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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.06749 |
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| _version_ | 1866908398651441152 |
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| author | Rossetti, Riccardo Reeves, Galen |
| author_facet | Rossetti, Riccardo Reeves, Galen |
| contents | This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each observation depends on the interactions among a finite number of unknown parameters. Our main results provide asymptotically exact formulas for the mutual information (equivalently, the free energy) as well as the minimum mean-squared error in the Bayes-optimal setting. We then apply this framework to derive sharp characterizations of statistical thresholds for two novel scenarios: (1) tensor estimation in heteroskedastic noise that is independent but not identically distributed, and (2) higher-order assignment problems, where the goal is to recover an unknown permutation from tensor-valued observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical Limits for Finite-Rank Tensor Estimation Rossetti, Riccardo Reeves, Galen Information Theory Statistics Theory This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each observation depends on the interactions among a finite number of unknown parameters. Our main results provide asymptotically exact formulas for the mutual information (equivalently, the free energy) as well as the minimum mean-squared error in the Bayes-optimal setting. We then apply this framework to derive sharp characterizations of statistical thresholds for two novel scenarios: (1) tensor estimation in heteroskedastic noise that is independent but not identically distributed, and (2) higher-order assignment problems, where the goal is to recover an unknown permutation from tensor-valued observations. |
| title | Statistical Limits for Finite-Rank Tensor Estimation |
| topic | Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2506.06749 |