An entropy-based approach for a robust least squares spline approximation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909076381761536 |
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| author | Brugnano, Luigi Giordano, Domenico Iavernaro, Felice Rubino, Giorgia |
| author_facet | Brugnano, Luigi Giordano, Domenico Iavernaro, Felice Rubino, Giorgia |
| contents | We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is prescribed to a desired (small) value. Acting on this error yields a robust regression method that automatically detects and removes outliers from the data during the fitting procedure, by assigning them a very small weight. We discuss the use of both spline functions and spline curves. A number of numerical illustrations have been included to disclose the potentialities of the maximal-entropy approach in different application fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08792 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An entropy-based approach for a robust least squares spline approximation Brugnano, Luigi Giordano, Domenico Iavernaro, Felice Rubino, Giorgia Numerical Analysis 65D10, 94A17 We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is prescribed to a desired (small) value. Acting on this error yields a robust regression method that automatically detects and removes outliers from the data during the fitting procedure, by assigning them a very small weight. We discuss the use of both spline functions and spline curves. A number of numerical illustrations have been included to disclose the potentialities of the maximal-entropy approach in different application fields. |
| title | An entropy-based approach for a robust least squares spline approximation |
| topic | Numerical Analysis 65D10, 94A17 |
| url | https://arxiv.org/abs/2309.08792 |