A randomized algorithm to reduce the support of discrete measures - Cosentino, F; Oberhauser, H; Abate, A (Curran Associates, 2021)
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}.