Abstract

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 metamodels using Meijer G-functions — a class of complex-valued contour integrals that depend on real-valued parameters, and whose solutions reduce to familiar algebraic, analytic and closed-form functions for different parameter settings. This parameterization enables efficient optimization of metamodels via gradient descent, and allows discovering the functional forms learned by a model with minimal a priori assumptions. We show that symbolic metamodeling provides a generalized framework for model interpretation — many common forms of model explanation can be analytically derived from a symbolic metamodel.