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

Machine learning methods such as support vector machines and random forests yield nonparametric prediction functions of the form y = $f(x_1,{\ldots},x_p)$. As a sequel to the previous article (Huh and Lee, 2008) for visualizing nonparametric functions, I propose more sensible graphs for visualizing y = $f(x_1,{\ldots},x_p)$ herein which has two clear advantages over the previous simple graphs. New graphs will show a small number of prototype curves of $f(x_1,{\ldots},x_{j-1},x_j,x_{j+1}{\ldots},x_p)$, revealing statistically plausible portion over the interval of $x_j$ which changes with ($x_1,{\ldots},x_{j-1},x_{j+1},{\ldots},x_p$). 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.