mlsanityData to 14 Oct 2026

Sampling and Integration of Logconcave Functions by Algorithmic Diffusion

arXiv 2411.13462 ↗First posted 20 Nov 2024cs.DS cs.LG math.STcited by 12

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Abstract (arXiv)

We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and matches the best-known complexities for the special case of uniform distributions on convex bodies. For the sampling problem, our output guarantees are significantly stronger than previously known, and lead to a streamlined analysis of statistical estimation based on dependent random samples.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 7 of its 37 references that are in the map. First posted on arXiv 20 Nov 2024.

Builds on

7 of 37 references.

References · 7

  1. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  2. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 86
  3. 2022Improved analysis for a proximal algorithm for samplingcited by 73
  4. 2022Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Spacecited by 28
  5. 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 19
  6. 2024Entropy contraction of the Gibbs sampler under log-concavitycited by 13
  7. 2020Reducing Isotropy and Volume to KLS: Faster Rounding and Volume Algorithmscited by 9

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 9.

12 papers.

  1. 2025Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyondcited by 11
  2. 2025Faster logconcave sampling from a cold start in high dimensioncited by 7
  3. 2025Oracle-based Uniform Sampling from Convex Bodiescited by 3
  4. 2026A unified complexity bound for logconcave samplingcited by 3
  5. 2026Beyond the d2.5-mixing bound for Dikin walks on polytopescited by 2
  6. 2026Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Runcited by 2
  7. 2026A proximal gradient algorithm for composite log-concave samplingcited by 1
  8. 2026Functional Stochastic Localizationcited by 0
  9. 2026The Geometry of Efficient Nonconvex Samplingcited by 0
  10. 2026Tight Bounds for Learning Polyhedra with a Margincited by 0
  11. 2026On two proofs of d2 mixing of weighted Dikin walkscited by 0
  12. 2026Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold startcited by 0