Explaining Machine Learning by Bootstrapping Partial Marginal Effects and Shapley Values

Thomas Cook, Zach Modig and Nathan Palmer
Authors registered in the RePEc Author Service: Greg M. Gupton

No RWP 21-12, Research Working Paper from Federal Reserve Bank of Kansas City

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. Boot- strapping 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; Artificial intelligence; Explainable machine learning; Shapley values; Model interpretation (search for similar items in EconPapers)
JEL-codes: C14 C15 C18 C45 C52 (search for similar items in EconPapers)
Pages: 39
Date: 2021-11-15, Revised 2024-08-06
New Economics Papers: this item is included in nep-big, nep-cmp, nep-ecm, nep-gth and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.kansascityfed.org/research/research-wo ... -and-shapley-values/ Full text (text/html)

Related works:
Working Paper: Explaining Machine Learning by Bootstrapping Partial Marginal Effects and Shapley Values (2024)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:fip:fedkrw:93596

Ordering information: This working paper can be ordered from

DOI: 10.18651/RWP2021-12

Access Statistics for this paper

More papers in Research Working Paper from Federal Reserve Bank of Kansas City Contact information at EDIRC.
Bibliographic data for series maintained by Kira Lillard ().