  The proliferation of large data sets and Bayesian inference techniques
motivates demand for better data sparsification. Coresets provide a principled
way of summarizing a large dataset via a smaller one that is guaranteed to
match the performance of the full data set on specific problems. Classical
coresets, however, neglect the underlying data distribution, which is often
continuous. We address this oversight by introducing Wasserstein measure
coresets, an extension of coresets which by definition takes into account
generalization. Our formulation of the problem, which essentially consists in
minimizing the Wasserstein distance, is solvable via stochastic gradient
descent. This yields an algorithm which simply requires sample access to the
data distribution and is able to handle large data streams in an online manner.
We validate our construction for inference and clustering.
