The Shapley Value in Machine Learning

Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic properties of the Shapley value. Then we give an overview of the most important applications of the Shapley value in machine learning: feature selection, explainability, multi-agent reinforcement learning, ensemble pruning, and data valuation. We examine the most crucial limitations of the Shapley value and point out directions for future research.

[1]  Yongchan Kwon,et al.  Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning , 2021, AISTATS.

[2]  Proceedings of the 30th ACM International Conference on Information & Knowledge Management , 2021 .

[3]  Daniel Deutch,et al.  Explanations for Data Repair Through Shapley Values , 2021, CIKM.

[4]  Lizhen Cui,et al.  GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning , 2021, ACM Trans. Intell. Syst. Technol..

[5]  Kun Kuang,et al.  Shapley Counterfactual Credits for Multi-Agent Reinforcement Learning , 2021, KDD.

[6]  Chris Dyer,et al.  Game-theoretic Vocabulary Selection via the Shapley Value and Banzhaf Index , 2021, NAACL.

[7]  Ariel D. Procaccia,et al.  If You Like Shapley Then You'll Love the Core , 2021, AAAI.

[8]  Quanshi Zhang,et al.  Interpreting Multivariate Shapley Interactions in DNNs , 2021, AAAI.

[9]  George Michailidis,et al.  Flow-based Attribution in Graphical Models: A Recursive Shapley Approach , 2021, ICML.

[10]  Joshua N. Cooper,et al.  Sampling Permutations for Shapley Value Estimation , 2021, J. Mach. Learn. Res..

[11]  Fragkiskos D. Malliaros,et al.  GraphSVX: Shapley Value Explanations for Graph Neural Networks , 2021, ECML/PKDD.

[12]  Daniel Fryer,et al.  Shapley values for feature selection: The good, the bad, and the axioms , 2021, IEEE Access.

[13]  Shuiwang Ji,et al.  On Explainability of Graph Neural Networks via Subgraph Explorations , 2021, ICML.

[14]  Benedek Rozemberczki,et al.  The Shapley Value of Classifiers in Ensemble Games , 2021, CIKM.

[15]  Sandhya Tripathi,et al.  Interpretable feature subset selection: A Shapley value based approach , 2020, 2020 IEEE International Conference on Big Data (Big Data).

[16]  Su-In Lee,et al.  Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression , 2020, AISTATS.

[17]  Tom Claassen,et al.  Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models , 2020, NeurIPS.

[18]  Scott M. Lundberg,et al.  Shapley Flow: A Graph-based Approach to Interpreting Model Predictions , 2020, AISTATS.

[19]  Aldo Lipani,et al.  A Multilinear Sampling Algorithm to Estimate Shapley Values , 2020, 2020 25th International Conference on Pattern Recognition (ICPR).

[20]  Proceedings of the 29th ACM International Conference on Information & Knowledge Management , 2020 .

[21]  Sihong Xie,et al.  Shapley Values and Meta-Explanations for Probabilistic Graphical Model Inference , 2020, CIKM.

[22]  Dawn Song,et al.  A Principled Approach to Data Valuation for Federated Learning , 2020, Federated Learning.

[23]  Lakhdar Sais,et al.  A Bayesian Monte Carlo method for computing the Shapley value: Application to weighted voting and bin packing games , 2020, Comput. Oper. Res..

[24]  Scott Sanner,et al.  Online Class-Incremental Continual Learning with Adversarial Shapley Value , 2020, AAAI.

[25]  James Zou,et al.  Efficient computation and analysis of distributional Shapley values , 2020, AISTATS.

[26]  Jean Feng,et al.  Efficient nonparametric statistical inference on population feature importance using Shapley values , 2020, ICML.

[27]  Damien de Mijolla,et al.  Shapley explainability on the data manifold , 2020, ICLR.

[28]  R. Sarkar,et al.  CGA: a new feature selection model for visual human action recognition , 2020, Neural Computing and Applications.

[29]  James Zou,et al.  A Distributional Framework for Data Valuation , 2020, ICML.

[30]  Sorelle A. Friedler,et al.  Problems with Shapley-value-based explanations as feature importance measures , 2020, ICML.

[31]  James Y. Zou,et al.  Neuron Shapley: Discovering the Responsible Neurons , 2020, NeurIPS.

[32]  Yang Liu,et al.  Federated Learning , 2019, Synthesis Lectures on Artificial Intelligence and Machine Learning.

[33]  Colin Rowat,et al.  Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability , 2019, NeurIPS.

[34]  Mukund Sundararajan,et al.  The many Shapley values for model explanation , 2019, ICML.

[35]  Ferenc Illés,et al.  Estimation of the Shapley value by ergodic sampling , 2019, ArXiv.

[36]  James Y. Zou,et al.  Data Shapley: Equitable Valuation of Data for Machine Learning , 2019, ICML.

[37]  Markus H. Gross,et al.  Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation , 2019, ICML.

[38]  Nezihe Merve Gürel,et al.  Towards Efficient Data Valuation Based on the Shapley Value , 2019, AISTATS.

[39]  Mukund Sundararajan,et al.  The Shapley Taylor Interaction Index , 2019, ICML.

[40]  Le Song,et al.  L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data , 2018, ICLR.

[41]  Arthur Gretton,et al.  Antithetic and Monte Carlo kernel estimators for partial rankings , 2018, Statistics and Computing.

[42]  M. de Rijke,et al.  Finding Influential Training Samples for Gradient Boosted Decision Trees , 2018, ICML.

[43]  Daniel Gómez,et al.  Improving polynomial estimation of the Shapley value by stratified random sampling with optimum allocation , 2017, Comput. Oper. Res..

[44]  Scott Lundberg,et al.  A Unified Approach to Interpreting Model Predictions , 2017, NIPS.

[45]  Percy Liang,et al.  Understanding Black-box Predictions via Influence Functions , 2017, ICML.

[46]  Talal Rahwan,et al.  Bounding the Estimation Error of Sampling-based Shapley Value Approximation With/Without Stratifying , 2013, ArXiv.

[47]  Jin Li,et al.  Feature evaluation and selection with cooperative game theory , 2012, Pattern Recognit..

[48]  Michael Wooldridge,et al.  Computational Aspects of Cooperative Game Theory , 2011, KES-AMSTA.

[49]  Daniel Gómez,et al.  Polynomial calculation of the Shapley value based on sampling , 2009, Comput. Oper. Res..

[50]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[51]  Nicholas R. Jennings,et al.  A linear approximation method for the Shapley value , 2008, Artif. Intell..

[52]  Anirban Dasgupta,et al.  Sampling algorithms and coresets for ℓp regression , 2007, SODA '08.

[53]  Eytan Ruppin,et al.  Feature Selection via Coalitional Game Theory , 2007, Neural Computation.

[54]  M. Josune Albizuri,et al.  Configuration values: Extensions of the coalitional Owen value , 2006, Games Econ. Behav..

[55]  Isabelle Guyon,et al.  An Introduction to Variable and Feature Selection , 2003, J. Mach. Learn. Res..

[56]  R. Dennis Cook,et al.  Detection of Influential Observation in Linear Regression , 2000, Technometrics.

[57]  Eyal Winter.  A Value for cooperative games with levels structure of cooperation , 1989 .

[58]  L. Shapley.  A Value for n-person Games , 1988 .

[59]  J. Hammersley.  SIMULATION AND THE MONTE CARLO METHOD , 1982 .

[60]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[61]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[62]  Zelei Liu.  GTG-Shapley: Eficient and Accurate Participant Contribution Evaluation in Federated Learning , 2022 .

[63]  2020 25th International Conference on Pattern Recognition (ICPR) , 2021 .

[64]  Archie C. Chapman,et al.  Approximating the Shapley Value Using Stratified Empirical Bernstein Sampling , 2021, IJCAI.

[65]  Yunjie Gu,et al.  SHAQ: Incorporating Shapley Value Theory into Q-Learning for Multi-Agent Reinforcement Learning , 2021, ArXiv.

[66]  M. Friedlander,et al.  Improving Fairness for Data Valuation in Federated Learning , 2021, ArXiv.

[67]  Bart Verheij,et al.  Artificial Intelligence , 2017, Communications in Computer and Information Science.

[68]  Peter A. Flach,et al.  Proceedings of the 28th International Conference on Machine Learning , 2011 .

[69]  V. Phan,et al.  Values , 2001, SIGGRAPH Video Review on Electronic Theater Program.

[70]  John Eccleston,et al.  Statistics and Computing , 2006 .

[71]  G. Laporte,et al.  Annals of Operations Research , 1996 .

[72]  M. V. Rossum,et al.  In Neural Computation , 2022 .

[73]  M. Wilkinson.  Management science , 1989, British Dental Journal.

[74]  Rudolf Henn,et al.  Mathematical Economics and Game Theory , 1977 .

[75]  D. M. Deighton,et al.  Computers in Operations Research , 1977, Aust. Comput. J..

[76]  G. Owen.  VALUES OF GAMES WITH A PRIORI UNIONS , 1977 .

[77]  G. Owen.  Multilinear Extensions of Games , 1972 .