Spacing of Information in Polynomial Regression

Polynomial regression with derivative information in nuclear reactor uncertainty quantification

We introduce a novel technique of uncertainty quantification using polynomial regression with derivative information and apply it to analyze the performance of a model of a sodium-cooled fast reactor. We construct a surrogate model as a goal-oriented projection onto an incomplete space of polynomials, find coordinates of projection by collocation, and use derivative information to reduce the nu...

Piecewise-Polynomial Regression Trees∗

A nonparametric function estimation method called SUPPORT (“Smoothed and Unsmoothed Piecewise-Polynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion of the data space. Partitioning is carried out recursively as in a tree-structured method. If the estimate is ...

Automatic polynomial wavelet regression

In Oh, Naveau and Lee (2001) a simple method is proposed for reducing the bias at the boundaries for wavelet thresholding regression. The idea is to model the regression function as a sum of wavelet basis functions and a low-order polynomial. The latter is expected to account for the boundary problem. Practical implementation of this method requires the choice of the order of the low-order poly...

Local Polynomial Regression

Stretchy Polynomial Regression

This article proposes a novel solution for stretchy polynomial regression learning. The solution comes in primal and dual closed-forms similar to that of ridge regression. Essentially, the proposed solution stretches the covariance computation via a power term thereby compresses or amplifies the estimation. Our experiments on both synthetic data and real-world data show effectiveness of the pro...