Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty
Gaussian process (GP) regression is widely used for uncertainty quantification, yet the standard formulation assumes noise-free covariates. When inputs are measured with error, this errors-in-variables (EIV) setting can lead to optimistically narrow posterior intervals and biased decisions. We study GP regression under input measurement uncertainty by representing each noisy input as a probability measure and defining covariance through Wasserstein distances between these measures. Building on this perspective, we instantiate a deterministic projected Wasserstein ARD (PWA) kernel whose one-dimensional components admit closed-form expressions and whose product structure yields a scalable, ...
| Authors | Hengrui Luo, Xiaoye S. Li, Yang Liu et al. |
|---|---|
| Primary category | stat.ME |
| Published | 18 March 2026 |
| Last updated at source | 18 March 2026 |
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