# Sharp Calibrated Gaussian Processes

## TL;DR

This paper introduces a flexible calibration method for Gaussian processes that improves the accuracy of predictive quantiles, ensuring better frequentist calibration and sharper confidence intervals in regression tasks.

## Contribution

A novel calibration approach for Gaussian processes that uses hyperparameters optimized for empirical calibration, enhancing the sharpness and reliability of predictive intervals.

## Key findings

- Outperforms existing calibration methods in sharpness.
- Yields well-calibrated predictive quantiles.
- Applicable under reasonable assumptions.

## Abstract

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.