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arXiv · 2309.08792

An entropy-based approach for a robust least squares spline approximation

Luigi Brugnano·Domenico Giordano·Felice Iavernaro·Giorgia Rubino
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Abstract

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.

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Luigi Brugnano, Domenico Giordano, Felice Iavernaro, Giorgia Rubino. 2023-09-15. An entropy-based approach for a robust least squares spline approximation. https://doi.org/10.1016/j.cam.2024.115773

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