A randomized algorithm to reduce the support of discrete measures
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 hu...
| Main Authors: | , , |
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| Format: | Conference item |
| Language: | English |
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Curran Associates
2021
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| _version_ | 1826309182720049152 |
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| author | Cosentino, F Oberhauser, H Abate, A |
| author_facet | Cosentino, F Oberhauser, H Abate, A |
| author_sort | Cosentino, F |
| collection | OXFORD |
| description | 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}. |
| first_indexed | 2024-03-07T07:30:21Z |
| format | Conference item |
| id | oxford-uuid:6a32a4f2-c8c9-4af5-9007-de93bc09dbc3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:30:21Z |
| publishDate | 2021 |
| publisher | Curran Associates |
| record_format | dspace |
| spelling | oxford-uuid:6a32a4f2-c8c9-4af5-9007-de93bc09dbc32023-01-13T11:21:34ZA randomized algorithm to reduce the support of discrete measuresConference itemhttp://purl.org/coar/resource_type/c_5794uuid:6a32a4f2-c8c9-4af5-9007-de93bc09dbc3EnglishSymplectic ElementsCurran Associates2021Cosentino, FOberhauser, HAbate, AGiven 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}. |
| spellingShingle | Cosentino, F Oberhauser, H Abate, A A randomized algorithm to reduce the support of discrete measures |
| title | A randomized algorithm to reduce the support of discrete measures |
| title_full | A randomized algorithm to reduce the support of discrete measures |
| title_fullStr | A randomized algorithm to reduce the support of discrete measures |
| title_full_unstemmed | A randomized algorithm to reduce the support of discrete measures |
| title_short | A randomized algorithm to reduce the support of discrete measures |
| title_sort | randomized algorithm to reduce the support of discrete measures |
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