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Demystifying Black-box Models with Symbolic Metamodels
Ahmed Alaa · Mihaela van der Schaar

Thu Dec 12 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #76

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. This parameterization enables efficient optimization of metamodels via gradient descent, and allows discovering the functional forms learned by a machine learning model with minimal a priori assumptions. We show that symbolic metamodeling provides an all-encompassing framework for model interpretation — all common forms of global and local explanations of a model can be analytically derived from its symbolic metamodel.

Author Information

Ahmed Alaa (UCLA)
Mihaela van der Schaar (University of Cambridge, Alan Turing Institute and UCLA)

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