Positively weighted kernel quadrature via subsampling
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules using only access to i.i.d. samples from the underlying measu...
| Main Authors: | , , |
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| Format: | Conference item |
| Language: | English |
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Curran Associates
2023
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| _version_ | 1811139165364944896 |
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| author | Hayakawa, S Oberhauser, H Lyons, T |
| author_facet | Hayakawa, S Oberhauser, H Lyons, T |
| author_sort | Hayakawa, S |
| collection | OXFORD |
| description | We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules using only access to i.i.d. samples from the underlying measure and evaluation of the kernel and that result in a small worst-case error. In addition to our theoretical results and the benefits resulting from convex weights, our experiments indicate that this construction can compete with the optimal bounds in well-known examples. |
| first_indexed | 2024-03-07T08:21:38Z |
| format | Conference item |
| id | oxford-uuid:6b9888dd-fb38-461a-b629-a61f13423a1f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:01:45Z |
| publishDate | 2023 |
| publisher | Curran Associates |
| record_format | dspace |
| spelling | oxford-uuid:6b9888dd-fb38-461a-b629-a61f13423a1f2024-04-30T12:04:50ZPositively weighted kernel quadrature via subsamplingConference itemhttp://purl.org/coar/resource_type/c_5794uuid:6b9888dd-fb38-461a-b629-a61f13423a1fEnglishSymplectic ElementsCurran Associates2023Hayakawa, SOberhauser, HLyons, TWe study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules using only access to i.i.d. samples from the underlying measure and evaluation of the kernel and that result in a small worst-case error. In addition to our theoretical results and the benefits resulting from convex weights, our experiments indicate that this construction can compete with the optimal bounds in well-known examples. |
| spellingShingle | Hayakawa, S Oberhauser, H Lyons, T Positively weighted kernel quadrature via subsampling |
| title | Positively weighted kernel quadrature via subsampling |
| title_full | Positively weighted kernel quadrature via subsampling |
| title_fullStr | Positively weighted kernel quadrature via subsampling |
| title_full_unstemmed | Positively weighted kernel quadrature via subsampling |
| title_short | Positively weighted kernel quadrature via subsampling |
| title_sort | positively weighted kernel quadrature via subsampling |
| work_keys_str_mv | AT hayakawas positivelyweightedkernelquadratureviasubsampling AT oberhauserh positivelyweightedkernelquadratureviasubsampling AT lyonst positivelyweightedkernelquadratureviasubsampling |