Optimal scaling for proximal MALA in high dimensions confirmed.
problem Optimizing sampling efficiency in high-dimensional target densities.
method Introduced and analyzed the proximal MALA algorithm, showing it maintains optimal scaling.
result Proximal MALA achieves optimal scaling in high dimensions with an average acceptance probability of 0.574.
MALA mixes efficiently under smoothness and isoperimetry assumptions.
problem Sampling from target densities efficiently.
method Metropolis-Adjusted Langevin algorithm (MALA) with smoothness and isoperimetry assumptions.
result MALA mixes in $O\left(\frac{(LΥ)^{\frac12}}{ψ_μ^2} \log\left(\frac{1}ε
ight)
ight)$ iterations.
New methods combine MALA and mGRAD for scalable Bayesian inference in high-dimensional state-space models.
problem Bayesian inference in high-dimensional state-space models with limited scalability.
method Combines gradient-based MALA and prior-informed mGRAD for scalable inference.
result Extends classical MCMC methods to handle multiple time steps and particles.
Improved MALA method for neural networks uncertainty quantification.
problem Uncertainty quantification in Bayesian neural networks.
method Corrected Stochastic MALA (csMALA) with a simplified correction term.
result Improved surrogate posterior for quantifying uncertainties in neural networks.
MALA mixes optimally in κ√d steps for log-concave sampling.
problem Sampling from log-concave distributions efficiently.
method Metropolis-Adjusted Langevin Algorithm (MALA) with warm start.
result Optimal minimax mixing time of κ√d iterations for log-concave distributions.
We consider the problem of sampling from a strongly log-concave density in R d \mathbb{R}^d R d , and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by simulating a Markov chain obtained from the discretization of an appropriate Langevin dif…
Gradient-based MCMC for discrete spaces improves sampling performance.
problem Sampling in discrete spaces using traditional methods is challenging.
method Introduced new discrete Metropolis-Hastings samplers inspired by MALA, with a novel preconditioning technique.
result Demonstrated strong empirical performance across various challenging sampling problems.
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.
Lower bounds on MALA and HMC for well-conditioned distributions.
problem Understanding the performance limits of Metropolized sampling methods.
method Analyzing the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator.
result Nearly-tight lower bound of Ω ~ ( κ d ) \widetildeΩ(κd) Ω ( κ d ) on the mixing time of MALA from an exponentially warm start. New sampling methods improve statistical efficiency for intractable targets.
problem Sampling from complex, intractable probability distributions.
method Gaussian invariant versions of RWM, MALA, and Hessian MALA.
result Gaussian invariant sampling leads to improved statistical efficiency.
A new framework RTK accelerates diffusion inference by breaking down the process into fewer, more efficient subproblems.
problem Efficiently generating data from trained diffusion models using discretized reverse SDEs or ODEs.
method Developed a general RTK framework that decomposes the diffusion process into fewer, more balanced subproblems, using MALA and ULD for sampling.
result The RTK-MALA and RTK-ULD algorithms achieve faster convergence rates and lower error compared to existing methods.
Improved log-concave sampling to O ( d 1 / 2 ) O(d^{1/2}) O ( d 1/2 ) with warm starts.
problem Sampling from strongly log-concave distributions efficiently.
method Warm starts and discretized underdamped Langevin diffusion.
result Achieved O ( d 1 / 2 ) O(d^{1/2}) O ( d 1/2 ) complexity for high-accuracy sampling. 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.
Combines MALA and Adam for efficient uncertainty quantification in deep learning.
problem Uncertainty estimation in deep neural networks.
method Integrates Metropolis Adjusted Langevin Algorithm (MALA) with momentum-based optimization (Adam) for efficient sampling from posterior distributions.
result The algorithm approximates the Gibbs posterior in total variation distance and efficiently quantifies epistemic uncertainty.
This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.
problem Lack of geometric ergodicity study in Riemannian manifold and Lagrangian Monte Carlo methods.
method Investigates a mixture of LMC and RMHMC with MMALA to achieve geometric ergodicity.
result Demonstrates geometric ergodicity in the mixture of LMC and RMHMC with MMALA.
Polynomial mixing times for simulated tempering in mixture sampling problems.
problem Sampling from mixtures of log-concave distributions with location shifts.
method Conductance decomposition applied to an auxiliary Markov chain on an augmented space.
result First polynomial-time guarantee for simulated tempering with MALA.
The paper proposes a Gibbs sampler for neural network posterior sampling.
problem Sampling from the posterior of neural networks.
method Adding noise to activations and using a Gibbs sampler.
result The Gibbs sampler achieves similar performance to MCMC methods on real and synthetic data.
We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical so…
Adversarial attacks on deep learning models have compromised their performance considerably. As remedies, a lot of defense methods were proposed, which however, have been circumvented by newer attacking strategies. In the midst of this ensuing arms race, the problem of robustness against adversarial attacks still remai…
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.
tBayes-MICE uses Bayesian MICE for time series data imputation.
problem Missing data in time series data.
method Bayesian MICE with MCMC, temporal features, and different samplers.
result tBayes-MICE reduces imputation errors and accounts for uncertainty.
HMC with leapfrog integrator mixes faster than MALA under certain smoothness conditions.
problem Analyzing the mixing time of HMC and MALA for sampling from smooth distributions.
method Bounding gradient complexity and leveraging invariance of joint distribution.
result Metropolized HMC with more leapfrog steps outperforms MALA in total variation distance.
We introduce a new family of MCMC samplers that combine auxiliary variables, Gibbs sampling and Taylor expansions of the target density. Our approach permits the marginalisation over the auxiliary variables yielding marginal samplers, or the augmentation of the auxiliary variables, yielding auxiliary samplers. The well…
New algorithm for sampling from distributions with thin tails.
problem Sampling from distributions with thin tails and theoretical guarantees.
method Proposes a Metropolized Algorithm With Optimization Step (MAO).
result Derives upper bounds on the mixing time of MAO.
The Langevin Markov chain algorithms are widely deployed methods to sample from distributions in challenging high-dimensional and non-convex statistics and machine learning applications. Despite this, current bounds for the Langevin algorithms are slower than those of competing algorithms in many important situations, …
High-dimensional unimodal distributions can cause MCMC methods to fail.
problem Failure of MCMC methods in high-dimensional unimodal distributions.
method Examples and theoretical analysis of MCMC methods, including Metropolis-Hastings adjusted methods.
result MCMC methods can take an exponential run-time for high-dimensional unimodal distributions.
A new Metropolis-Hastings algorithm uses Gaussian Processes to speed up sampling from complex models.
problem Sampling from computationally expensive probabilistic models.
method Two-stage Metropolis-Hastings algorithm with a Gaussian Process surrogate model.
result The approach learns the target distribution while sampling, eliminating the need for pre-training.
Bayesian DDR models complex multivariate distributions.
problem Modeling relationships between multivariate distributions with differing dimensions.
method Generalized Bayesian framework using sliced Wasserstein distance and MALA for inference.
result Posterior consistency and robust fits demonstrated in simulations and real data.
This work improves VAEs using MCMC methods for better variational bounds.
problem Improving the expressiveness of variational distributions in VAEs.
method Entropy-based adaptation for MALA/HMC chains to optimize tighter variational bounds.
result Higher held-out log-likelihoods and improved generative metrics.
Improved particle filters for estimating model parameters using differentiable resampling.
problem Inability to differentiate sampling and resampling steps in particle filters.
method Extended reparameterisation trick to include stochastic input, enabling differentiation. Used p-MCMC and NUTS for parameter estimation.
result NUTS improves mixing of Markov chain and produces more accurate results in less time.
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.
Enhances SMC² with Hessian info for more efficient posterior approximation.
problem Improving accuracy and efficiency in Bayesian inference.
method Integrates second-order information (Hessian) into SMC²'s proposal distribution.
result Second-order proposals lead to more accurate posterior approximations and better step-size selection.
Improved sampling algorithm with state-of-the-art complexity bounds.
problem Efficient sampling from various probability distributions.
method Proximal sampler with inexact restricted Gaussian oracle.
result State-of-the-art complexity bounds in almost all settings.
Recent semi-supervised anomaly detection methods that are trained using small labeled anomaly examples and large unlabeled data (mostly normal data) have shown largely improved performance over unsupervised methods. However, these methods often focus on fitting abnormalities illustrated by the given anomaly examples on…
This paper improves sampling from complex distributions using Langevin dynamics.
problem Pathological behaviors in normalizing flows for complex distributions.
method A Metropolis adjusted Langevin algorithm (MALA) to sample in the latent space.
result The method preserves tractability of the likelihood and works with any pre-trained NF network.
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.
A new algorithm improves sampling for graph learning models.
problem Euclidean proposals struggle near the boundary of PSD matrices.
method ConeMALA, a geometry-aware Langevin algorithm.
result ConeMALA achieves higher ESS/sec and stable diagnostics.
The paper develops a method to infer model parameters and shared dynamics from related physical systems using data.
problem Calibrating models to match data when detailed system properties and laws are unknown.
method Hierarchical Bayesian framework, adaptive surrogate models, bilevel optimization.
result Joint estimation of individual model parameters and shared dynamics using data from related systems.