A new decentralized Bayesian learning method using Metropolis-adjusted Hamiltonian Monte Carlo.
problem Decentralized Bayesian learning with uncertainty quantification.
method Metropolis-adjusted Hamiltonian Monte Carlo in a decentralized federated learning setting.
result Theoretical guarantees and numerical effectiveness of the method on non-convex problems.
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.
We introduce an adaptive output-sensitive Metropolis-Hastings algorithm for probabilistic models expressed as programs, Adaptive Lightweight Metropolis-Hastings (AdLMH). The algorithm extends Lightweight Metropolis-Hastings (LMH) by adjusting the probabilities of proposing random variables for modification to improve c…
Oracle inequality for sparse neural nets adapts to unknown structure.
problem Sparse deep neural nets in nonparametric regression.
method Gibbs posterior distribution with Metropolis-adjusted Langevin algorithms and mixture of uniform priors.
result Oracle inequality showing adaptation to unknown regularity and structure, achieving minimax-optimal rate of convergence.
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 method samples Jeffreys prior for objective Bayesian inference.
problem Sampling from Jeffreys prior is challenging.
method Metropolis-Adjusted Langevin Algorithm
result Samples can be directly used in Bayesian methods.
Algorithm samples constrained stochastic differential equations.
problem Sampling stochastic differential equations with complex constraints.
method Pathspace Metropolis-adjusted manifold sampling.
result Demonstrated effectiveness in various constrained conditions.
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 sampling method improves accuracy for constrained spaces.
problem Sampling from constrained convex subsets of R^d.
method Metropolis-adjusted Preconditioned Langevin Algorithm.
result High-accuracy sampling with polylogarithmic error dependence.
We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of Metropolis-Hastings tests yield variable data consumed per sample, with only constant factor reductions versus using the full dataset for each sample. Here we present…
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.
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.
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.
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…
Study optimizes step size for Metropolis algorithm in non-identifiable cases.
problem Optimizing step size for Metropolis algorithm in non-identifiable models.
method Analytical derivation of average acceptance rate for non-identifiable cases.
result Developed optimization principle for step size based on average acceptance rate.
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.
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.
AMAGOLD improves stochastic gradient MCMC by infrequent Metropolis-Hastings corrections.
problem Bias in stochastic gradient Hamiltonian Monte Carlo (SGHMC).
method AMAGOLD infrequently uses Metropolis-Hastings corrections to remove bias, with a fixed step size schedule.
result AMAGOLD converges to the target distribution with a fixed, rather than a diminishing, step size, and at most a constant factor slower convergence rate.
New method improves sampling from high-dimensional target densities.
problem Sampling from high-dimensional target densities using Monte Carlo algorithms.
method Extends Metropolis-Adjusted Langevin Diffusion algorithm with random precondition matrix modeling.
result Significantly improves performance and computational efficiency over standard MCMC 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. 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.
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.
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.
High quality risk adjustment in health insurance markets weakens insurer incentives to engage in inefficient behavior to attract lower-cost enrollees. We propose a novel methodology based on Markov Chain Monte Carlo methods to improve risk adjustment by clustering diagnostic codes into risk groups optimal for health ex…
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.
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.
Paper develops a framework to discover bioprocessing regulatory mechanisms using symbolic and statistical learning.
problem Challenges in modeling complex intracellular regulation, stochastic system behavior, and limited experimental data.
method Symbolic and statistical learning framework based on stochastic differential equations and Bayesian learning.
result Improved sample efficiency and robust model selection compared to state-of-the-art approaches.
Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the default is to use random walk Metropolis to update the parameter values. We show …
Optimizes Metropolis-Hastings algorithms for efficient sampling in high dimensions.
problem Efficiently sampling from complex target distributions in high-dimensional spaces.
method Analyzes and optimizes the Barker proposal and other locally-balanced algorithms.
result Derives optimal noise distribution and balancing function for the Barker proposal.
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. We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed measure, which can be robustly optimised over the parameters of the proposal di…
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, …
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.
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.
This work improves convergence guarantees for unadjusted HMC in KL and Rényi divergences.
problem Understanding convergence properties of unadjusted HMC in divergences like KL and Rényi.
method One-shot couplings to establish regularization and lift convergence bounds.
result Quantitative control of relative density mismatch and warm-start requirements.
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.
New sampler tackles complex discrete energy landscapes efficiently.
problem Stagnation in gradient-based discrete samplers for non-convex settings.
method DREXEL sampler with Replica Exchange and Adjusted Metropolis.
result Proves samplers satisfy detailed balance and converge to target distribution.
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.
New MCMC method improves sampling from multimodal distributions.
problem Sampling from multimodal distributions is challenging for classical MCMC methods.
method Interpolating along the diffusion path, preserving mode weights and mixing properties.
result MAD-Path sampler improves global exploration and mode-weight estimation.
Proposes a hierarchical model for learning discrete Bayesian networks with shrinkage.
problem Learning discrete Bayesian networks with high-order interactions and cell probabilities.
method Hierarchical Dirichlet shrinkage model with Metropolis-adjusted Langevin algorithm for sampling.
result Efficiently learns graph structure and selects between DAGs from sparse count data.
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.
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.
Introduces DF framework for sampling decisions from target distributions.
problem Sampling from target distributions with additional guidance.
method DF framework based on MDP and Path Integral Diffusion.
result DF enhances guided sampling across various applications.
Modified Metropolis algorithm ensures convergence for multivariate binary distributions with fixed-order updates.
problem Infeasibility of standard Metropolis algorithm for multivariate binary distributions with fixed-order updates.
method Proposed a modified Metropolis transition operator ensuring irreducibility and convergence.
result Ensures convergence to the limiting distribution in multivariate binary case with fixed-order updates.
New MCMC method corrects bias without extra cost.
problem Correcting bias in MCMC algorithms without additional computational cost.
method Generalized Markov Chain Importance Sampling methods.
result Proposed methods are more efficient than Metropolis-Hastings versions.
SMTM improves MCMC sampling in high dimensions with multiple proposals and stereographic integration.
problem Improving MCMC performance in high-dimensional sampling.
method Integrating multiple-try Metropolis with stereographic MCMC framework.
result SMTM outperforms classical MTM and other methods in high-dimensional sampling.