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.
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…
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.
Develops algorithm to differentiate Metropolis-Hastings for optimization.
problem Optimizing intractable densities with discrete components.
method Fuses stochastic automatic differentiation with Markov chain coupling schemes.
result Unbiased and low-variance gradient estimator for intractable densities.
Study on Metropolis-within-Gibbs schemes for high-dimensional Bayesian models.
problem Improving the scalability of MCMC methods for complex Bayesian models.
method Relating convergence properties to conditional conductance for non-conjugate hierarchical models.
result Established dimension-free convergence results for Metropolis-within-Gibbs schemes.
cKAM improves adaptive sampling by incorporating a cyclical stepsize scheme.
problem Adaptive Metropolis algorithms can get stuck in local modes.
method cKAM uses a cyclical stepsize scheme to encourage exploration and escape from local modes.
result cKAM successfully escapes local modes and converges to the true posterior distribution.
Improved spectral gap for MwG with adaptive RWM proposals.
problem Improving mixing efficiency of MwG for log-concave distributions.
method Using adaptive RWM proposals tuned to match conditional variances of log-concave target distributions.
result Established a spectral gap lower bound of order O(1/κd) for MwG. 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.
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.
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…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis…
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.
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.
Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often expressed as complicated multi-dimensional integrals. Unfortunately, analytical expressi…
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.
A new two-step MH method for Bayesian EL computation.
problem Complex likelihood support in Bayesian EL.
method Hierarchical Metropolis Hastings with reversible jump MCMC.
result Improved sampling from BayesEL posteriors.
New tuning rules for Metropolis algorithms derived from Bayesian large-sample asymptotics.
problem Optimal scaling in random-walk Metropolis algorithms under realistic assumptions.
method Large-sample asymptotics to derive weak convergence results and tuning guidelines.
result Tuning guidelines consistent with previous ones when target density is product form, accounting for correlation structure.
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.
Recent works propose using the discriminator of a GAN to filter out unrealistic samples of the generator. We generalize these ideas by introducing the implicit Metropolis-Hastings algorithm. For any implicit probabilistic model and a target distribution represented by a set of samples, implicit Metropolis-Hastings oper…
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 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.
A DP method selects best sparse models in high dimensions efficiently.
problem Model selection in high-dimensional sparse linear regression under privacy constraints.
method Differential privacy (DP) with exponential mechanism and Metropolis-Hastings algorithm.
result The method identifies active features quickly under privacy constraints.
The study examines convergence of stochastic processes on large graphs and adjacency matrices.
problem Analyzing convergence of stochastic processes on large graphs and adjacency matrices.
method Introduced new metrics on the space of measure-valued graphons and used them to show convergence of random trajectories to deterministic curves.
result The Metropolis chain converges to a deterministic gradient flow curve on the space of graphons under certain conditions.
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.
A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the…
New bounds for MCMC on discrete spaces without dimension dependence.
problem High-dimensional statistical convergence analysis of MCMC methods.
method Combining multicommodity flow and single-element drift conditions.
result Informed Metropolis-Hastings algorithms achieve relaxation times independent of dimension.
Bayesian inference via standard Markov Chain Monte Carlo (MCMC) methods is too computationally intensive to handle large datasets, since the cost per step usually scales like Θ(n) in the number of data points n. We propose the Scalable Metropolis-Hastings (SMH) kernel that exploits Gaussian concentration of the pos…
LIC compiles probabilistic models to generate efficient MCMC proposals.
problem Creating accurate Metropolis-Hastings proposals for Bayesian inference.
method Integrates probabilistic graphical models and neural networks in an open-source framework to optimize proposal distributions.
result LIC produces more efficient and robust MCMC proposals compared to existing methods.
Exact minibatch MH method improves scalability for large datasets.
problem Inexactness in minibatch MH methods causes inference errors.
method TunaMH proposes an exact minibatch MH method with a tunable batch size.
result TunaMH is asymptotically optimal in terms of batch size.
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.
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 MCMC methods improve efficiency for large network inference.
problem Efficiency of Metropolis within Gibbs for large networks.
method Combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo.
result New methods outperform Metropolis within Gibbs on synthetic and real networks.
Relational learning can be used to augment one data source with other correlated sources of information, to improve predictive accuracy. We frame a large class of relational learning problems as matrix factorization problems, and propose a hierarchical Bayesian model. Training our Bayesian model using random-walk Metro…
Pseudo-marginal Metropolis-Hastings (pmMH) is a powerful method for Bayesian inference in models where the posterior distribution is analytical intractable or computationally costly to evaluate directly. It operates by introducing additional auxiliary variables into the model and form an extended target distribution, w…
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.
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 …
We apply the hybrid Monte Carlo (HMC) algorithm to the financial time sires analysis of the stochastic volatility (SV) model for the first time. The HMC algorithm is used for the Markov chain Monte Carlo (MCMC) update of volatility variables of the SV model in the Bayesian inference. We compute parameters of the SV mod…
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In th…
Bayesian inference for expensive likelihoods using Langevin Monte Carlo with NF.
problem Sampling from complex posterior distributions with expensive likelihoods.
method Deterministic Langevin equation with NF gradient, Metropolis-Hastings updates.
result Competitive performance compared to state-of-the-art methods.
The exchange algorithm is studied for its convergence and asymptotic variance.
problem Theoretical limitations of the exchange algorithm in sampling from doubly-intractable distributions.
method Theoretical analysis of the exchange algorithm's convergence speed and asymptotic variance.
result The exchange algorithm converges at a geometric rate and satisfies a Central Limit Theorem.
A new algorithm speeds up rerandomization for better experiment balance.
problem Achieving optimal covariate balance in randomized experiments.
method Metropolis-Hastings framework with sampling-importance resampling.
result PSRSRR achieves significant speedups while maintaining statistical guarantees.
New method improves blockchain analysis by handling temporal changes and scalability.
problem Limited focus on evolving nature and scalability of blockchain transaction networks.
method Incremental approach with Metropolis-Hastings random walks.
result Comparable performance in node classification tasks with reduced computational overhead.
We introduce the Metropolis-Hastings generative adversarial network (MH-GAN), which combines aspects of Markov chain Monte Carlo and GANs. The MH-GAN draws samples from the distribution implicitly defined by a GAN's discriminator-generator pair, as opposed to standard GANs which draw samples from the distribution defin…
Can we make Bayesian posterior MCMC sampling more efficient when faced with very large datasets? We argue that computing the likelihood for N datapoints in the Metropolis-Hastings (MH) test to reach a single binary decision is computationally inefficient. We introduce an approximate MH rule based on a sequential hypoth…
We consider the problem of sampling from a strongly log-concave density in Rd, 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…
The computation of Bayesian estimates of system parameters and functions of them on the basis of observed system performance data is a common problem within system identification. This is a previously studied issue where stochastic simulation approaches have been examined using the popular Metropolis--Hastings (MH) alg…
Paper presents a fast, private MH algorithm for large-scale Bayesian inference.
problem Privacy-preserving Bayesian inference for large-scale data.
method Developed a novel DP-MH algorithm using minibatches.
result First exact and fast DP MH algorithm with privacy, scalability, and efficiency trade-offs.