Gaussian Function On Response Surface Estimation

Abstract: We propose a new framework for 2-D interpreting (features and samples) black-box machine learning models via a metamodeling technique, by which we study the output and input relationships of the underlying machine learning model. The metamodel can be estimated from data generated via a trained complex model by running the computer experiment on samples of data in the region of interest. We utilize a Gaussian process as a surrogate to capture the response surface of a complex model, in which we incorporate two parts in the process: interpolated values that are modeled by a stationary Gaussian process Z governed by a prior covariance function, and a mean function mu that captures the known trends in the underlying model. The optimization procedure for the variable importance parameter theta is to maximize the likelihood function. This theta corresponds to the correlation of individual variables with the target response. There is no need for any pre-assumed models since it depends on empirical observations. Experiments demonstrate the potential of the interpretable model through quantitative assessment of the predicted samples.