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arXiv · 2006.01757

A Randomized Algorithm to Reduce the Support of Discrete Measures

Francesco Cosentino·Harald Oberhauser·Alessandro Abate
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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 $ 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}.

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Francesco Cosentino, Harald Oberhauser, Alessandro Abate. 2020-06-02. A Randomized Algorithm to Reduce the Support of Discrete Measures. https://arxiv.org/abs/2006.01757

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