mlsanityData to 7 Oct 2026

Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms

arXiv 2305.15988 ↗First posted 25 May 2023stat.ML cs.LG stat.COcited by 4

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Abstract (arXiv)

We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte Carlo (MCMC) methods derived from discretizations of the overdamped Langevin diffusions, which are commonly known as Langevin Monte Carlo algorithms. Furthermore, we are also interested in two nonsmooth cases for which a large class of proximal MCMC methods have been developed: (i) a nonsmooth prior is considered with a Gaussian mixture likelihood; (ii) a Laplacian mixture distribution. Such nonsmooth and non-log-concave sampling tasks arise from a wide range of applications to Bayesian inference and imaging inverse problems such as image deconvolution. We perform numerical simulations to compare the performance of most commonly used Langevin Monte Carlo algorithms.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 107 of its 204 references that are in the map. First posted on arXiv 25 May 2023.

Builds on

107 of 204 references.

References · 107

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38 more
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50 most cited of 107 All 107 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptionscited by 4
  2. 2025Beyond Scores: Proximal Diffusion Modelscited by 3
  3. 2025Langevin Monte-Carlo Provably Learns Depth Two Neural Nets at Any Size and Datacited by 1
  4. 2026Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental studycited by 0