We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with regression and classification tasks on different datasets.

A robust and adaptive smartphone-based colorimetric sensing platform is reported. It utilizes multiple regression analysis to address nonlinear concurrent variations of variables. The instrument can perform measurement with improved accuracy over a wide range where both color intensity information signal varies independently often simultaneously. the smartphone in-built flash LED ( λ = 400–700 ...

Statistical calibration using linear regression is a useful statistical tool having many applications. Calibration for infinitely many future $y$-values requires the construction of simultaneous tolerance intervals (STI's). As calibration often involves only two variables $x$ and $y$ and polynomial regression is probably the most frequently used model for relating $y$ with $x$, construction of ...

We extend the common linear functional regression model to the case where the dependency of a scalar response on a functional predictor is of polynomial rather than linear nature. Focusing on the quadratic case, we demonstrate the usefulness of the polynomial functional regression model which encompasses linear functional regression as a special case. Our approach works under mild conditions fo...

Evolutionary Polynomial Regression (EPR) is a recently developed hybrid regression method that combines the best features of conventional numerical regression techniques with the genetic programming/symbolic regression technique. The original version of EPR works with formulae based on true or pseudo-polynomial expressions using a single-objective genetic algorithm. Therefore, to obtain a set o...

Local polynomial regression (Fan & Gijbels, 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this paper, we significantly accelerate the computation of local polynomial estimates ...