Visualizing Multi-Variable Prediction Functions by Segmented k-CPG's

Abstract

Machine learning methods such as support vector machines and random forests yield nonparametric prediction functions of the form y = f(x_1 ,..., x_p ) . As a sequel to the previous article (Huh and Lee, 2008) for visualizing nonparametric functions, I propose more sensible graphs for visualizing y = f(x_1 ,..., x_p ) herein which has two clear advantages over the previous simple graphs. New graphs will show a small number of prototype curves of f(x_1 ,..., x_{j-1} , x_j , x_{j+1} ..., x_p ), revealing statistically plausible portion over the interval of x_j which changes with (x_1 ,..., x_{j-1}, x_{j+1}, ..., x_p ). To complement the visual display, matching importance measures for each of p predictor variables are produced. The proposed graphs and importance measures are validated in simulated settings and demonstrated for an environmental study.