Shapley Values
A mathematical concept originating from cooperative game theory, proposed by Lloyd Shapley in 1953 for fairly distributing the joint payoff among multiple participants. In machine learning, Shapley values are widely used for feature attribution, measuring each feature's average marginal contribution to model predictions.
Core Facts
The theoretical basis of SHAP comes from the concept of Shapley values in cooperative game theory, proposed by Nobel Prize-winning economist Lloyd Shapley in 1953; in 2017, Lundberg and Lee introduced it into the field of machine learning.
SHAP基于博弈论中的Shapley值，能够量化每个特征对最终预测结果的贡献度，是目前工业界应用最广泛的解释性工具之一
Timeline (last 90 days)
Common attribution methods include Shapley values, counterfactual reasoning and feature importance ranking, which are often presented in prediction functions as contribution rankings or driver factor lists.
On a purely additive model, the results of leave-one-out and Shapley are completely identical.
No matter how many samples are taken, efficiency always holds exactly when estimating the Shapley value by permutation sampling, because within each permutation the marginal contributions telescope to v(full set) − v(empty set).
The Shapley value can assign negative points to a feature to indicate that the feature lowered the predicted value.
The Shapley value can be computed by three independent algorithms—the factorial formula, permutation averaging, and Möbius inversion—and yield consistent results.
In the same interaction model, the Shapley value gives 5 points to each of the two features, totaling 10 points, matching the predicted value.
In the redundant feature scenario (two features carrying exactly the same information), leave-one-out gives both 0 points, while Shapley gives each copy 4 points.
Exactly computing the Shapley value requires summing over 2^n subsets; for n=20 about 1 million model evaluations are needed, and for n=30 more than 1 billion, which is infeasible in practice.
Shapley values satisfy four axioms—efficiency, symmetry, dummy, and additivity—and are considered the theoretically fairest method of feature attribution.
The paper proves that the distance corresponding to the representation induced by log-odds is exactly equal to the ℓ1 distance between analytical Shapley value vectors.
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All Facts (13)
The theoretical basis of SHAP comes from the concept of Shapley values in cooperative game theory, proposed by Nobel Prize-winning economist Lloyd Shapley in 1953; in 2017, Lundberg and Lee introduced it into the field of machine learning.
65%VerifiedSHAP基于博弈论中的Shapley值，能够量化每个特征对最终预测结果的贡献度，是目前工业界应用最广泛的解释性工具之一
65%UnverifiedCommon attribution methods include Shapley values, counterfactual reasoning and feature importance ranking, which are often presented in prediction functions as contribution rankings or driver factor lists.
50%UnverifiedThe Shapley value can assign negative points to a feature to indicate that the feature lowered the predicted value.
50%UnverifiedThe Shapley value can be computed by three independent algorithms—the factorial formula, permutation averaging, and Möbius inversion—and yield consistent results.
50%UnverifiedIn the same interaction model, the Shapley value gives 5 points to each of the two features, totaling 10 points, matching the predicted value.
50%UnverifiedIn the redundant feature scenario (two features carrying exactly the same information), leave-one-out gives both 0 points, while Shapley gives each copy 4 points.
50%UnverifiedOn a purely additive model, the results of leave-one-out and Shapley are completely identical.
50%UnverifiedExactly computing the Shapley value requires summing over 2^n subsets; for n=20 about 1 million model evaluations are needed, and for n=30 more than 1 billion, which is infeasible in practice.
50%UnverifiedNo matter how many samples are taken, efficiency always holds exactly when estimating the Shapley value by permutation sampling, because within each permutation the marginal contributions telescope to v(full set) − v(empty set).
50%UnverifiedThe paper proves that the distance corresponding to the representation induced by log-odds is exactly equal to the ℓ1 distance between analytical Shapley value vectors.
50%UnverifiedShapley values satisfy four axioms—efficiency, symmetry, dummy, and additivity—and are considered the theoretically fairest method of feature attribution.
50%UnverifiedThe paper provides an analytical form of Shapley values for weighted naive Bayes (a closed-form analytical solution requiring no sampling).
50%