  As data becomes the fuel driving technological and economic growth, a
fundamental challenge is how to quantify the value of data in algorithmic
predictions and decisions. For example, in healthcare and consumer markets, it
has been suggested that individuals should be compensated for the data that
they generate, but it is not clear what is an equitable valuation for
individual data. In this work, we develop a principled framework to address
data valuation in the context of supervised machine learning. Given a learning
algorithm trained on $n$ data points to produce a predictor, we propose data
Shapley as a metric to quantify the value of each training datum to the
predictor performance. Data Shapley value uniquely satisfies several natural
properties of equitable data valuation. We develop Monte Carlo and
gradient-based methods to efficiently estimate data Shapley values in practical
settings where complex learning algorithms, including neural networks, are
trained on large datasets. In addition to being equitable, extensive
experiments across biomedical, image and synthetic data demonstrate that data
Shapley has several other benefits: 1) it is more powerful than the popular
leave-one-out or leverage score in providing insight on what data is more
valuable for a given learning task; 2) low Shapley value data effectively
capture outliers and corruptions; 3) high Shapley value data inform what type
of new data to acquire to improve the predictor.
