Demystifying Black-box Models with Symbolic Metamodels

Understanding the predictions of a machine learning model can be as crucial as the model's accuracy in many application domains. However, the black-box nature of most highly-accurate (complex) models is a major hindrance to their interpretability. To address this issue, we introduce the symbolic metamodeling framework -- a general methodology for interpreting predictions by converting "black-box" models into "white-box" functions that are understandable to human subjects. A symbolic metamodel is a model of a model, i.e., a surrogate model of a trained (machine learning) model expressed through a succinct symbolic expression that comprises familiar mathematical functions and can be subjected to symbolic manipulation. We parameterize symbolic metamodels using Meijer G-functions -- a class of complex-valued contour integrals that depend on scalar parameters, and whose solutions reduce to familiar elementary, algebraic, analytic and closed-form functions for different parameter settings.