Generative Modeling via Hierarchical Tensor 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_ | 1866911364332650496 |
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| author | Peng, Yifan Chen, Yian Stoudenmire, E. Miles Khoo, Yuehaw |
| author_facet | Peng, Yifan Chen, Yian Stoudenmire, E. Miles Khoo, Yuehaw |
| contents | We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this tensor network. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density. An analysis of estimation error demonstrates the effectiveness of this method through several numerical experiments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_05305 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generative Modeling via Hierarchical Tensor Sketching Peng, Yifan Chen, Yian Stoudenmire, E. Miles Khoo, Yuehaw Numerical Analysis Machine Learning 15A69, 62Gxx We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this tensor network. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density. An analysis of estimation error demonstrates the effectiveness of this method through several numerical experiments. |
| title | Generative Modeling via Hierarchical Tensor Sketching |
| topic | Numerical Analysis Machine Learning 15A69, 62Gxx |
| url | https://arxiv.org/abs/2304.05305 |