Gaussian Process Regression under Computational and Epistemic Misspecification
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916421033787392 |
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| author | Sanz-Alonso, Daniel Yang, Ruiyi |
| author_facet | Sanz-Alonso, Daniel Yang, Ruiyi |
| contents | Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Loève expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Our theory also accounts for epistemic misspecification in the choice of kernel parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09225 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gaussian Process Regression under Computational and Epistemic Misspecification Sanz-Alonso, Daniel Yang, Ruiyi Numerical Analysis Statistics Theory Machine Learning Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Loève expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Our theory also accounts for epistemic misspecification in the choice of kernel parameters. |
| title | Gaussian Process Regression under Computational and Epistemic Misspecification |
| topic | Numerical Analysis Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2312.09225 |