Efficient Shapley performance attribution for least-squares regression

We consider the performance of a least-squares regression model, as judged by out-of-sample R 2 . Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between features. Evaluating the Shapley values exactly requires solving...

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Bibliographic Details
Published in:Statistics and computing 2024-10, Vol.34 (5), Article 149
Main Authors: Bell, Logan, Devanathan, Nikhil, Boyd, Stephen
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computer Science
Least squares method
Original Paper
Probability and Statistics in Computer Science
Regression models
Statistical Theory and Methods
Statistics and Computing/Statistics Programs
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Summary:We consider the performance of a least-squares regression model, as judged by out-of-sample R 2 . Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between features. Evaluating the Shapley values exactly requires solving a number of regression problems that is exponential in the number of features, so a Monte Carlo-type approximation is typically used. We focus on the special case of least-squares regression models, where several tricks can be used to compute and evaluate regression models efficiently. These tricks give a substantial speed up, allowing many more Monte Carlo samples to be evaluated, achieving better accuracy. We refer to our method as least-squares Shapley performance attribution (LS-SPA), and describe our open-source implementation.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-024-10459-9