Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators,…
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48 results for “MCMC Estimator”
New analysis of SGD with MCMC gradient estimator shows convergence rate and saddle point escape.
problem Analyzing SGD with MCMC gradient estimator under complex conditions.
method Introduced MCMC-SGD, analyzed convergence rate and saddle point escape using Bernstein inequality.
result Proven first order convergence rate and saddle point escape at least steps.
We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for observations is estimated from a random subset of observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smal…
The paper proposes methods to estimate MCMC quality with couplings, bounding Wasserstein distance.
problem Improving MCMC efficiency without sacrificing asymptotic consistency.
method Estimators based on couplings of Markov chains to assess quality of asymptotically biased sampling methods.
result Empirical upper bounds of Wasserstein distance for assessing MCMC quality.
New MCMC method estimates differential privacy from multiple MIAs without worst-case assumptions.
problem Bayesian estimation of differential privacy from membership inference attacks.
method Bayesian estimation via MCMC algorithm (MCMC-DP-Est).
result More cautious privacy analysis with joint estimation of MIA strengths and privacy parameter.
Stochastic gradient MCMC (SG-MCMC) has played an important role in large-scale Bayesian learning, with well-developed theoretical convergence properties. In such applications of SG-MCMC, it is becoming increasingly popular to employ distributed systems, where stochastic gradients are computed based on some outdated par…
Proposes MIVI for efficient posterior estimation and design of MCMC transitions.
problem Efficiently estimating posterior distributions in constrained time.
method Combines variational inference and MCMC with a variational distribution and optimized Markov chain.
result Optimized Markov chain improves variational distribution and vice versa, leading to more accurate posteriors.
Paper compares MCMC-based copula methods for exchange option pricing.
problem Pricing exchange options using copulas and MCMC.
method Risk-neutral pricing, copulas, and MCMC algorithm.
result Different copula models provide similar option prices except Gumbel.
Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluationsstat.ML
Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substantially faster than MCMC at practically no compromises in predict…
The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets…
New method merges MCMC samples without distributional assumptions.
problem Efficiently merging MCMC samples from disjoint subsets.
method Diffusion generative modelling for density approximation.
result Outperforms existing methods on high-dimensional problems.
New sampler reduces MCMC complexity for Bayesian variable selection.
problem High-dimensional Bayesian variable selection with high computation complexity.
method Variable-complexity subset weighted-Tempered Gibbs Sampler (wTGS) with Rao-Blackwellized estimator.
result Variances of Rao-Blackwellized estimator are smaller than those of subset wTGS.
Variational MCMCcs.LG
We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly because this approximation tends to underestimate the true variance and other features…
We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling literature to estimate the log-likelihood accurately using only a small fraction of …
APINNs use neural networks to solve MCMC problems efficiently.
problem Accurate Bayesian parameter estimation for systems governed by PDEs.
method Construct an offline PINN-UQ model and refine it on the fly using MCMC samples.
result Guaranteed approximation error less than a residual error threshold.
On Cyclical MCMC Samplingstat.CO
Cyclical MCMC tackles high-dimensional multimodal distributions, showing convergence under certain conditions.
problem High-dimensional multimodal posterior distributions in deep learning.
method Cyclical MCMC framework that tracks tempered versions of the target distribution over time.
result Cyclical MCMC converges to the target distribution under fast mixing kernels but fails in slow mixing cases.
Integration of Active Learning and MCMC Sampling for Efficient Bayesian Calibration of Mechanical Propertiesphysics.comp-ph
Study improves Bayesian calibration of mechanical properties using active learning and MCMC.
problem Inference of spatially varying material parameters in computational mechanics.
method Comprehensive comparative study of surrogate models and MCMC algorithms.
result Active learning strategy outperforms a priori trained models in posterior estimation.
It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly with dataset size. A popular class of methods for solving this issue is stochastic gradient MCMC. These methods use a noisy estimate of the gradient of the log posterior, which reduces the per iteration computational cost of the algorithm. Despi…
Markov chain Monte Carlo (MCMC) is widely regarded as one of the most important algorithms of the 20th century. Its guarantees of asymptotic convergence, stability, and estimator-variance bounds using only unnormalized probability functions make it indispensable to probabilistic programming. In this paper, we introduce…
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, s…
A new Monte Carlo sampling method derived from reverse diffusion.
problem Sampling from complex distributions, especially multi-modal ones.
method Transforming score matching into mean estimation; estimating means of regularized posterior distributions.
result rdMC can approximate sampling with any desired accuracy and is significantly faster than MCMC for complex distributions.
Fast Doubly-Adaptive MCMC to Estimate the Gibbs Partition Function with Weak Mixing Time Boundsstat.ML
New method reduces Gibbs partition function estimation complexity.
problem Estimating partition functions of Gibbs distributions.
method Doubly-adaptive MCMC with adaptive cooling schedule and mean estimator.
result Outperforms state-of-the-art algorithms in computational complexity and robustness.
NEO combines orbits to sample and estimate complex distributions.
problem Sampling and normalizing complex distributions.
method NEO-IS and NEO-MCMC using invertible maps and orbits.
result NEO provides unbiased estimators and explores multimodal targets.
The paper develops methods for high-dimensional inference in Markov random fields.
problem Statistical inference for high-dimensional Markov random fields.
method Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization.
result The proposed methods achieve -consistency and false discovery rate control.
Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfoldingcond-mat.dis-nn
Deep unfolding accelerates MCMC-based COP solvers.
problem Optimizing combinatorial problems with MCMC and gradient descent.
method Combines MCMC and gradient descent, trains step sizes, uses variance estimation for non-differentiable MCMC.
result Significantly accelerates convergence speed for COPs.
New method improves performance of Hamiltonian MCMC for log Z estimation.
problem Estimating tight bounds on log Z for unnormalized distributions.
method Uncorrected Hamiltonian Annealing (UHA) using reparameterization gradients.
result Better performance and easier parameter tuning compared to existing methods.
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…
Bayesian neural networks tutorial via MCMC in Python.
problem Bayesian inference for parameter estimation and uncertainty quantification in deep learning models.
method MCMC sampling methods to implement Bayesian inference, including advanced proposal distributions.
result Challenges in sampling multi-modal posterior distributions for Bayesian neural networks.
A novel Bayesian framework for private linear regression with MCMC.
problem Private linear regression in a distributed setting.
method Generative statistical model, MCMC algorithms, fast Bayesian estimation.
result The proposed methods provide well-rounded estimation and prediction.
New variational flows improve Monte Carlo and normalization tasks.
problem Intractable global optimum in expressive variational families.
method Constructing asymptotically exact variational flows from involutive MCMC kernels.
result Provable total variation convergence of new variational families.
We introduce Tempered Geodesic Markov Chain Monte Carlo (TG-MCMC) algorithm for initializing pose graph optimization problems, arising in various scenarios such as SFM (structure from motion) or SLAM (simultaneous localization and mapping). TG-MCMC is first of its kind as it unites asymptotically global non-convex opti…
FKEE estimates expectations without samples, using diffusion bridges and PINNs.
problem Estimating expectations without large sample sizes.
method Diffusion bridge models and Feynman-Kac operator approximation using PINNs.
result Significantly reduces variance and improves efficiency.
State space models (SSMs) are a flexible approach to modeling complex time series. However, inference in SSMs is often computationally prohibitive for long time series. Stochastic gradient MCMC (SGMCMC) is a popular method for scalable Bayesian inference for large independent data. Unfortunately when applied to depende…
Neural network estimates network models efficiently.
problem Estimating flexible ERGMs is challenging due to intractable normalizing constants.
method Trains a neural network on parameter-simulation pairs to invert and estimate parameters quickly and in parallel.
result The method performs well in practice and accommodates extra network statistics.
The paper optimizes private data sharing by selecting statistics and using MCMC for Bayesian inference.
problem Optimizing private data sharing by selecting statistics and performing Bayesian inference.
method Promotes Fisher information for statistic selection and proposes MCMC algorithms for inference.
result The Fisher information of the privatized statistic predicts the relative performance of the statistic in Bayesian estimation.
Optimizes MCMC chains with neural control variates.
problem Reducing variance in Markov Chain Monte Carlo (MCMC) simulations.
method Uses neural networks as control variates to minimize asymptotic variance.
result Derives optimal convergence rate under various ergodicity assumptions.
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters of an MCMC algorithm. Here we take a different approach and, similarly to paralle…
A new method de-randomizes MCMC dynamics using the Stein operator.
problem Estimating complex target distributions in Bayesian inference.
method De-randomized kernel-based particle samplers that discretize the fiber-gradient Hamiltonian flow.
result GSVGD de-randomizes complex MCMC dynamics, maintaining high sample quality.
Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and state-space models still scales poorly; each MCMC transition takes linear time i…
New method for MCMC models without perfect or sequential samplers.
problem Bayesian inference for complex models with intractable terms.
method Utilizes tractable independence model to construct unbiased estimates.
result Scalable method for high-dimensional models.
Centered plug-in estimators reduce bias in Wasserstein distance estimation.
problem Conservative bias in plug-in estimators of Wasserstein distances.
method Centering procedure based on linear combinations to reduce bias.
result Centered plug-in estimators provide informative upper and lower bounds on Wasserstein distances.
We propose a novel framework of estimating systemic risk measures and risk allocations based on Markov chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By consi…
A new MCMC method combines low and high-fidelity models to reduce computation.
problem Inefficient computation of expensive target densities in scientific applications.
method Pseudo-marginal MCMC approach using a telescoping series of low-fidelity models.
result Asymptotically exact multi-fidelity MCMC algorithms for reduced computational cost.
Develops variational inference for Neyman-Scott processes for faster sampling.
problem Slow mixing time in MCMC for posterior sampling in Neyman-Scott processes.
method Variational inference algorithm for Neyman-Scott processes, minimizing KL divergence.
result Achieves better prediction performance than MCMC with limited computational time.
Estimates covariance matrices using Markov chain Monte Carlo with improved sample complexity.
problem Complexity of covariance matrix estimation for Gibbs distributions.
method Uses Markov chain Monte Carlo with conditions on the chain's spectral gap and Poincaré inequality.
result Achieves similar sample complexity as i.i.d. samples with better query complexity.
This project compares MCMC and VI for Bayesian PMF on MovieLens.
problem Intractable posterior distribution in PMF.
method Employed MCMC and VI for Bayesian inference on MovieLens.
result VI converges faster, MCMC provides more accurate estimates.
Develops methods to estimate gradient of EIG for Bayesian Experimental Design.
problem Optimizing Bayesian inference through efficient experimental design.
method Introduces UEEG-MCMC and BEEG-AP methods for estimating EIG gradient.
result Both methods improve upon existing benchmarks in EIG optimization.
MixFlows uses a mixture of flows for efficient variational inference.
problem Efficient and reliable variational inference for complex models.
method A new variational family of mixed flows with efficient algorithms and convergence guarantees.
result MixFlows provides more reliable posterior approximations and comparable sample quality to MCMC methods.