Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909469141630976 |
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| author | Sheng, Nan Tang, Xun Chen, Haoxuan Ying, Lexing |
| author_facet | Sheng, Nan Tang, Xun Chen, Haoxuan Ying, Lexing |
| contents | The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant calculations. This work addresses this challenge by performing a particle-based high-dimensional parametric density estimation subroutine, and the input to the subroutine is Gibbs samples generated by leveraging advanced sampling techniques. Specifically, to generate Gibbs samples, we employ ensemble-based annealed importance sampling, a population-based approach for sampling multimodal distributions. These samples are then processed using functional hierarchical tensor sketching, a tensor-network-based density estimation method for high-dimensional distributions, to obtain the numerical representation of the Gibbs distribution. We successfully apply the proposed approach to complex Ginzburg-Landau models with hundreds of variables. In particular, we show that the approach proposed is successful at addressing the metastability issue under difficult numerical cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors Sheng, Nan Tang, Xun Chen, Haoxuan Ying, Lexing Numerical Analysis Computational Physics Data Analysis, Statistics and Probability The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant calculations. This work addresses this challenge by performing a particle-based high-dimensional parametric density estimation subroutine, and the input to the subroutine is Gibbs samples generated by leveraging advanced sampling techniques. Specifically, to generate Gibbs samples, we employ ensemble-based annealed importance sampling, a population-based approach for sampling multimodal distributions. These samples are then processed using functional hierarchical tensor sketching, a tensor-network-based density estimation method for high-dimensional distributions, to obtain the numerical representation of the Gibbs distribution. We successfully apply the proposed approach to complex Ginzburg-Landau models with hundreds of variables. In particular, we show that the approach proposed is successful at addressing the metastability issue under difficult numerical cases. |
| title | Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors |
| topic | Numerical Analysis Computational Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2501.17143 |