On sample complexity for covariance estimation via the unadjusted Langevin algorithm
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 7 of its 17 references that are in the map. First posted on arXiv 29 Jan 2026.
Builds on
7 of 17 references.
References · 7
- 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
- 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
- 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
- 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
- 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
- 2022Concentration of the Langevin Algorithm's Stationary Distributioncited by 5
- 2024Covariance estimation using Markov chain Monte Carlocited by 2
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Citing papers per year: 2026: 1.
1 paper.