美联储-用自举部分边际效应和Shapley值解释机器学习（英）

Finance and Economics Discussion SeriesFederal Reserve Board, Washington, D.C.ISSN 1936-2854 (Print)ISSN 2767-3898 (Online)Explaining Machine Learning by Bootstrapping Partial MarginalEffects and Shapley ValuesThomas R. Cook, Zach D. Modig, Nathan M. Palmer2024-075Please cite this paper as:Cook, Thomas R., Zach D. Modig, and Nathan M. Palmer (2024). “Explaining MachineLearning by Bootstrapping Partial Marginal Effects and Shapley Values,” Finance and Eco-nomics Discussion Series 2024-075. Washington: Board of Governors of the Federal ReserveSystem, https://doi.org/10.17016/FEDS.2024.075.NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminarymaterials circulated to stimulate discussion and critical comment. The analysis and conclusions set forthare those of the authors and do not indicate concurrence by other members of the research staff or theBoard of Governors. References in publications to the Finance and Economics Discussion Series (other thanacknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.Explaining Machine Learning by Bootstrapping PartialMarginal Effects and Shapley ValuesThomas R. Cook∗†Zach Modig†‡Nathan M. Palmer†‡August 6, 2024AbstractMachine learning and artificial intelligence are often described as “black boxes.”Traditional linear regression is interpreted through its marginal relationships as cap-tured by regression coefficients. We show that the same marginal relationship can bedescribed rigorously for any machine learning model by calculating the slope of the par-tial dependence functions, which we call the partial marginal effect (PME). We provethat the PME of OLS is analytically equivalent to the OLS regression coefficient. Boot-strapping provides standard errors and confidence intervals around the point estimatesof the PMEs.We apply the PME to a hedonic house pricing example and demon-strate that the PMEs of neural networks, support vector machines, random forests, andgradient boosting models reveal the non-linear relationships discovered by the machinelearning models and allow direct comparison between those models and a traditionallinear regression. Finally we extend PME to a Shapley value decomposition and explorehow it can be used to further explain model outputs.JEL Classifications: C14, C18, C15, C45, C521IntroductionMachine learning (ML) and artificial intelligence (AI) methods are often regarded as a blackbox: they may capture useful interactions and nonlinearities in data, but the shape and∗Federal Reserve Bank of Kansas CityEmail: thomas.cook@kc.frb.org†The views expressed in this article are those of the authors and do not necessarily reflect the views ofthe Federal Reserve Board, the Federal Reserve Bank of Kansas City or the Federal Reserve System.‡Federal Reserve Board of GovernorsEmail: nathan.m.palmer@frb.gov1nature of the relationships are difficult to ascertain. There is a growing appetite to use MLmodels in finance