FW-Shapley: Real-time Estimation of Weighted Shapley Values

TL;DR

Fast Weighted Shapley (FW-Shapley), an amortized framework for efficiently computing weighted Shapley values using a learned estimator, and shows that the estimator's training procedure is theoretically valid even though it does not use ground truth Weighted Shapley values during training.

Abstract

Fair credit assignment is essential in various machine learning (ML) applications, and Shapley values have emerged as a valuable tool for this purpose. However, in critical ML applications such as data valuation and feature attribution, the uniform weighting of Shapley values across subset cardinalities leads to unintuitive credit assignments. To address this, weighted Shapley values were proposed as a generalization, allowing different weights for subsets with different cardinalities. Despite their advantages, similar to Shapley values, Weighted Shapley values suffer from exponential compute costs, making them impractical for high-dimensional datasets. To tackle this issue, we present two key contributions. Firstly, we provide a weighted least squares characterization of weighted Shapley values. Next, using this characterization, we propose Fast Weighted Shapley (FW-Shapley), an amortized framework for efficiently computing weighted Shapley values using a learned estimator. We further show that our estimator's training procedure is theoretically valid even though we do not use ground truth Weighted Shapley values during training. On the feature attribution task, we outperform the learned estimator FastSHAP by $27\%$ (on average) in terms of Inclusion AUC. For data valuation, we are much faster (14 times) while being comparable to the state-of-the-art KNN Shapley.

Figures (9)

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• Figure : (a) $n = 100$
• Figure : (a) $n = 100$
• Figure : (b) $n = 500$

Theorems & Definitions (6)

• Proposition 2.1
• Proposition 2.2
• Lemma 5.1
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