Sampling Methods for Inner Product Sketching
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911998499880960 |
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| author | Daliri, Majid Freire, Juliana Musco, Christopher Santos, Aécio Zhang, Haoxiang |
| author_facet | Daliri, Majid Freire, Juliana Musco, Christopher Santos, Aécio Zhang, Haoxiang |
| contents | Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated weighted sampling theoretically and empirically outperform popular linear sketching methods like Johnson-Lindentrauss projection and CountSketch for the ubiquitous problem of inner product estimation. We further develop this finding by introducing and analyzing two alternative sampling-based methods. In contrast to the computationally expensive algorithm in Bessa et al., our methods run in linear time (to compute the sketch) and perform better in practice, significantly beating linear sketching on a variety of tasks. For example, they provide state-of-the-art results for estimating the correlation between columns in unjoined tables, a problem that we show how to reduce to inner product estimation in a black-box way. While based on known sampling techniques (threshold and priority sampling) we introduce significant new theoretical analysis to prove approximation guarantees for our methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_16157 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sampling Methods for Inner Product Sketching Daliri, Majid Freire, Juliana Musco, Christopher Santos, Aécio Zhang, Haoxiang Databases Data Structures and Algorithms Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated weighted sampling theoretically and empirically outperform popular linear sketching methods like Johnson-Lindentrauss projection and CountSketch for the ubiquitous problem of inner product estimation. We further develop this finding by introducing and analyzing two alternative sampling-based methods. In contrast to the computationally expensive algorithm in Bessa et al., our methods run in linear time (to compute the sketch) and perform better in practice, significantly beating linear sketching on a variety of tasks. For example, they provide state-of-the-art results for estimating the correlation between columns in unjoined tables, a problem that we show how to reduce to inner product estimation in a black-box way. While based on known sampling techniques (threshold and priority sampling) we introduce significant new theoretical analysis to prove approximation guarantees for our methods. |
| title | Sampling Methods for Inner Product Sketching |
| topic | Databases Data Structures and Algorithms |
| url | https://arxiv.org/abs/2309.16157 |