Polynomial Order Prediction Using a Classifier Trained on Meta-Measurements

Abstract

Polynomial regression is still widely used in engineering and economics where polynomials of low order (usually less than tenth order) are being fitted to experimental data. However, the fundamental problem of selecting the optimal order of the polynomial to be fitted to experimental data is not a straightforward problem. This paper investigates the performance of automated methods for predicting the order of the polynomial that can be fitted on the decision boundary formed between two classes in a pattern recognition problem. We have investigated statistical methods and proposed a method of predicting the order of the polynomial. Our proposed machine learning method is computing a number of measurements on the input data which are used by a classifier trained offline to predict the order of the polynomial that should be fitted to the decision boundary. We have considered two matching scenarios. One scenario is where we have counted only the exact matches as being correct and another scenario in which we count as correct an exact match and higher polynomial orders. Experimental results on synthetic data show that our proposed method predicts the exact order of the polynomial with 31.90% accuracy as opposed to 13.22% of the best statistical method, but it also under-estimates the true order almost twice as often when compared to statistical methods of predicting the order of the polynomial to be fitted to the same data points.