Efficient Computation and Analysis of Distributional Shapley Values

Yongchan Kwon, Manuel A. Rivas, James Zou
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:793-801, 2021.

Abstract

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values into a statistical framework and can be applied to identify data points that are useful (or harmful) to a learning algorithm. Estimating DShapley is computationally expensive, however, and this can be a major challenge to using it in practice. Moreover, there has been little mathematical analyses of how this value depends on data characteristics. In this paper, we derive the first analytic expressions for DShapley for the canonical problems of linear regression, binary classification, and non-parametric density estimation. These analytic forms provide new algorithms to estimate DShapley that are several orders of magnitude faster than previous state-of-the-art methods. Furthermore, our formulas are directly interpretable and provide quantitative insights into how the value varies for different types of data. We demonstrate the practical efficacy of our approach on multiple real and synthetic datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-kwon21a, title = { Efficient Computation and Analysis of Distributional Shapley Values }, author = {Kwon, Yongchan and A. Rivas, Manuel and Zou, James}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {793--801}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/kwon21a/kwon21a.pdf}, url = {https://proceedings.mlr.press/v130/kwon21a.html}, abstract = { Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values into a statistical framework and can be applied to identify data points that are useful (or harmful) to a learning algorithm. Estimating DShapley is computationally expensive, however, and this can be a major challenge to using it in practice. Moreover, there has been little mathematical analyses of how this value depends on data characteristics. In this paper, we derive the first analytic expressions for DShapley for the canonical problems of linear regression, binary classification, and non-parametric density estimation. These analytic forms provide new algorithms to estimate DShapley that are several orders of magnitude faster than previous state-of-the-art methods. Furthermore, our formulas are directly interpretable and provide quantitative insights into how the value varies for different types of data. We demonstrate the practical efficacy of our approach on multiple real and synthetic datasets. } }
Endnote
%0 Conference Paper %T Efficient Computation and Analysis of Distributional Shapley Values %A Yongchan Kwon %A Manuel A. Rivas %A James Zou %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-kwon21a %I PMLR %P 793--801 %U https://proceedings.mlr.press/v130/kwon21a.html %V 130 %X Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values into a statistical framework and can be applied to identify data points that are useful (or harmful) to a learning algorithm. Estimating DShapley is computationally expensive, however, and this can be a major challenge to using it in practice. Moreover, there has been little mathematical analyses of how this value depends on data characteristics. In this paper, we derive the first analytic expressions for DShapley for the canonical problems of linear regression, binary classification, and non-parametric density estimation. These analytic forms provide new algorithms to estimate DShapley that are several orders of magnitude faster than previous state-of-the-art methods. Furthermore, our formulas are directly interpretable and provide quantitative insights into how the value varies for different types of data. We demonstrate the practical efficacy of our approach on multiple real and synthetic datasets.
APA
Kwon, Y., A. Rivas, M. & Zou, J.. (2021). Efficient Computation and Analysis of Distributional Shapley Values . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:793-801 Available from https://proceedings.mlr.press/v130/kwon21a.html.

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