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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.21717 |
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| _version_ | 1866910020806901760 |
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| author | Nakakita, Shogo |
| author_facet | Nakakita, Shogo |
| contents | We establish sample complexity guarantees for estimating the covariance matrix of a strongly log-concave smooth distribution using the unadjusted Langevin algorithm (ULA). We quantitatively compare our complexity estimates on single-chain ULA with embarrassingly parallel ULA and derive that the sample complexity of the single-chain approach is smaller than that of embarrassingly parallel ULA by a logarithmic factor in the dimension and the reciprocal of the prescribed precision, with the difference arising from effective bias reduction through burn-in. The key technical contribution is a concentration bound for the sample covariance matrix around its expectation, derived via a log-Sobolev inequality for the joint distribution of ULA iterates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21717 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On sample complexity for covariance estimation via the unadjusted Langevin algorithm Nakakita, Shogo Probability Machine Learning 65C05 (Primary) 60J05, 62F12 (Secondary) We establish sample complexity guarantees for estimating the covariance matrix of a strongly log-concave smooth distribution using the unadjusted Langevin algorithm (ULA). We quantitatively compare our complexity estimates on single-chain ULA with embarrassingly parallel ULA and derive that the sample complexity of the single-chain approach is smaller than that of embarrassingly parallel ULA by a logarithmic factor in the dimension and the reciprocal of the prescribed precision, with the difference arising from effective bias reduction through burn-in. The key technical contribution is a concentration bound for the sample covariance matrix around its expectation, derived via a log-Sobolev inequality for the joint distribution of ULA iterates. |
| title | On sample complexity for covariance estimation via the unadjusted Langevin algorithm |
| topic | Probability Machine Learning 65C05 (Primary) 60J05, 62F12 (Secondary) |
| url | https://arxiv.org/abs/2601.21717 |