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Shapley Marginal Surplus for Strong Models

Daniel de Marchi, Michael Kosorok, Scott de Marchi

TL;DR

The paper tackles the gap between model-based Shapley explanations and the true data-generating process (DGP) by introducing Shapley Marginal Surplus for Strong Models (SMSSM). SMSSM samples a space of candidate models, evaluates feature marginal surpluses within subsets, and uses a Shapley-value framework to infer feature importance with respect to the DGP, rather than a single predictive model. Theoretical results establish asymptotic selectivity under a universal-approximator model class and a calibration condition on the loss threshold, while empirical results on simulated and real data show SMSSM outperforms LOCO, MCR, and attributive SHAP/XGBoost metrics in identifying true covariate importance under multicollinearity and complex dependencies. The work highlights a path toward inferential explanations in ML that respect the DGP, while acknowledging computational tradeoffs and outlining directions for efficiency improvements and meta-model-guided sampling.

Abstract

Shapley values have seen widespread use in machine learning as a way to explain model predictions and estimate the importance of covariates. Accurately explaining models is critical in real-world models to both aid in decision making and to infer the properties of the true data-generating process (DGP). In this paper, we demonstrate that while model-based Shapley values might be accurate explainers of model predictions, machine learning models themselves are often poor explainers of the DGP even if the model is highly accurate. Particularly in the presence of interrelated or noisy variables, the output of a highly predictive model may fail to account for these relationships. This implies explanations of a trained model's behavior may fail to provide meaningful insight into the DGP. In this paper we introduce a novel variable importance algorithm, Shapley Marginal Surplus for Strong Models, that samples the space of possible models to come up with an inferential measure of feature importance. We compare this method to other popular feature importance methods, both Shapley-based and non-Shapley based, and demonstrate significant outperformance in inferential capabilities relative to other methods.

Shapley Marginal Surplus for Strong Models

TL;DR

The paper tackles the gap between model-based Shapley explanations and the true data-generating process (DGP) by introducing Shapley Marginal Surplus for Strong Models (SMSSM). SMSSM samples a space of candidate models, evaluates feature marginal surpluses within subsets, and uses a Shapley-value framework to infer feature importance with respect to the DGP, rather than a single predictive model. Theoretical results establish asymptotic selectivity under a universal-approximator model class and a calibration condition on the loss threshold, while empirical results on simulated and real data show SMSSM outperforms LOCO, MCR, and attributive SHAP/XGBoost metrics in identifying true covariate importance under multicollinearity and complex dependencies. The work highlights a path toward inferential explanations in ML that respect the DGP, while acknowledging computational tradeoffs and outlining directions for efficiency improvements and meta-model-guided sampling.

Abstract

Shapley values have seen widespread use in machine learning as a way to explain model predictions and estimate the importance of covariates. Accurately explaining models is critical in real-world models to both aid in decision making and to infer the properties of the true data-generating process (DGP). In this paper, we demonstrate that while model-based Shapley values might be accurate explainers of model predictions, machine learning models themselves are often poor explainers of the DGP even if the model is highly accurate. Particularly in the presence of interrelated or noisy variables, the output of a highly predictive model may fail to account for these relationships. This implies explanations of a trained model's behavior may fail to provide meaningful insight into the DGP. In this paper we introduce a novel variable importance algorithm, Shapley Marginal Surplus for Strong Models, that samples the space of possible models to come up with an inferential measure of feature importance. We compare this method to other popular feature importance methods, both Shapley-based and non-Shapley based, and demonstrate significant outperformance in inferential capabilities relative to other methods.
Paper Structure (17 sections, 8 equations, 1 figure, 3 tables, 1 algorithm)

This paper contains 17 sections, 8 equations, 1 figure, 3 tables, 1 algorithm.

Table of Contents

  1. Problem Introduction
  2. Theoretical Preliminaries
  3. Subset Functions
  4. Game Theory and Shapley Values
  5. Selective Importance for Universal Approximators
  6. Refit-Based Importance for Selective Feature Importance
  7. Conformal Inference and LOCO
  8. Model Class Reliance
  9. Shapley Marginal Surplus for Strong Models
  10. Methods and Data
  11. Simulated Data
  12. Real-World Data
  13. Results
  14. Simulated Data Test
  15. Real Data Results
  16. ...and 2 more sections

Figures (1)

  • Figure 1: Most feature importance methods take the model as truth, going straight from creating a model to calculating importance (red arrow). Our procedure adds the intermediate step of calculating the validity of the class of models (black arrows), which dramatically improves feature importance allocation.