Working Paper

Explaining Machine Learning by Bootstrapping Partial Marginal Effects and Shapley Values

Abstract: Machine learning and artificial intelligence are often described as “black boxes.” Traditional linear regression is interpreted through its marginal relationships as captured by regression coefficients. We show that the same marginal relationship can be described rigorously for any machine learning model by calculating the slope of the partial dependence functions, which we call the partial marginal effect (PME). We prove that the PME of OLS is analytically equivalent to the OLS regression coefficient. Bootstrapping provides standard errors and confidence intervals around the point estimates of the PMEs. We apply the PME to a hedonic house pricing example and demonstrate that the PMEs of neural networks, support vector machines, random forests, and gradient boosting models reveal the non-linear relationships discovered by the machine learning models and allow direct comparison between those models and a traditional linear regression. Finally we extend PME to a Shapley value decomposition and explore how it can be used to further explain model outputs.

Keywords: Machine learning; House prices; Statistical inference;

JEL Classification: C14; C18; C15; C45; C52;

https://doi.org/10.17016/FEDS.2024.075

Bibliographic Information

Provider: Board of Governors of the Federal Reserve System (U.S.)

Part of Series: Finance and Economics Discussion Series

Publication Date: 2024-09-20

Number: 2024-075