Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918395272757248 |
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| author | Luo, Hengrui Li, Xiaoye S. Liu, Yang Noack, Marcus Qiang, Ji Risser, Mark D. |
| author_facet | Luo, Hengrui Li, Xiaoye S. Liu, Yang Noack, Marcus Qiang, Ji Risser, Mark D. |
| contents | 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, positive-definite kernel on distributions. Unlike latent-input GP models, PWA-based GPs (\PWAGPs) handle input noise without introducing unobserved covariates or Monte Carlo projections, making uncertainty quantification more transparent and robust. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17271 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty Luo, Hengrui Li, Xiaoye S. Liu, Yang Noack, Marcus Qiang, Ji Risser, Mark D. Methodology Machine Learning 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, positive-definite kernel on distributions. Unlike latent-input GP models, PWA-based GPs (\PWAGPs) handle input noise without introducing unobserved covariates or Monte Carlo projections, making uncertainty quantification more transparent and robust. |
| title | Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2603.17271 |