论文标题
一种随机算法，以减少离散度量的支持
A Randomized Algorithm to Reduce the Support of Discrete Measures
论文作者
论文摘要
鉴于$ n $原子支持的离散概率度量和一组$ n $真实值的功能，存在一种概率措施，该措施在原始$ n $原子的$ n+1 $的子集中得到了支持，并且在针对每个$ n $函数集成时具有相同的均值。如果$ n \ gg n $这会大大降低复杂性。我们通过负锥对barycenter进行简单的几何表征，并得出一种随机算法，该算法通过“贪婪的几何抽样”来计算这种新度量。然后，我们研究其属性，并根据合成和现实世界的数据进行基准测试，以表明它在$ n \ gg n $ stremime中可能非常有益。可以在\ url {https://github.com/fracose/recombination_random_algos}上获得Python实现。
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}.
