New method controls bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin.
problem Bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin samplers.
method Delocalization of bias technique applied to these samplers.
result Control W 2 W_2 W 2 bias with O ( K ) O(\sqrt{K}) O ( K ) integration steps for high-dimensional distributions. New methods improve efficiency of sampling algorithms for complex systems.
problem Efficiently sampling from complex, high-dimensional probability distributions.
method Randomized Runge-Kutta-Nyström methods tailored for Hamiltonian flows.
result Quantitative 5 / 2 5/2 5/2 -order L 2 L^2 L 2 -accuracy in approximating Hamiltonian flows. ULA rapidly converges to target distribution without convexity assumptions.
problem Sampling from complex probability distributions efficiently.
method Unadjusted Langevin Algorithm with KL and Rényi divergence guarantees.
result ULA converges in KL divergence under log-Sobolev inequality.
New analysis of Langevin Monte Carlo via convex optimization.
problem Sampling from logconcave smooth and non-smooth target distributions.
method Formulation as a convex optimization problem, analysis using convex optimization techniques.
result Non-asymptotic analysis of Unadjusted Langevin Algorithm and new sampling methods.
The unadjusted Langevin algorithm converges faster for some variables in high dimensions.
problem Sampling probability distributions in high-dimensional settings.
method Analysis of the unadjusted Langevin algorithm for strongly log-concave distributions.
result The delocalization of bias effect allows for faster convergence for a small number of variables.
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.
New algorithm samples from complex non-convex distributions.
problem Sampling from non-convex, non-smooth distributions with superlinear gradients.
method Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA)
result Non-asymptotic convergence bounds in Wasserstein-2 distance for SG-TULA.
ULA estimates covariance of log-concave distributions efficiently.
problem Estimating covariance matrices of log-concave distributions efficiently.
method Unadjusted Langevin algorithm (ULA) for sampling and covariance estimation.
result Sample complexity of single-chain ULA is smaller than that of parallel ULA by a logarithmic factor.
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 analyzes convergence rates of Langevin dynamics and Proximal Sampler using Φ Φ Φ -divergence.
problem Analyzing convergence rates of Langevin dynamics and Proximal Sampler.
method Extending mixing time analyses to Φ Φ Φ -divergence, using strong data processing inequalities. result Convergence of Φ Φ Φ -divergence to 0 exponentially fast along Unadjusted Langevin Algorithm and Proximal Sampler. 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.
The paper studies sampling high-dimensional distributions using the Unadjusted Langevin Algorithm.
problem Sampling high-dimensional probability distributions with known densities.
method Euler discretization of the Langevin SDE for sampling.
result Non-asymptotic bounds for convergence in Wasserstein and total variation distances.
PLA improves sampling from distributions under isoperimetry with faster KL divergence convergence.
problem Sampling from distributions with KL divergence under isoperimetry.
method Proximal Langevin Algorithm (PLA) with KL and Rényi divergence convergence guarantees.
result PLA achieves faster KL divergence convergence rates than ULA under log-Sobolev inequality.
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.
A new algorithm SLA reduces bias in sampling from measures using Langevin dynamics.
problem Reducing bias in sampling from complex target measures using Langevin dynamics.
method Proposed symmetrized Langevin algorithm (SLA) to correct bias in ULA.
result SLA is consistent for Gaussian target measures, while ULA is not.
New Langevin algorithm works well even for rough distributions.
problem Sampling from non-smooth distributions.
method Simple Langevin algorithm without smoothness assumptions.
result Algorithm performs well even with discontinuous gradients.
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.
Analyzes learning and applying preconditioners in MCMC for efficiency.
problem Improving efficiency of MCMC algorithms.
method Non-asymptotic analysis of schemes that learn preconditioners.
result Established non-asymptotic guarantees for preconditioned ULA.
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.
A new estimator improves efficiency of MC algorithms.
problem Efficiency of Markov chain algorithms.
method Markov chain importance sampling (MCIS).
result Improves error per CPU cycle, often significantly.
New algorithm improves stability and efficiency of neural network training.
problem Stability and efficiency issues in adaptive optimization for neural networks.
method Polygonal approximations for SDEs with monotone coefficients, providing stability and addressing vanishing gradients.
result TheoPouLa algorithm shows superior performance over popular adaptive optimizers.
The paper provides privacy guarantees for MCMC algorithms using Langevin dynamics.
problem Ensuring differential privacy in MCMC algorithms.
method Novel methodology combining Girsanov's theorem and perturbation trick.
result Established (Rényi) DP guarantees for Langevin algorithms.
New algorithms improve sampling from constrained distributions.
problem Generating samples from distributions under constraints.
method Kinetic Langevin dynamics and splitting schemes.
result Improved complexity bounds over existing methods.
New schemes improve error estimates for sampling from non-log-concave distributions.
problem Improving sampling from non-log-concave distributions with super-linear drift growth.
method Developed tamed Euler and randomized Euler schemes with error estimates.
result Near-optimal error bounds for sampling and optimization problems.
Robustly estimates posterior with adversarial outliers using Rob-ULA.
problem Estimating posterior distribution in the presence of adversarial outliers.
method Proposes Rob-ULA, a robust variant of ULA, and provides finite-sample analysis.
result Sampling from p T p_T p T with e x t d i s t ( p T , p ∗ ) ≤ ε e x t s f a c c + i l d e O ( ε ) ext{dist}(p_T, p^*) \leq \varepsilon_{ extsf{acc}} + ilde{\mathcal{O}}(ε) e x t d i s t ( p T , p ∗ ) ≤ ε e x t s f a cc + i l d e O ( ε ) after T = i l d e O ( d / ε e x t s f a c c ) T= ilde{\mathcal{O}}(d/\varepsilon_{ extsf{acc}}) T = i l d e O ( d / ε e x t s f a cc ) iterations. New algorithms for sampling and optimization without tuning.
problem Efficient sampling and optimization over probability measures.
method Optimization on the space of probability measures, using gradient flows.
result Strong theoretical guarantees and similar performance to optimally tuned algorithms.
Stochastic EM with biased MCMC improves inference stability.
problem Intractable E-step in EM algorithm.
method Stochastic approximation with biased MCMC.
result ULA is more stable and sometimes faster than MALA.
MALA improves sampling from log-concave densities with faster mixing times.
problem Sampling from strongly log-concave densities efficiently.
method Discretization of Langevin diffusion with accept-reject step.
result MALA requires O ( κ d log ( 1 / δ ) ) \mathcal{O} \big(κd \log(1/δ) \big) O ( κ d log ( 1/ δ ) ) steps for TV error δ δ δ . New algorithm TUSLA improves learning of non-convex neural networks.
problem Optimizing non-convex loss functions in neural networks with superlinear gradient growth.
method Tamed Unadjusted Stochastic Langevin Algorithm (TUSLA) based on SGLD with taming technology.
result Finite-time guarantees for TUSLA to find approximate minimizers of empirical and population risks.
New method samples from non-log-concave distributions with weak dissipativity.
problem Sampling from distributions that are not log-concave and weakly dissipative.
method Taming scheme tailored to growth and decay properties of the target distribution.
result Explicit non-asymptotic guarantees for KL, TV, and Wasserstein distances.
NF-ULA combines Langevin Monte Carlo with normalizing flows for imaging inverse problems.
problem Solving inverse problems in imaging with uncertainty quantification.
method Langevin Monte Carlo with normalizing flow prior.
result NF-ULA outperforms competing methods for severely ill-posed inverse problems.
New method improves sampling from score-based models by correcting bias.
problem Bias in sampling from score-based diffusion models.
method Metropolis-Hastings or Barker's accept-reject steps to correct bias, using the score function.
result Improves sample quality on synthetic and image datasets, yielding consistent gains in FID.
New algorithm improves latent variable model estimation.
problem Estimating parameters in latent variable models.
method Jarzynski-adjusted Langevin algorithm (JALA) for SMC methods.
result JALA-EM provides maximum marginal likelihood estimate.
A new sampler for complex discrete distributions efficiently updates all variables in parallel.
problem Sampling complex high-dimensional discrete distributions efficiently and accurately.
method Discrete Langevin proposal (DLP) for parallel coordinate updates with controlled stepsize.
result DLP efficiently explores high-dimensional and strongly correlated variables with asymptotic bias of zero for log-quadratic distributions.
LMC achieves sqrt(d) dependence in sampling error, improving previous bounds.
problem Analyzing sampling error in Langevin Monte Carlo.
method Refined mean-square analysis for discretizations of contractive SDEs.
result Establishes i l d e O ( d / ε ) ilde{O}(\sqrt{d}/ε) i l d e O ( d / ε ) mixing time bound for LMC. New method accelerates Bayesian imaging using Langevin sampling.
problem Bayesian inference in imaging inverse problems with convex geometry.
method Stochastic relaxed proximal-point iteration targeting posterior distribution.
result Accelerated convergence for κ κ κ -strongly log-concave targets. Statistical finite elements use Langevin dynamics to efficiently handle uncertainty quantification.
problem Uncertainty quantification in finite element models with observed data.
method Langevin dynamics, unadjusted Langevin algorithm (ULA), for sampling posterior distributions.
result ULA provides a scalable and efficient method for characterizing the posterior distribution of statFEM models.
Improved sampling from complex distributions with reduced bias.
problem Reducing bias in high-dimensional sampling algorithms.
method Hierarchical entropy analysis to weaken assumptions and expand scope.
result Bias reduction in low-dimensional marginals scales with lower dimension, not full dimension.
The paper studies how quickly samples from Langevin dynamics become independent.
problem Understanding the dependence between samples along Langevin dynamics and related algorithms.
method Measures dependence via Φ Φ Φ -mutual information and proves strong data processing inequalities. result The Φ Φ Φ -mutual information between samples decreases exponentially to zero. Generative model uses Schrödinger bridges for stable sampling.
problem Sampling from unknown distributions with limited training samples.
method Combines Schrödinger bridges and Langevin dynamics.
result Effective stability and generation of samples within convex hull.
This paper analyzes the bias of inexact MCMC methods in high dimensions.
problem Understanding the bias of inexact MCMC methods in high-dimensional spaces.
method Establishing bounds on Wasserstein distances between inexact MCMC methods and target distributions.
result The asymptotic bias of ULA and uHMC depends on key quantities related to the target distribution or the stationary probability measure of the scheme.
LMC algorithm converges to target in Chi-squared and Renyi divergence.
problem Sampling from target distribution using LMC with strong dissipativity and smoothness conditions.
method LMC algorithm with strong dissipativity and first-order smoothness, initialized with Gaussian.
result LMC reaches ε-neighborhood of target in Chi-squared and Renyi divergence in O(λ²dε⁻¹) steps.
New method improves sampling efficiency in complex stochastic systems.
problem Sampling efficiency in nonconvex stochastic gradient cases.
method Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo.
result Quantitative Gaussian concentration bounds and convergence rates established.
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.
Noise-free sampling method using Wasserstein proximal for faster convergence.
problem Sampling from distributions governed by potential functions.
method Deterministic score-based MCMC with regularized Wasserstein proximal.
result Improved mixing time bounds for Gaussian distributions compared to ULA and MALA.
New analysis for learning and applying preconditioners in MCMC improves efficiency.
problem Improving efficiency of MCMC algorithms by modifying them with preconditioners.
method Analyzes and compares computational costs of MCMC schemes with and without preconditioners.
result Establishes non-asymptotic guarantees for MCMC algorithms that learn and use preconditioners.
The paper analyzes the trade-off between computational savings and statistical error in approximating diffusions and Markov chains.
problem The trade-off between computational savings and statistical error in approximating diffusions and Markov chains.
method Develops general results on the Wasserstein distance between equilibrium distributions of two diffusions, and applies these results to derive finite-sample error bounds for approximate Langevin dynamics and zig-zag sampling.
result Characterizes the computational-statistical trade-off and provides insights into when approximate methods can lead to more accurate samples.
Develops algorithms for Bayesian inference with Plug & Play priors, ensuring convergence and well-posedness.
problem Bayesian imaging inverse problems with implicit priors defined by denoising algorithms.
method Introduces PnP-ULA and PnP-SGD algorithms for Monte Carlo sampling and MAP inference, proving convergence under realistic assumptions.
result Proves convergence of PnP-ULA and PnP-SGD algorithms for Bayesian inference with PnP priors, targeting a well-posed decision-theoretic model.