A package to automate formation and evaluation of multivariate polynomial regression models, especially as an alternative to neural networks and other machine learning algorithms.
An important feature is that dummy variables are handled properly, so that for instance powers of a dummy variable do not exist as duplicates of the original.
Note: This library is used in the qeML package; qeML (“quick and easy machine learning”) provides a convenient, consistent interface to various machine learning algorithms, including polynomial regression via polyreg. There is also a polynomial version of ridge regression. Other than special purposes, it is recommended that the user try the qeMLinterface, rather than using polyreg directly.
In Polynomial Regression As an Alternative to Neural Nets, by Cheng, Khomtchouk, Matloff and Mohanty, 2018, it is argued that dense, feedforward neural networks are essentially polynomial regression models. This was extended in Towards a Mathematical Framework to Inform Neural Network Modelling via Polynomial Regression. by Morala, Cifuentes, Lillo, and Iñaki Ucar. The point is then, why go through the problems of neural networks–convergence, local minima and so on–when can can work more simply with polynomials?
Of course, it is not quite that simple. If we start with p variables in our model, the d-degree polynomial version will have O(pd) variables, which can easily become computationally challenging. Nevertheless, our experiments have had quite encouraging results.
The main functions are polyfit() and predict.polyFit(). One can fit either regression or classification models.
Programmer/engineer 2000 Census data, Silicon Valley, built-in to the package.
data(pef)
# model wage income, fitting a degree-2 model
pfout <- polyFit(pef[,c(1,2,3,4,6,5)],2,use='lm')
# predict wage of person like that in row 1, but age 40 and female
newx <- pef[1,-5]
newx$age <- 48
newx$sex <- 1
predict(pfout,newx) # about $84,330