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A Randomized Algorithm to Reduce the Support of Discrete Measures
Francesco Cosentino · Harald Oberhauser · Alessandro Abate

Wed Dec 09 07:10 AM -- 07:20 AM (PST) @ Orals & Spotlights: Probabilistic/Causality
in Orals & Spotlights Track 19: Probabilistic/Causality »
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 $ N \gg 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 $N\gg n$ regime. A Python implementation is available at \url{https://github.com/FraCose/Recombination_Random_Algos}.

Author Information

Francesco Cosentino (University of Oxford)
Harald Oberhauser (University of Oxford)
Alessandro Abate (University of Oxford)

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