Gaussian Function On Response Surface Estimation
This work addresses the problem of interpreting black-box machine learning models for practitioners who need to understand input-output relationships, offering an incremental approach to model interpretability.
This paper proposes a new framework for interpreting 2-D black-box machine learning models by using a Gaussian process as a surrogate metamodel. The metamodel captures the response surface by combining interpolated values from a stationary Gaussian process and a mean function for known trends, with variable importance optimized by maximizing the likelihood function.
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.