Fast Computation of Leave-One-Out Cross-Validation for $k$-NN Regression
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913597624418304 |
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| author | Kanagawa, Motonobu |
| author_facet | Kanagawa, Motonobu |
| contents | We describe a fast computation method for leave-one-out cross-validation (LOOCV) for $k$-nearest neighbours ($k$-NN) regression. We show that, under a tie-breaking condition for nearest neighbours, the LOOCV estimate of the mean square error for $k$-NN regression is identical to the mean square error of $(k+1)$-NN regression evaluated on the training data, multiplied by the scaling factor $(k+1)^2/k^2$. Therefore, to compute the LOOCV score, one only needs to fit $(k+1)$-NN regression only once, and does not need to repeat training-validation of $k$-NN regression for the number of training data. Numerical experiments confirm the validity of the fast computation method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast Computation of Leave-One-Out Cross-Validation for $k$-NN Regression Kanagawa, Motonobu Machine Learning Data Structures and Algorithms Computation Methodology We describe a fast computation method for leave-one-out cross-validation (LOOCV) for $k$-nearest neighbours ($k$-NN) regression. We show that, under a tie-breaking condition for nearest neighbours, the LOOCV estimate of the mean square error for $k$-NN regression is identical to the mean square error of $(k+1)$-NN regression evaluated on the training data, multiplied by the scaling factor $(k+1)^2/k^2$. Therefore, to compute the LOOCV score, one only needs to fit $(k+1)$-NN regression only once, and does not need to repeat training-validation of $k$-NN regression for the number of training data. Numerical experiments confirm the validity of the fast computation method. |
| title | Fast Computation of Leave-One-Out Cross-Validation for $k$-NN Regression |
| topic | Machine Learning Data Structures and Algorithms Computation Methodology |
| url | https://arxiv.org/abs/2405.04919 |