  Coresets are small, weighted summaries of larger datasets, aiming at
providing provable error bounds for machine learning (ML) tasks while
significantly reducing the communication and computation costs. To achieve a
better trade-off between ML error bounds and costs, we propose the first
framework to incorporate quantization techniques into the process of coreset
construction. Specifically, we theoretically analyze the ML error bounds caused
by a combination of coreset construction and quantization. Based on that, we
formulate an optimization problem to minimize the ML error under a fixed budget
of communication cost. To improve the scalability for large datasets, we
identify two proxies of the original objective function, for which efficient
algorithms are developed. For the case of data on multiple nodes, we further
design a novel algorithm to allocate the communication budget to the nodes
while minimizing the overall ML error. Through extensive experiments on
multiple real-world datasets, we demonstrate the effectiveness and efficiency
of our proposed algorithms for a variety of ML tasks. In particular, our
algorithms have achieved more than 90% data reduction with less than 10%
degradation in ML performance in most cases.
