Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in general performing exact inference requires all of the data to be processed at eac…
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48 results for “Stochastic Gradient Markov Chain Monte Carlo”
The paper proposes a new method to estimate optimal policies using MCMC.
problem Estimating the optimal policy for systems with unknown dynamics and reward functions.
method Using Markov Chain Monte Carlo to generate samples from the posterior distribution of parameters conditioned on optimality.
result The method provably converges to the globally optimal stochastic policy with similar variance to policy gradient methods.
Gradient learning optimises MCMC proposal distributions.
problem Intractable targets in MCMC sampling.
method Gradient-based optimisation of proposal distributions using a maximum entropy regularised objective function.
result Our method can outperform traditional MCMC algorithms, including Hamiltonian Monte Carlo.
Enhances sample diversity in SGMCMC for better uncertainty estimation in BNNs.
problem Limited sample diversity in SGMCMC affects uncertainty estimation and model performance.
method Reparameterizes neural network weights to produce a more diverse set of samples.
result The proposed approach achieves superior performance in image classification tasks, including OOD robustness.
New method corrects bias in stochastic gradient samplers.
problem Bias in stochastic gradient samplers.
method Gradient-Guided Monte Carlo with stochastic gradients.
result Corrected sampler yields nonzero acceptance probabilities.
New method for accurate Bayesian inference in GLMMs for large-scale data.
problem Challenges in scalable Bayesian inference for GLMMs due to intractable marginal likelihood and high computational cost.
method Stochastic gradient Markov Chain Monte Carlo (SGMCMC) algorithm using Fisher's identity for gradient estimation.
result Accurate posterior inference in large-sample settings with properly calibrated uncertainty.
New gradient estimator improves training for normalizing flows.
problem Training normalizing flows for complex models.
method Developed a new gradient estimator for Stochastic Gradient Descent.
result Significantly faster and more precise training for φ^4 model.
For large matrix factorisation problems, we develop a distributed Markov Chain Monte Carlo (MCMC) method based on stochastic gradient Langevin dynamics (SGLD) that we call Parallel SGLD (PSGLD). PSGLD has very favourable scaling properties with increasing data size and is comparable in terms of computational requiremen…
This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as Metropolis-Hastings, are known to run prohibitively slowly as the dataset size in…
The paper provides privacy guarantees for MCMC algorithms using Langevin dynamics.
problem Ensuring differential privacy in MCMC algorithms.
method Novel methodology combining Girsanov's theorem and perturbation trick.
result Established (Rényi) DP guarantees for Langevin algorithms.
Paper explores SVGD for Bayesian inference, linking deterministic and stochastic dynamics.
problem Bayesian inference and Markov chain Monte Carlo methods.
method Stein variational gradient descent (SVGD) with deterministic and stochastic dynamics.
result Identifies Stein-Fisher information as the leading order contribution in the long-time and many-particle regime.
Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great computational burden in big data applications. In contrast to MCMC methods, Stochastic Gra…
JaxSGMC simplifies SG-MCMC for Bayesian deep learning.
problem Uncertainty quantification in deep learning models.
method Modular stochastic gradient MCMC in JAX.
result Facilitates trustworthy neural network predictions.
Markov chain Monte Carlo (MCMC) algorithms for hidden Markov models often rely on the forward-backward sampler. This makes them computationally slow as the length of the time series increases, motivating the development of sub-sampling-based approaches. These approximate the full posterior by using small random subsequ…
New algorithm speeds up MCMC for deep learning models.
problem Large biases in SGMCMC for big data.
method Adaptive replica exchange SGMCMC (reSGMCMC).
result Achieves state-of-the-art results on various datasets.
New algorithms for Bayesian inference in decentralized learning.
problem Bayesian inference in decentralized learning settings.
method Decentralized SGLD and Decentralized SGHMC.
result Convergence of iterates to target distribution in 2-Wasserstein distance.
Improved sampling for network community detection.
problem Inefficient sampling from network partition posterior distributions.
method Merge-split Markov chain Monte Carlo for efficient sampling.
result Significantly improved mixing time and correct sampling.
Relativistic Monte Carlostat.ML
Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time discretizations and performs poorly if there is a mismatch between the spatial geo…
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.
SGBD algorithm improves robustness in Bayesian sampling.
problem Inefficiency of existing MCMC algorithms in large datasets.
method Extends Barker MCMC to stochastic gradient framework, introducing bias-corrected version.
result SGBD is more robust to hyperparameter tuning and gradient noise.
MCMC-driven learningstat.ML
Unified framework for MCMC and machine learning problems.
problem Intersection of MCMC and machine learning problems.
method Unified framework integrating various MCMC and machine learning techniques.
result Translation and generalization of theory and methods.
New algorithms improve sampling from Bayesian deep learning models.
problem Sampling from the posterior of deep neural networks is inefficient.
method Adaptive SGMCMC algorithms with biased drift.
result Proposed algorithms significantly outperform existing methods.
LS-SGLD improves SGLD's convergence rate and accuracy.
problem Slow convergence and high variance in SGLD.
method Laplacian smoothing technique applied to SGLD.
result LS-SGLD achieves smaller 2-Wasserstein distance error.
We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for this setting based on stochastic gradient Hamiltonian Monte Carlo sampling (SGHMC) …
Recent advances in stochastic gradient techniques have made it possible to estimate posterior distributions from large datasets via Markov Chain Monte Carlo (MCMC). However, when the target posterior is multimodal, mixing performance is often poor. This results in inadequate exploration of the posterior distribution. A…
New neural network method simplifies high-dimensional data.
problem Scalability issues in nonlinear sufficient dimension reduction.
method Stochastic neural network with adaptive gradient algorithm.
result Proposed method outperforms existing methods on large-scale data.
New method adapts to unknown mixing time in stochastic optimization.
problem Optimizing with Markovian data where mixing time is unknown.
method Combines MLMC gradient estimation with adaptive learning.
result Achieves optimal convergence rate for convex problems.
Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimationstat.ML
Efficiently estimates marginal likelihood using SGAIS.
problem Estimating marginal likelihood in i.i.d. data settings.
method Stochastic Gradient Annealed Importance Sampling (SGAIS).
result Significantly faster and more accurate estimates of marginal likelihood.
A new method for efficient inference in probabilistic programs with mixed support.
problem Challenges in inference for programs with both continuous and discrete latent variables.
method Stochastic gradient Markov Chain Monte Carlo algorithms.
result Outperforms existing composing inference baselines and works almost as well as inference in marginalized versions.
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.
Unified framework for isotropic SG noise in posterior sampling.
problem Bayesian posterior sampling with practical and robust methods.
method Designing a novel, isotropic SG noise approach with fixed learning rate.
result Competitive and practical method compared to state-of-the-art.
Lower bounds show many sampling algorithms need many gradient queries.
problem Sampling from strongly log-concave densities in high dimensions.
method Information theory and stochastic gradient methods.
result Lower bound on number of gradient queries needed.
We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a reproducing kernel Hilbert space. We here focus on modelling nonlinear covariance s…
New adaptive temperature selection improves parallel tempering efficiency.
problem Enhancing mixing in multi-modal distributions using parallel tempering.
method Adaptive temperature selection using policy gradient approach.
result Lower integrated autocorrelation times achieved compared to traditional methods.
Enhanced Markov chain sampler learns network statistics faster.
problem Learning network statistics efficiently.
method Integrates graph Forman curvature into Markov chain transition probabilities and stationary distribution.
result Curved Markov chain Monte Carlo achieves faster convergence.
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.
New method improves Bayesian inference for large models.
problem Bayesian inference in large-scale models like neural networks.
method Non-parametric variational approximation with a modified Langevin algorithm.
result Improves convergence speed and accuracy compared to existing methods.
A new gradient flow framework for distributionally robust optimization.
problem Optimizing under uncertainty with worst-case distributional constraints.
method Gradient flow theory applied to distributionally robust optimization.
result Practical algorithms for sampling from worst-case distributions.
Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic s…
STANLEY improves sampling for complex data models.
problem Training Energy-Based models with intractable normalizing constants.
method Anisotropic Langevin Dynamics with gradient-informed covariance.
result Geometrically uniformly ergodic Markov Chain for sampling.
We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method based on an interacting pool of standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an extended space. We present empirical results that show significant improv…
DCDC calculates convergence rates for Markov chains using neural networks.
problem Computing precise convergence rates for Markov chains is hard.
method Developed a neural network-based algorithm (DCDC) to bound convergence rates in Wasserstein distance.
result Demonstrated effective convergence bounds for real-world Markov chains.
We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and achieves both faster speed and higher accuracy at every iteration than the current sta…
Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility models with skewness driven by hidden Markov Chain with switching.
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.
We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCM…
From Monte Carlo to Las Vegas: Improving Restricted Boltzmann Machine Training Through Stopping Setscs.LG
We propose a Las Vegas transformation of Markov Chain Monte Carlo (MCMC) estimators of Restricted Boltzmann Machines (RBMs). We denote our approach Markov Chain Las Vegas (MCLV). MCLV gives statistical guarantees in exchange for random running times. MCLV uses a stopping set built from the training data and has maximum…
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.