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

TL;DR

This paper introduces a robust spline approximation method that maximizes entropy under a mean squared error constraint, effectively detecting and removing outliers during data fitting.

Contribution

It presents a novel entropy-based weighted least squares spline approach that enhances robustness and outlier detection in noisy datasets.

Findings

Effective outlier detection during spline fitting

Robust regression with automatic outlier removal

Versatile application to spline functions and curves

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.