2022-06-28-agussurja22a.md

title	booktitle	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
On the Convergence of the Shapley Value in Parametric Bayesian Learning Games	Proceedings of the 39th International Conference on Machine Learning	Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian learning games where players perform a Bayesian inference using their combined data, and the posterior-prior KL divergence is used as the characteristic function. We show that for any two players, under some regularity conditions, their difference in Shapley value converges in probability to the difference in Shapley value of a limiting game whose characteristic function is proportional to the log-determinant of the joint Fisher information. As an application, we present an online collaborative learning framework that is asymptotically Shapley-fair. Our result enables this to be achieved without any costly computations of posterior-prior KL divergences. Only a consistent estimator of the Fisher information is needed. The effectiveness of our framework is demonstrated with experiments using real-world data.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	agussurja22a	0	On the Convergence of the Shapley Value in Parametric {B}ayesian Learning Games	180	196	180-196	180	false	Agussurja, Lucas and Xu, Xinyi and Low, Bryan Kian Hsiang	given family Lucas Agussurja given family Xinyi Xu given family Bryan Kian Hsiang Low	2022-06-28		Proceedings of the 39th International Conference on Machine Learning	162	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v162/agussurja22a/agussurja22a.pdf