Approximating the shapley value via multi-issue decompositions

The Shapley value provides a fair method for the division of value in coalitional games. Motivated by the application of crowdsourcing for the collection of suitable labels and features for regression and classification tasks, we develop a method to approximate the Shapley value by identifying a suitable decomposition into multiple issues, with the decomposition computed by applying a graph partitioning to a pairwise similarity graph induced by the coalitional value function. The method is significantly faster and more accurate than existing random-sampling based methods on both synthetic data and data representing user contributions in a real world application of crowdsourcing to elicit labels and features for classification.

[1]  J. S. Mateo.  The Shapley Value , 2012 .

[2]  Francis Edward Su,et al.  The Shapley value of phylogenetic trees , 2005, Journal of mathematical biology.

[3]  Xiaotie Deng,et al.  On the Complexity of Cooperative Solution Concepts , 1994, Math. Oper. Res..

[4]  Vishal Misra,et al.  On Cooperative Settlement Between Content, Transit, and Eyeball Internet Service Providers , 2008, IEEE/ACM Transactions on Networking.

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

[6]  Santosh S. Vempala,et al.  On clusterings-good, bad and spectral , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[7]  C. Papadimitriou,et al.  On the value of private information , 2001 .

[8]  D. Naiman,et al.  INCLUSION-EXCLUSION-BONFERRONI IDENTITIES AND INEQUALITIES FOR DISCRETE TUBE-LIKE PROBLEMS VIA EULER CHARACTERISTICS , 1992 .

[9]  Michel Grabisch,et al.  An axiomatic approach to the concept of interaction among players in cooperative games , 1999, Int. J. Game Theory.

[10]  H. Young,et al.  Handbook of Game Theory with Economic Applications , 2015 .

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

[12]  Avanidhar Subrahmanyam,et al.  The Value of Private Information , 2005 .

[13]  Amos J. Storkey,et al.  Machine Learning Markets , 2011, AISTATS.

[14]  Vincent Conitzer,et al.  Computing Shapley Values, Manipulating Value Division Schemes, and Checking Core Membership in Multi-Issue Domains , 2004, AAAI.

[15]  Abraham Neyman,et al.  Uniqueness of the Shapley Value , 1989 .

[16]  Eyal Winter.  Chapter 53 The shapley value , 2002 .

[17]  Miklós Pintér,et al.  Regression games , 2011, Ann. Oper. Res..

[18]  Moshe Tennenholtz,et al.  Solving Cooperative Reliability Games , 2011, UAI.

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

[20]  Jacob D. Abernethy,et al.  A Collaborative Mechanism for Crowdsourcing Prediction Problems , 2011, NIPS.

[21]  David Wettstein,et al.  Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value , 2001, J. Econ. Theory.

[22]  Vishal Misra,et al.  The Shapley Profit for Content , Transit and Eyeball Internet Service Providers , 2010 .

[23]  Shapley Value.  COOPERATIVE GAMES : CORE AND SHAPLEY VALUE , 2022 .

[24]  A. Roth.  The Shapley value , 2005, Game Theory.

[25]  S. Hart,et al.  Bargaining and Value , 1996 .

[26]  Yoav Shoham,et al.  Marginal contribution nets: a compact representation scheme for coalitional games , 2005, EC '05.