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2019 Higher order Langevin Monte Carlo algorithm
Sotirios Sabanis, Ying Zhang
Electron. J. Statist. 13(2): 3805-3850 (2019). DOI: 10.1214/19-EJS1615

Abstract

A new (unadjusted) Langevin Monte Carlo (LMC) algorithm with improved rates in total variation and in Wasserstein distance is presented. All these are obtained in the context of sampling from a target distribution $\pi$ that has a density $\hat{\pi}$ on $\mathbb{R}^{d}$ known up to a normalizing constant. Moreover, $-\log\hat{\pi}$ is assumed to have a locally Lipschitz gradient and its third derivative is locally Hölder continuous with exponent $\beta \in (0,1]$. Non-asymptotic bounds are obtained for the convergence to stationarity of the new sampling method with convergence rate $1+\beta/2$ in Wasserstein distance, while it is shown that the rate is 1 in total variation even in the absence of convexity. Finally, in the case where $-\log \hat{\pi}$ is strongly convex and its gradient is Lipschitz continuous, explicit constants are provided.

Citation

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Sotirios Sabanis. Ying Zhang. "Higher order Langevin Monte Carlo algorithm." Electron. J. Statist. 13 (2) 3805 - 3850, 2019. https://doi.org/10.1214/19-EJS1615

Information

Received: 1 November 2018; Published: 2019
First available in Project Euclid: 3 October 2019

zbMATH: 07113731
MathSciNet: MR4015336
Digital Object Identifier: 10.1214/19-EJS1615

Subjects:
Primary: 62L10, 65C05

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Vol.13 • No. 2 • 2019
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