Automatic Coefficient-Style Interpretation of Gaussian Process Regressions: Bridging Bayesian Nonparametrics and Econometric Reporting

Abstract

Econometric practice prioritizes globally interpretable coefficients from parametric models, yet such interpretability can be misleading under functional form misspecification and heterogeneous marginal effects. Gaussian process (GP) regression offers a principled Bayesian non-parametric alternative with calibrated predictive uncertainty, but its function-valued output is not immediately compatible with coefficient-centric reporting standards. We propose an automatic interpretation framework that translates a fitted GP into segment-wise, coefficient-like summaries with full uncertainty quantiffication. The method estimates a GP model, extracts the posterior derivative (marginal effect function), and automatically partitions the covariate support into segments with piecewise-constant slopes. Segment selection uses an elbow criterion that identifies structural breaks without manual knot placement. Uncertainty is propagated via posterior function sampling, yielding credible intervals for each segment-level coefficient.Simulations comparing our approach against ordinary least squares and generalized additive models demonstrate that the framework recovers interpretable effect patterns while achieving substantially lower estimation error and better uncertainty calibration than alternatives. Three empirical applications reveal economically and physically meaningful heterogeneity across diverse domains: the marginal effect of income on house prices is 2.5 times larger in lower-income neighborhoods; returns to education are seven times larger for post-secondary schooling; and the fuel efficiency penalty of vehicle weight is twice as severe for lighter vehicles.