Question

When using SHAP values to explain a black-box model’s prediction for a specific patient, what is the fundamental game-theoretic property that ensures the contribution of each feature sums up to the total model output?

Accepted Answer

The fundamental game-theoretic property that ensures the contributions of each feature sum up to the total model output is called Efficiency. In the context of cooperative game theory, which forms the mathematical foundation of SHAP (SHapley Additive exPlanations), a game consists of players collaborating to achieve a total payout. When applied to machine learning, the players are the input features of a model, and the total payout is the difference between the model&#x27;s prediction for a specific patient and the average prediction across the entire dataset. The Efficiency property dictates that the sum of the individual contributions, known as SHAP values, must exactly equal the total difference between the actual prediction and the baseline average. This property guarantees that no information is lost or created during the attribution process, effectively distributing the entire model output among the contributing features. For example, if a model predicts a 70 percent risk of disease for a patient while the average risk in the population is 20 percent, the SHAP values for all features must sum to 50 percent to fully explain the deviation from the average.

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When using SHAP values to explain a black-box model’s prediction for a specific patient, what is the fundamental game-theoretic property that ensures the contribution of each feature sums up to the total model output?