Interpretable semi-parametric regression models with defined error bounds

Unreliable extrapolation of data-driven models hinders their applicability not only in safety-related domains. The paper discusses how model interpretability and uncertainty estimates can address this problem. A new semi-parametric approach is proposed for providing an interpretable model with improved accuracy by combining a symbolic regression model with a residual Gaussian Process. While the learned symbolic model is highly interpretable the residual model usually is not. However, by limiting the output of the residual model to a defined range a worst-case guarantee can be given in the sense that the maximal deviation from the symbolic model is always below a defined limit. The limitation of the residual model can include the uncertainty estimate of the Gaussian Process, thus giving the residual model more impact in high-confidence regions. When ranking the accuracy and interpretability of several different approaches on the SARCOS data benchmark the proposed combination yields the best result.