SLMC improves sampling efficiency for high-dimensional distributions.
problem Sampling from high-dimensional distributions is computationally challenging.
method SLMC projects Langevin updates onto subsampled eigenblocks of a time-varying preconditioner.
result SLMC offers superior adaptability and computational efficiency compared to traditional methods.
Paper analyzes and accelerates Langevin Monte Carlo methods using large deviations theory.
problem High-dimensional sampling problems in machine learning.
method Unified approach using large deviations theory to study and accelerate Langevin dynamics variants.
result Efficiency of Langevin dynamics variants demonstrated through numerical experiments.
Unified approach for sampling non-differentiable and heavy-tailed targets.
problem Sampling non-differentiable and heavy-tailed distributions using Langevin algorithms.
method Anchored Langevin dynamics, which modifies the Langevin diffusion with a smooth reference potential and multiplicative scaling.
result Non-asymptotic guarantees in the 2-Wasserstein distance to the target distribution.
Improved sampling for high-dimensional posteriors with underdamped Langevin.
problem Scalability issues in high-dimensional problems with approximate Thompson sampling.
method Underdamped Langevin Monte Carlo for accelerated posterior concentration.
result Logarithmic regret improvement from i l d e O ( d ) \mathcal{ ilde O}(d) i l d e O ( d ) to i l d e O ( d ) \mathcal{ ilde O}(\sqrt{d}) i l d e O ( d ) . Optimal preconditioning improves Langevin sampling efficiency.
problem Improving sampling efficiency in high-dimensional target distributions.
method Optimal preconditioning using Fisher information, applied to MALA.
result Adaptive MCMC scheme significantly outperforms other methods.
A new method for sampling from complex distributions using Langevin samplers.
problem Sampling from unnormalized Boltzmann densities.
method Probability flow ODE derived from linear stochastic interpolants, employing Langevin samplers.
result Efficient simulation of the flow with non-asymptotic convergence rate.
Study Langevin Monte Carlo for sampling non-log-concave distributions.
problem Sampling from non-log-concave distributions, especially Gaussian mixtures.
method Discretizations of overdamped Langevin diffusions.
result Numerical simulations compare Langevin Monte Carlo algorithms' performance.
New algorithm improves sampling from constrained spaces.
problem Sampling from constrained spaces efficiently.
method Metropolis-adjusted Mirror Langevin algorithm.
result Unbiased sampling with improved mixing time.
New Langevin Monte Carlo algorithms for sampling from nonsmooth distributions.
problem Sampling from distributions with nonsmooth convex composite potentials.
method Leveraging Bregman--Moreau envelopes and proximal operators in mirror descent.
result Efficiency in sampling from nonsmooth distributions, extending existing methods.
Alternative sampling method for autoregressive models using Langevin dynamics.
problem Efficiently sampling from autoregressive models.
method Initialize sequences with white noise and follow Langevin dynamics on global log-likelihood.
result Parallelizes and generalizes sampling process for autoregressive models.
New Langevin algorithms improve sampling efficiency in high dimensions.
problem Sampling from log-concave and smooth distributions in high dimensions.
method Combining splitting and accurate integration methods for P P P -th order Langevin dynamics. result LMC algorithms converge faster with better dimension dependence as P P P increases. New method uses higher-order Langevin dynamics for efficient parallel sampling.
problem Efficient parallel sampling from high-dimensional log-concave distributions.
method Combines higher-order Langevin dynamics with blockwise Lagrange polynomial interpolation.
result Reduces the number of parallel points required for a target accuracy.
New methods use transport maps to improve Langevin dynamics for sampling.
problem Sampling high-dimensional, non-Gaussian distributions efficiently.
method Apply transport maps to accelerate Langevin dynamics convergence.
result Discretized processes converge to target distribution with non-asymptotic bounds.
This paper resolves the Langevin Algorithm's mixing time for log-concave distributions.
problem Resolving the mixing time of the Langevin Algorithm for log-concave sampling.
method Introducing Privacy Amplification by Iteration to analyze Rényi divergence and Optimal Transport smoothing.
result Optimal mixing bounds for the Langevin Algorithm in log-concave sampling settings.
Langevin autoencoders improve deep latent variable models with efficient posterior sampling.
problem Efficient posterior sampling in deep latent variable models using MCMC.
method Amortized Langevin dynamics (ALD) replaces datapoint-wise sampling with encoder updates.
result ALD is valid as an MCMC algorithm with the target posterior as a stationary distribution.
The Riemannian Langevin Algorithm samples from manifolds efficiently.
problem Sampling from distributions on manifolds with log-Sobolev inequality.
method Riemannian Langevin Algorithm, log-Sobolev inequality, self-concordance extension, stochastic smoothness bounding.
result The Riemannian Langevin Algorithm converges rapidly to the target density.
Score matching method improves image generation quality.
problem Score matching method underperforms GANs in metrics like Fréchet Inception Distance.
method DSM-ALS with denoising and improved sampling techniques.
result Score matching methods can match GANs in image generation quality.
Combining diffusion models with Langevin dynamics improves posterior sampling efficiency.
problem Sampling from noisy posterior distributions efficiently.
method Annealed Langevin dynamics combined with diffusion models.
result Achieves posterior sampling in polynomial time with a weaker score error bound.
Langevin MCMC samples efficiently from Riemannian manifolds with geometric Euler-Murayama analysis.
problem Efficient sampling from Gibbs distributions on Riemannian manifolds.
method Geometric Langevin MCMC, discretization error bound, contraction guarantee for Langevin Diffusion.
result Langevin MCMC iterates converge to the target distribution after a number of steps proportional to the inverse square of the desired accuracy.
Paper tackles Bayesian image restoration in low-photon Poisson imaging problems.
problem Bayesian inference in challenging low-photon Poisson imaging problems.
method Plug-and-play (PnP) Langevin sampling strategies with accelerated methods and mirror sampling.
result Effective PnP Langevin sampling methods for low-photon Poisson imaging problems.
Paper proposes new Langevin samplers for sampling from log-concave distributions with superlinear gradient growth.
problem Sampling from log-concave distributions with superlinear gradient growth.
method Proposes two novel discretizations of kinetic Langevin SDEs, showing contractivity and log-Sobolev inequality.
result Establishes non-asymptotic bounds in 2-Wasserstein distance between sampled distributions and target measures.
Noise-corrected Langevin algorithm improves sampling from noisy data.
problem Sampling from noisy data with biased score function.
method Noise-corrected Langevin algorithm using noisy score function.
result Bias due to noisy data is removed, improving sampling accuracy.
Langevin Dynamics fails to sample from mixture distributions efficiently.
problem Analyzing Langevin Dynamics for sampling from mixture distributions.
method Theoretical analysis of Langevin Dynamics and proposing Chained-Langevin Dynamics.
result Langevin Dynamics fails to sample from mixture distributions efficiently.
New algorithms improve sampling from complex distributions.
problem Sampling from complex probability distributions efficiently.
method Regime-switching Langevin dynamics and Monte Carlo algorithms.
result Convergence guarantees and iteration complexities provided.
Proves convergence of PSGLA for sampling non-convex potentials.
problem Sampling from non-convex potentials with stability.
method Combines ULA and proximal optimization with stability analysis.
result First proof of convergence for PSGLA on non-convex potentials.
Novel method for nonlinear data assimilation using Langevin sampling.
problem Nonlinear data assimilation challenges in Bayesian filtering.
method Score-based sequential Langevin sampling (SSLS) with dynamic models and annealing.
result Asymptotic stability and error bounds for local posterior sampling.
Improved Langevin algorithms with prior diffusion achieve dimension-independent convergence for non-log-concave distributions.
problem Understanding the dimension dependency of computational complexity in high-dimensional sampling.
method Investigation of prior diffusion technique for log-Sobolev inequality target distributions.
result Modified Langevin algorithm achieves dimension-independent KL divergence convergence.
Efficient event generation for collider phenomenology using parallel Langevin sampling and learned Stein diagnostics.
problem Event generation for precision collider phenomenology.
method Parallel Langevin sampling with learned Stein diagnostics.
result Relaxation time is estimated using a data-driven approach.
ICSGLD improves efficiency in posterior sampling for big data.
problem Efficient posterior sampling for large datasets.
method Embarrassingly parallel multiple-chain CSGLD with efficient interactions.
result ICSGLD is more efficient than a single-chain CSGLD.
The paper develops methods for sampling from log-concave distributions with constraints.
problem Sampling from log-concave distributions with constraints.
method Randomized midpoint discretization of Langevin diffusions with various projections.
result New convergence guarantees for constrained Langevin algorithms.
New algorithm samples Bayesian neural networks for improved calibration.
problem Improving calibration of Bayesian neural networks.
method Symmetric Minibatch Splitting-UBU (SMS-UBU) algorithm.
result SMS-UBU provides better calibration performance than standard methods.
Improved error estimate for SGLD sampling algorithm.
problem Establishing a precise error bound for SGLD.
method Sharp uniform-in-time error estimate for SGLD under mild assumptions.
result Uniform-in-time O ( η 2 ) O(η^2) O ( η 2 ) bound for KL-divergence between SGLD and Langevin diffusion. First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.
problem Analyzing generalization error for first order discretizations of Langevin diffusion.
method Providing a sufficient smoothness condition to show that first order methods can achieve arbitrarily runtime complexity for a given expected generalization error.
result First order methods can achieve arbitrarily runtime complexity with additional smoothness assumptions.
Efficiently samples posterior distributions using Langevin dynamics.
problem Challenges in generating diverse posterior samples in high-dimensional spaces.
method Simulates Langevin dynamics in the noise space of a pre-trained generative model.
result Noise-space Langevin dynamics approximates the posterior without restarting the full sampling chain.
Hybrid method improves sampling from multimodal distributions.
problem Sampling from multimodal posterior distributions efficiently.
method Jump-Diffusion Langevin Dynamics hybrid with Metropolis.
result Calibrated hybrid method outperforms pure methods.
New algorithm speeds up sampling from complex distributions.
problem Efficiently sampling from non-log-concave distributions.
method Stochastic Proximal Samplers (SPS) based on SGLD and MALA.
result SPS-SGLD and SPS-MALA achieve faster sampling with reduced gradient complexity.
L-Cool improves image and language translation by cooling low-density samples.
problem Improving translation performance on fringe samples in unsupervised domain translation.
method Performing Langevin dynamics to move low-density samples towards high-density areas.
result L-Cool enhances state-of-the-art methods in image and language translation tasks.
This work accelerates constrained sampling using large deviation principles.
problem Sampling constrained probability distributions efficiently.
method Large deviation principles applied to skew-reflected non-reversible Langevin dynamics.
result The skew-symmetric matrix accelerates convergence and reduces asymptotic variance.
MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.
problem Sampling from heavy-tailed and multimodal distributions when neither target nor proposal densities can be evaluated.
method Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA) with Score Balance Matching.
result MAFLA significantly improves finite-time sampling accuracy over unadjusted fractional Langevin dynamics.
The paper proposes a neural network architecture inspired by Langevin Monte Carlo for sampling from target distributions.
problem Sampling from complex target distributions efficiently.
method A neural network architecture inspired by Langevin Monte Carlo is proposed to map samples from a simple reference distribution to samples from the target.
result The proposed neural network architecture achieves approximation rates in the Wasserstein-2 distance for smooth, log-concave target distributions.
New sampling method for heavy-tailed distributions using Langevin Algorithm.
problem Sampling from heavy-tailed distributions efficiently.
method Transformed Unadjusted Langevin Algorithm on specific transformations.
result Polynomial-order oracle complexities for certain heavy-tailed densities.
A scalable framework uses Langevin sampling to approximate neural network models of evolving processes.
problem Uncertainty quantification in neural network models of dynamic systems.
method Flexible data model based on NODE, joint learning of data model and posterior parameters, Langevin sampling.
result Demonstrated performance on chemical reaction and material physics data, compared favorably to variational inference.
Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossibl…
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte Carlo methods. We propose a new sampling algorithm based on a birth-death mechanis…
Adaptive Langevin dynamics reduces bias in Bayesian inference with mini-batching.
problem Bias in posterior sampling due to mini-batching in Bayesian inference.
method Adaptive Langevin dynamics with dynamical friction to correct noise.
result Quantified bias in posterior distribution due to mini-batching.
Improved sampling efficiency with Random Reshuffling for Langevin dynamics.
problem Sampling efficiency in stochastic gradient algorithms.
method Random Reshuffling for Stochastic Gradient Langevin Dynamics (SGLD).
result Random Reshuffling leads to improved performance in sampling.
We propose a new Stein self-repulsive dynamics for obtaining diversified samples from intractable un-normalized distributions. Our idea is to introduce Stein variational gradient as a repulsive force to push the samples of Langevin dynamics away from the past trajectories. This simple idea allows us to significantly de…
Improved convergence for non-log-concave sampling.
problem Sampling from non-log-concave distributions.
method Novel conductance analysis of SGLD with auxiliary Markov Chain.
result SGLD achieves ε-sampling error with fewer evaluations.