Multivariate Density Estimation via Variance-Reduced Sketching
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912357272256512 |
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| author | Peng, Yifan Khoo, Yuehaw Wang, Daren |
| author_facet | Peng, Yifan Khoo, Yuehaw Wang, Daren |
| contents | Multivariate density estimation is of great interest in various scientific and engineering disciplines. In this work, we introduce a new framework called Variance-Reduced Sketching (VRS), specifically designed to estimate multivariate density functions with a reduced curse of dimensionality. Our VRS framework conceptualizes multivariate functions as infinite-size matrices/tensors, and facilitates a new sketching technique motivated by the numerical linear algebra literature to reduce the variance in density estimation problems. We demonstrate the robust numerical performance of VRS through a series of simulated experiments and real-world data applications. Notably, VRS shows remarkable improvement over existing neural network density estimators and classical kernel methods in numerous distribution models. Additionally, we offer theoretical justifications for VRS to support its ability to deliver density estimation with a reduced curse of dimensionality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multivariate Density Estimation via Variance-Reduced Sketching Peng, Yifan Khoo, Yuehaw Wang, Daren Machine Learning Numerical Analysis Methodology Multivariate density estimation is of great interest in various scientific and engineering disciplines. In this work, we introduce a new framework called Variance-Reduced Sketching (VRS), specifically designed to estimate multivariate density functions with a reduced curse of dimensionality. Our VRS framework conceptualizes multivariate functions as infinite-size matrices/tensors, and facilitates a new sketching technique motivated by the numerical linear algebra literature to reduce the variance in density estimation problems. We demonstrate the robust numerical performance of VRS through a series of simulated experiments and real-world data applications. Notably, VRS shows remarkable improvement over existing neural network density estimators and classical kernel methods in numerous distribution models. Additionally, we offer theoretical justifications for VRS to support its ability to deliver density estimation with a reduced curse of dimensionality. |
| title | Multivariate Density Estimation via Variance-Reduced Sketching |
| topic | Machine Learning Numerical Analysis Methodology |
| url | https://arxiv.org/abs/2401.11646 |