On the Convergence of the Shapley Value in Parametric Bayesian Learning Games

Bryan Kian, Hsiang Low, Xinyi Xu, Lucas Agussurja

Code that ran

We have not lifted any functions out of this paper's repositories yet, so there is nothing we have run. If it links a repository, it is listed below.

Repositories linked to this paper

XinyiYS/Parametric-Bayesian-Learning-Games — marked official in Papers with Code; named in the paper

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

Abstract

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 posteriorprior 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.

For agents

The same record, over MCP at https://syntology.ai/mcp:

get_harvested_code_for_paper("2205.07428")
get_code_for_paper("2205.07428")
have("2205.07428")

Connect an agent — have() is free.