Study improves sampling from non-log-concave distributions using Fisher information.
problem Sampling from non-log-concave distributions with high Fisher information guarantees.
method Proximal sampler with RGO implementation, leveraging log-concave sampling results.
result Improved complexity guarantee in relative Fisher information for non-log-concave sampling.
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 algorithms improve convergence rates for non-log-concave sampling and log-partition estimation.
problem Efficiently sampling from non-log-concave distributions and estimating their log-partition function.
method Analysis of information-based complexity, study of polynomial-time sampling algorithms.
result Optimal rates for sampling and log-partition estimation sometimes exceed those for optimization.
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.
The paper sets lower bounds for sampling non-log-concave distributions using Fisher information.
problem Understanding the complexity of sampling non-log-concave distributions.
method Proves two lower bounds using Fisher information in the context of sampling.
result Lower bounds on the complexity of sampling non-log-concave distributions, ruling out high-accuracy algorithms.
New sampling algorithm for non-log-concave distributions requires many queries.
problem Sampling from non-log-concave distributions with good accuracy.
method Lower bound on query complexity and algorithm for sampling.
result Tight query complexity characterization for sampling from non-log-concave distributions.
Study improves sampling from complex distributions using annealed Langevin Monte Carlo.
problem Sampling from non-log-concave and multimodal distributions.
method Annealed Langevin Monte Carlo algorithm with theoretical guarantees.
result Oracle complexity of O(dβ²A²/ε⁶) for achieving ε² accuracy in Kullback-Leibler divergence.
We construct a compact symplectic manifold with a Hamiltonian circle action for which the Duistermaat-Heckman function is not log-concave.
Paper tackles sampling from non-log-concave distributions using denoising diffusion.
problem Sampling from non-log-concave distributions efficiently.
method DDMC framework, Zeroth-Order Diffusion Monte Carlo (ZOD-MC) algorithm.
result ZOD-MC achieves inverse polynomial dependence on sampling accuracy, efficient for low dimensions.
New sampling method guarantees approximate first-order stationary points for non-convex functions.
problem Sampling from non-log-concave densities with non-convex potential functions.
method Averaged Langevin Monte Carlo with complexity analysis.
result Langevin Monte Carlo outputs a sample with ε-relative Fisher information after O(L²d²/ε²) iterations.
Improved sampling from non-log-concave distributions with polynomial query complexity.
problem Sampling from distributions with non-log-concave densities efficiently.
method Combining Ornstein-Uhlenbeck process assumptions and polynomial moment conditions.
result Polynomial query complexity improvement over previous methods.
New algorithm reduces variance in stochastic gradient estimation.
problem Optimizing the variance of stochastic gradient algorithms for non-log-concave distributions.
method Developed a Multi-index Antithetic Stochastic Gradient Algorithm (MASGA) that is independent of the distribution's structure.
result MASGA achieves performance comparable to Monte Carlo estimators with unbiased samples.
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.
This paper improves low-precision sampling using SGHMC for deep learning models.
problem Enhancing training efficiency of deep neural networks with low-precision training.
method Investigates low-precision sampling via Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) for both log-concave and non-log-concave distributions.
result Low-precision SGHMC achieves quadratic improvement in error compared to SGLD for non-log-concave distributions.
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.
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.
New method uses weighted SDEs to improve sampling from complex distributions.
problem Sampling from highly non-log-concave distributions.
method Introduces weighted stochastic differential equations to augment diffusion-based samplers.
result Demonstrates improved exploration of nonconvex or multimodal landscapes.
New method improves sampling from non-convex distributions using HFHR dynamics.
problem Sampling from non-log-concave densities with non-convex potential functions.
method Hessian-free high-resolution dynamics (HFHR) with reflection/synchronous coupling.
result HFHR dynamics converges faster than kinetic Langevin dynamics (KLD) for non-convex potentials.
This paper tackles denoising of complex measures using optimal transport and curvature analysis.
problem Denoising of complex, possibly non-log-concave measures.
method Score function and optimal transport theory to revert Langevin diffusion chains.
result The difficulty of denoising depends on the curvature complexity of the initial measure at specific SNR scales.
Improved sampling guarantees for weakly log-concave distributions.
problem Sampling from distributions that are not strongly log-concave.
method Proximal sampler with convergence guarantees under weaker assumptions.
result New state-of-the-art sampling guarantees for various target distributions.
We study the problem of sampling from the power posterior distribution in Bayesian Gaussian mixture models, a robust version of the classical posterior. This power posterior is known to be non-log-concave and multi-modal, which leads to exponential mixing times for some standard MCMC algorithms. We introduce and study …
As an important Markov Chain Monte Carlo (MCMC) method, stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. However, SGLD typically suffers from slow convergence rate due to its large variance caused by the stochastic gradient. In order to allev…
New sampling method using regularized Wasserstein proximal for Gibbs distributions.
problem Sampling from Gibbs distributions with numerical stability and efficiency.
method Preconditioned regularized Wasserstein proximal operator.
result Discrete-time convergence analysis and explicit bias characterization.
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.
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.
New framework uses PDE for no-regret generative modeling.
problem Developing efficient generative models for complex distributions.
method Iterative refinement of Brenier maps using mirror gradient descent.
result Converges to optimal Brenier map under various step-size schedules.
We study the problem of sampling from a distribution p ∗ ( x ) ∝ exp ( − U ( x ) ) p^*(x) \propto \exp\left(-U(x)\right) p ∗ ( x ) ∝ exp ( − U ( x ) ) , where the function U U U is L L L -smooth everywhere and m m m -strongly convex outside a ball of radius R R R , but potentially nonconvex inside this ball. We study both overdamped and underdamped Langevin MCMC and establish upper bound…
Algorithm samples from composite log-concave distributions using gradient evaluations and restricted Gaussian oracles.
problem Sampling from composite log-concave distributions with limited gradient evaluations.
method Proximal gradient algorithm with RGO for g g g and strong/strongly convex conditions for f f f . result Achieves ε ε ε error in total variation distance in O ~ ( κ d log 4 ( 1 / ε ) ) \widetilde{\mathcal O}(κ\sqrt d \log^4(1/ε)) O ( κ d log 4 ( 1/ ε )) iterations. 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.
This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several approximative methods have been proposed. The expectation propagation (EP) has been found …
Accelerates sampling from Gibbs distributions using ARWP method.
problem Sampling from Gibbs distributions efficiently.
method ARWP method, combining Nesterov acceleration and regularized Wasserstein proximal.
result ARWP exhibits higher contraction rate and faster tail exploration.
LaPSRL achieves optimal regret for isoperimetric RL distributions.
problem Designing RL algorithms with sublinear regret for non-log-concave distributions.
method Posterior Sampling (PSRL) and Langevin sampling (LaPSRL) for isoperimetric distributions.
result LaPSRL achieves order-optimal regret and subquadratic complexity.
New bounds for generative models under weaker assumptions.
problem Establishing convergence guarantees for generative models under weak assumptions.
method Non-asymptotic 2-Wasserstein distance bounds for probability flow ODEs under weak log-concavity and Lipschitz continuity.
result Concrete convergence rates for generative models, including non-log-concave distributions.
Optimal convex loss function improves regression coefficient estimation.
problem Asymptotic variance improvement in linear regression estimation.
method Score matching extension for log-concave projection.
result Semiparametric estimator attains minimal asymptotic covariance.
Poisson Midpoint Method improves Langevin Dynamics for diffusion models.
problem Slow convergence of LMC in diffusion models requiring many small steps.
method Poisson Midpoint Method approximates LMC with larger steps, proving quadratic speed up.
result Poisson Midpoint Method maintains quality of DDPM with fewer calls.
OLLA framework efficiently samples from constrained distributions with nonconvex constraints.
problem Sampling from constrained distributions with nonconvex constraints is challenging.
method Overdamped Langevin with Landing (OLLA) framework that handles both equality and inequality constraints.
result OLLA converges exponentially fast to the constrained target density in W 2 W_2 W 2 distance. The paper proves optimizability implies inequalities for sampling.
problem Optimizing functions via Gradient Flow and sampling from Gibbs measures.
method Gradient Flow and Lyapunov potentials to establish inequalities.
result Optimizability via Gradient Flow implies Poincaré and Log-Sobolev Inequalities.