtained without relying on deterministic or approximate noise models. The proposed theory enables chance-constrained control that explicitly accounts for uncertain, input-dependent disturbances. This work provides a foundation for reliable data-driven modeling and control under realistic noise conditions.
Title: Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions
Authors: Ito, Y.
Appears in: 2025 American Control Conference
Presented: July 10, 2025