Explaining Machine Learning by Bootstrapping Partial Marginal Effects and Shapley Values

Thomas Cook, Zach Modig and Nathan Palmer

No 2024-075, Finance and Economics Discussion Series from Board of Governors of the Federal Reserve System (U.S.)

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 (search for similar items in EconPapers)
JEL-codes: C14 C15 C18 C45 C52 (search for similar items in EconPapers)
Pages: 40 p.
Date: 2024-09-20
New Economics Papers: this item is included in nep-big, nep-cmp, nep-ecm and nep-gth
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Persistent link: https://EconPapers.repec.org/RePEc:fip:fedgfe:2024-75

DOI: 10.17016/FEDS.2024.075

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