Nonlinear MCMC improves Bayesian machine learning sampling.
problem Sampling problems in Bayesian machine learning.
method Nonlinear MCMC technique with convergence guarantees.
result Improves sampling in Bayesian neural networks.
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48 results for “MCMC convergence”
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.
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.
This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform no…
Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of th…
It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel conce…
This review article surveys data augmentation MCMC algorithms.
problem Sampling from intractable probability distributions.
method Comprehensive study of DA MCMC algorithms, their convergence properties, and acceleration strategies.
result Synthesizes recent developments and provides insights for researchers.
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.
Stochastic gradient Markov Chain Monte Carlo (SG-MCMC) has been developed as a flexible family of scalable Bayesian sampling algorithms. However, there has been little theoretical analysis of the impact of minibatch size to the algorithm's convergence rate. In this paper, we prove that under a limited computational bud…
This study compares parallel SMC and MCMC for Bayesian deep learning, showing SMC parallel is faster.
problem Efficiently performing Bayesian deep learning with parallel computing.
method Compared sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) in parallel settings.
result Parallel SMC achieves similar convergence as a single SMC but with reduced communication time.
Normalized random measures (NRMs) provide a broad class of discrete random measures that are often used as priors for Bayesian nonparametric models. Dirichlet process is a well-known example of NRMs. Most of posterior inference methods for NRM mixture models rely on MCMC methods since they are easy to implement and the…
TensorFlow Probability MCMC toolkit improves MCMC efficiency for modern hardware.
problem Inefficient MCMC algorithms on modern hardware.
method Design and implementation of a new MCMC toolkit for TensorFlow.
result Improved MCMC efficiency on modern hardware.
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…
This paper analyzes MCMC algorithms on large graphs using Dirichlet forms.
problem Analyzing the behavior of MCMC algorithms in high-dimensional problems.
method Utilizes Mosco convergence of Dirichlet forms to study RWM algorithm on large graphs.
result Demonstrates the advantages of Dirichlet form approach over standard diffusion methods.
New method reduces computational cost for Bayesian inference.
problem High computational cost in Bayesian inference.
method Coreset MCMC, a Markov chain targeting coreset posterior.
result Coreset MCMC provides higher quality posterior approximations and reduced computational cost.
New couplings improve understanding of molecular dynamics convergence.
problem Understanding convergence of Andersen dynamics in high dimensions.
method Presented couplings to obtain sharp convergence bounds in the Wasserstein sense.
result Sharp convergence bounds in the Wasserstein sense without global convexity.
LSB is a new MCMC method for discrete spaces that reduces target evaluations.
problem Sampling in discrete domains with high efficiency and adaptability.
method Local self-balancing proposals, mutual information objective, self-balancing learning.
result LSB converges with fewer target evaluations compared to existing methods.
This paper develops tools for nonreversible MCMC with convergence guarantees.
problem Designing nonreversible MCMC kernels with convergence guarantees.
method Develops tools for nonreversible Markov kernels using conditional invertible transforms.
result Ensures nonreversible kernels have the desired invariance property and lead to convergent algorithms.
Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and distributed systems such as compute clusters. Recent work has proposed running i…
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.
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
problem Slow convergence of Krylov subspace solvers for ill-conditioned matrices.
method Graph neural surrogate and Bayesian optimization for AI-tuned MCMC parameters.
result 50% reduction in iterations to convergence on unseen system.
Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such challenges culminate to lack of convergence to the parameter posterior. Nevertheless, thi…
Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with limitations in practice: MCMC methods can be computationally demanding; VI methods …
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.
The book covers scalable MCMC methods for Bayesian learning.
problem Scalability issues in Bayesian learning with large datasets.
method Advanced MCMC algorithms, including stochastic gradient, non-reversible, and continuous time methods.
result Substantial advances in practical and theoretical Bayesian computation.
The posteriors over neural network weights are high dimensional and multimodal. Each mode typically characterizes a meaningfully different representation of the data. We develop Cyclical Stochastic Gradient MCMC (SG-MCMC) to automatically explore such distributions. In particular, we propose a cyclical stepsize schedul…
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.
New KSDs control moments in approximations, improving diagnostics and tests.
problem Inability of standard KSDs to control moment convergence.
method Developed alternative diffusion KSDs under sufficient conditions.
result First KSDs to exactly characterize q-Wasserstein convergence.
New MCMC methods map high-dimensional problems to spheres for better mixing.
problem Mixing issues in high-dimensional distributions, especially heavy-tailed ones.
method Stereographic Markov Chain Monte Carlo (MCMC) methods that map high-dimensional problems to spheres.
result Uniformly ergodic samplers for various distributions, including heavy-tailed ones, with faster convergence in higher dimensions.
Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphi…
Improved sampling accuracy in SG-MCMC methods via non-uniform gradient subsampling.
problem Computational inefficiency and sampling error in stochastic gradient MCMC methods.
method Proposes a non-uniform subsampling scheme to reduce sampling error in EWSG, a variant of SG-MCMC.
result EWSG reduces sampling error compared to uniform subsampling, improving accuracy without sacrificing convergence speed.
New Langevin method achieves third order convergence for strongly log-concave distributions.
problem Sampling from complex distributions efficiently.
method Underdamped Langevin diffusion with third order convergence.
result Achieves 2-Wasserstein error of ε in O(√d/ε^1/3) steps under additional Lipschitz condition.
Moving Target Monte Carlostat.CO
New algorithm MTMC reduces MCMC evaluation costs.
problem High-dimensional sampling with intractable posterior evaluations.
method Iteratively updated approximation of posterior distribution for acceptance rate.
result Approximation converges to true posterior as iterations increase.
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.
Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide conditions under which an appropriate scaling allows to improve the error bounds in…
New model improves MCMC efficiency and multi-modal distribution exploration.
problem Inefficient and slow MCMC methods for complex distributions.
method Deep involutive generative models for Metropolis-Hastings updates.
result Deep involutive models can learn complex MCMC updates efficiently.
This paper tackles sampling issues in latent space EBMs by introducing diffusion-based amortization.
problem Degenerate MCMC sampling quality hinders latent space EBM learning and generation quality.
method Introduces diffusion-based amortization for long-run MCMC sampling.
result The learned amortization of MCMC is a valid long-run MCMC sampler.
Stochastic Stein Discrepancies improve inference efficiency.
problem Intractable computation of Stein discrepancies.
method Subsampled approximations of Stein operators.
result Stochastic Stein Discrepancies inherit convergence properties of standard SDs.
Split-Merge MCMC (Monte Carlo Markov Chain) is one of the essential and popular variants of MCMC for problems when an MCMC state consists of an unknown number of components. It is well known that state-of-the-art methods for split-merge MCMC do not scale well. Strategies for rapid mixing requires smart and informative …
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.
Neural network MCMC sampler maximizes proposal entropy for efficient sampling.
problem Inefficient sampling from complex probability distributions.
method Proposes a neural network MCMC sampler that maximizes proposal entropy.
result Significantly higher efficiency in various sampling tasks.
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.
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.
Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we explore this idea using steps of the Hamiltonian Monte Carlo (HMC) algorithm, an e…
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…
Improved sampling for Bayesian neural networks reduces vanishing acceptance rates and increases predictive accuracy.
problem Sampling inefficiency in Bayesian neural networks, especially with deep architectures and large datasets.
method Approximate blocked Gibbs sampling to partition and sample subgroups of parameters.
result Increased predictive accuracy and quantification of predictive uncertainty in classification tasks.
KSD Thinning uses KSD to thin MCMC samples efficiently.
problem Efficiently representing posterior distributions in Bayesian inference.
method KSD Thinning: retains only samples exceeding a KSD threshold.
result Established convergence and complexity tradeoffs for KSD Thinning.
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.