A randomized algorithm to reduce the support of discrete measures

Conference item

Given a discrete probability measure supported on NN atoms and a set of nn real-valued functions, there exists a probability measure that is supported on a subset of n+1n+1 of the original NN atoms and has the same mean when integrated against each of the nn functions. If N≫nN≫n this results in a huge reduction of complexity. We give a simple geometric characterization of barycenters via negative cones and derive a randomized algorithm that computes this new measure by greedy geometric sampling''. We then study its properties, and benchmark it on synthetic and real-world data to show that it can be very beneficial in the N≫nN≫n regime. A Python implementation is available at \url{https://github.com/FraCose/Recombination_Random_Algos}.

Authors: Cosentino, F; Oberhauser, H; Abate, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Curran Associates
• Host title: Advances in Neural Information Processing Systems 33 (NeurIPS 2020)
• Volume: 19
• Pages: 15100-15110
• Publication date: 2021-07-01
• Acceptance date: 2020-09-25
• Event title: 34th Conference on Neural Information Processing Systems (NeurIPS 2020)
• Event location: Virtual event
• Event website: https://neurips.cc/Conferences/2020
• Event start date: 2020-12-06
• Event end date: 2020-12-12
• ISBN: 9781713829546
• Language: English
• Keywords: FFR