A Randomized Algorithm to Reduce the Support of Discrete Measures

arXiv2006.01757MaRDI QIDQ6341948

Alessandro Abate, Harald Oberhauser, Unnamed Author

Publication date: 2 June 2020

Abstract: Given a discrete probability measure supported on $N$ atoms and a set of $n$ real-valued functions, there exists a probability measure that is supported on a subset of $n+1$ of the original $N$ atoms and has the same mean when integrated against each of the $n$ functions. If $Nggn$ 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 $Nggn$ regime. A Python implementation is available at url{https://github.com/FraCose/Recombination_Random_Algos}.

Has companion code repository: https://github.com/FraCose/Recombination_Random_Algos

This page was built for publication: A Randomized Algorithm to Reduce the Support of Discrete Measures