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As data becomes the fuel driving technological and economic growth, afundamental challenge is how to quantify the value of data in algorithmicpredictions and decisions. For example, in healthcare and consumer markets, ithas been suggested that individuals should be compensated for the data thatthey generate, but it is not clear what is an equitable valuation forindividual data. In this work, we develop a principled framework to addressdata valuation in the context of supervised machine learning. Given a learningalgorithm trained on $n$ data points to produce a predictor, we propose dataShapley as a metric to quantify the value of each training datum to thepredictor performance. Data Shapley value uniquely satisfies several naturalproperties of equitable data valuation. We develop Monte Carlo andgradient-based methods to efficiently estimate data Shapley values in practicalsettings where complex learning algorithms, including neural networks, aretrained on large datasets. In addition to being equitable, extensiveexperiments across biomedical, image and synthetic data demonstrate that dataShapley has several other benefits: 1) it is more powerful than the popularleave-one-out or leverage score in providing insight on what data is morevaluable for a given learning task; 2) low Shapley value data effectivelycapture outliers and corruptions; 3) high Shapley value data inform what typeof new data to acquire to improve the predictor.

Data Shapley: Equitable Valuation of Data for Machine Learning