Gaussian Function On Response Surface Estimation

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 μ that captures the known trends in the underlying model. The optimization procedure for the variable importance parameter θ is to maximize the likelihood function. This θ 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.