Towards Efficient Data Valuation Based on the Shapley Value

{\em ``How much is my data worth?''} is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining prospective compensation when data breaches happen. In this paper, we study the problem of \emph{data valuation} by utilizing the Shapley value, a popular notion of value which originated in coopoerative game theory. The Shapley value defines a unique payoff scheme that satisfies many desiderata for the notion of data value. However, the Shapley value often requires \emph{exponential} time to compute. To meet this challenge, we propose a repertoire of efficient algorithms for approximating the Shapley value. We also demonstrate the value of each training instance for various benchmark datasets.