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.

翻译：本文考虑含噪声数据集上的加权最小二乘样条逼近问题。通过将权重解释为概率分布，我们在均方误差被约束为预期（较小）值的条件下最大化其关联熵。对该误差的作用产生了一种鲁棒回归方法，该方法能在拟合过程中自动检测并剔除数据中的异常点，为其分配极小的权重。我们分别讨论了样条函数与样条曲线的应用场景。文中包含大量数值实例，以揭示最大熵方法在不同应用领域中的潜力。