mlsanityData to 7 Oct 2026

Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space

arXiv 2202.01908 ↗First posted 3 Feb 2022cs.LG cs.DScited by 28

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Abstract (arXiv)

We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in very high dimension, upwards of 100,000, can be sampled efficiently textitin practice. Our algorithm incorporates constraints into the Riemannian version of Hamiltonian Monte Carlo and maintains sparsity. This allows us to achieve a mixing rate independent of smoothness and condition numbers. On benchmark data sets in systems biology and linear programming, our algorithm outperforms existing packages by orders of magnitude. In particular, we achieve a 1,000-fold speed-up for sampling from the largest published human metabolic network (RECON3D). Our package has been incorporated into the COBRA toolbox.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 15 of its 58 references that are in the map. First posted on arXiv 3 Feb 2022.

Builds on

15 of 58 references.

References · 15

  1. 2018Pyro: Deep Universal Probabilistic Programmingcited by 379
  2. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  3. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 117
  4. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  5. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  6. 2020Exponential ergodicity of mirror-Langevin diffusionscited by 37
  7. 2017Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computationcited by 32
  8. 2020Logsmooth Gradient Concentration and Tighter Runtimes for Metropolized Hamiltonian Monte Carlocited by 22
  9. 2016Stochastic Quasi-Newton Langevin Monte Carlocited by 14
  10. 2016Geodesic Walks in Polytopescited by 13
  11. 2019Introducing an Explicit Symplectic Integration Scheme for Riemannian Manifold Hamiltonian Monte Carlocited by 10
  12. 2020Convergence of Gibbs Sampling: Coordinate Hit-and-Run Mixes Fastcited by 9
3 more
  1. 2018Universal Barrier is n-Self-Concordantcited by 6
  2. 2020Volesti: Volume Approximation and Sampling for Convex Polytopes in Rcited by 6
  3. 2020On the mixing time of coordinate Hit-and-Runcited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 5; 2024: 9; 2025: 4; 2026: 4.

28 papers.

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  1. 2023Diffusion Models for Constrained Domainscited by 60
  2. 2023Metropolis Sampling for Constrained Diffusion Modelscited by 28
  3. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 21
  4. 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 18
  5. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  6. 2024Sampling and Integration of Logconcave Functions by Algorithmic Diffusioncited by 12
  7. 2022Sampling in Constrained Domains with Orthogonal-Space Variational Gradient Descentcited by 11
  8. 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
  9. 2022Condition-number-independent convergence rate of Riemannian Hamiltonian Monte Carlo with numerical integratorscited by 10
  10. 2024Constrained Sampling with Primal-Dual Langevin Monte Carlocited by 10
  11. 2025Constrained Diffusers for Safe Planning and Controlcited by 9
  12. 2023Sampling with Barriers: Faster Mixing via Lewis Weightscited by 7
16 more
  1. 2024Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamicscited by 7
  2. 2025Faster logconcave sampling from a cold start in high dimensioncited by 7
  3. 2022Unbiased constrained sampling with Self-Concordant Barrier Hamiltonian Monte Carlocited by 6
  4. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  5. 2024R'enyi-infinity constrained sampling with d3 membership queriescited by 3
  6. 2025New affine invariant ensemble samplers and their dimensional scalingcited by 3
  7. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2
  8. 2024PolytopeWalk: Sparse MCMC Sampling over Polytopescited by 1
  9. 2026Manifold Sampling via Entropy Maximizationcited by 1
  10. 2026Uncertainty-Aware Gaussian Map for Vision-Language Navigationcited by 1
  11. 2026Beyond the d2.5-mixing bound for Dikin walks on polytopescited by 1
  12. 2022Sampling Ex-Post Group-Fair Rankingscited by 0
  13. 2022Sampling Constrained Continuous Probability Distributions: A Reviewcited by 0
  14. 2024Log-Concave Coupling for Sampling Neural Net Posteriorscited by 0
  15. 2025Sampling with Shielded Langevin Monte Carlo Using Navigation Potentialscited by 0
  16. 2026Kinetic Langevin Splitting Schemes for Constrained Samplingcited by 0