[Paper Review] A $k$-additive Choquet integral-based approach to approximate the SHAP values for local interpretability in machine learning

Guilherme Dean Pelegrina, Leonardo Tomazeli Duarte+1 more|arXiv (Cornell University)|Nov 3, 2022

Multi-Criteria Decision Making4 citations

TL;DR

This paper proposes a k-additive Choquet integral-based method to approximate SHAP values for local model interpretability in machine learning, reducing computational cost by leveraging k-additive games. The approach maintains high fidelity to exact SHAP values while requiring fewer model evaluations—especially effective with 3-additive approximation (3_ADD-SHAP), which outperforms Kernel SHAP in efficiency with minimal accuracy loss.

ABSTRACT

Besides accuracy, recent studies on machine learning models have been addressing the question on how the obtained results can be interpreted. Indeed, while complex machine learning models are able to provide very good results in terms of accuracy even in challenging applications, it is difficult to interpret them. Aiming at providing some interpretability for such models, one of the most famous methods, called SHAP, borrows the Shapley value concept from game theory in order to locally explain the predicted outcome of an instance of interest. As the SHAP values calculation needs previous computations on all possible coalitions of attributes, its computational cost can be very high. Therefore, a SHAP-based method called Kernel SHAP adopts an efficient strategy that approximate such values with less computational effort. In this paper, we also address local interpretability in machine learning based on Shapley values. Firstly, we provide a straightforward formulation of a SHAP-based method for local interpretability by using the Choquet integral, which leads to both Shapley values and Shapley interaction indices. Moreover, we also adopt the concept of $k$-additive games from game theory, which contributes to reduce the computational effort when estimating the SHAP values. The obtained results attest that our proposal needs less computations on coalitions of attributes to approximate the SHAP values.

Motivation & Objective

• Address the high computational cost of exact SHAP value computation in complex machine learning models.
• Improve efficiency of local interpretability methods without sacrificing interpretability quality.
• Provide a model-agnostic approach that supports both individual feature contributions and feature interaction effects.
• Reduce over-parametrization and computational burden by using k-additive games in the Choquet integral framework.
• Enable practical deployment of SHAP-like explanations in real-world applications with limited computational resources.

Proposed method

• Formulate local interpretability using the Choquet integral with parameters directly linked to Shapley values, enabling both individual and interaction effects.
• Introduce k-additive games to limit the number of coalitions considered, reducing the number of required model evaluations.
• Use the 3-additive variant (3_ADD-SHAP) as a key approximation strategy, balancing flexibility and computational efficiency.
• Adapt the SHAP framework via the Choquet integral to maintain desirable properties like local accuracy, missingness, and consistency.
• Approximate SHAP values by sampling coalitions under the k-additive constraint, minimizing the number of predictions needed.
• Ensure interpretability fidelity by preserving the game-theoretic properties of Shapley values while reducing complexity.

Experimental results

Research questions

• RQ1 Can the Choquet integral be used as a direct and interpretable framework for computing SHAP values?
• RQ2 How does the use of k-additive games reduce the number of required model evaluations in SHAP approximation?
• RQ3 What is the trade-off between computational efficiency and approximation accuracy when using k-additive models?
• RQ4 How does the 3_ADD-SHAP variant compare to Kernel SHAP in terms of efficiency and fidelity to exact SHAP values?
• RQ5 Can the proposed method maintain the key interpretability properties (local accuracy, consistency, missingness) under approximation?

Key findings

• The k-additive Choquet integral-based approach significantly reduces the number of model evaluations required to approximate SHAP values, especially with the 3_ADD-SHAP variant.
• The 3_ADD-SHAP method achieves high approximation accuracy with minimal deviation from exact SHAP values, even when using fewer than all possible coalitions.
• The proposed method maintains the desirable properties of SHAP, including local accuracy, missingness, and consistency, due to its foundation in game-theoretic principles.
• Compared to Kernel SHAP, the proposed method requires fewer predictions to achieve comparable or better interpretability performance in tested scenarios.
• The k-additive formulation avoids over-parametrization in low-evaluation regimes, improving stability and generalization of the explanation.
• Numerical experiments confirm that the approximation error introduced by k-additivity is negligible, particularly for 3_ADD-SHAP, ensuring reliable local interpretability.