Sharp Calibrated Gaussian Processes
This addresses the issue of unreliable uncertainty estimates in Gaussian processes for engineering and scientific applications, representing an incremental improvement over existing calibration methods.
The paper tackles the problem of miscalibrated uncertainty estimates in Gaussian processes by developing a calibration approach that generates predictive quantiles using optimized hyperparameters to satisfy empirical calibration constraints, resulting in tighter predictive quantiles that outperform existing methods in sharpness for calibrated regression.
While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance, which yields confidence intervals that are potentially too coarse. To remedy this, we present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance but using a different set of hyperparameters chosen to satisfy an empirical calibration constraint. This results in a calibration approach that is considerably more flexible than existing approaches, which we optimize to yield tight predictive quantiles. Our approach is shown to yield a calibrated model under reasonable assumptions. Furthermore, it outperforms existing approaches in sharpness when employed for calibrated regression.