Convergence Analysis of function-on-function Polynomial regression model
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911294491197440 |
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| author | Gupta, Naveen Sampath, Sivananthan |
| author_facet | Gupta, Naveen Sampath, Sivananthan |
| contents | In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence rates for estimation and prediction error by employing general (spectral) regularization under a general smoothness condition without imposing any additional conditions on the index function. We also establish lower bounds for any learning algorithm to explain the optimality of our convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00549 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of function-on-function Polynomial regression model Gupta, Naveen Sampath, Sivananthan Statistics Theory In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence rates for estimation and prediction error by employing general (spectral) regularization under a general smoothness condition without imposing any additional conditions on the index function. We also establish lower bounds for any learning algorithm to explain the optimality of our convergence rates. |
| title | Convergence Analysis of function-on-function Polynomial regression model |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2512.00549 |