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…
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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…
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 algorithm tunes SGMCMC hyperparameters for scalable Bayesian inference.
problem Tuning hyperparameters for SGMCMC is challenging due to lack of principled methods.
method Proposes a bandit-based algorithm using Stein discrepancies to tune hyperparameters.
result The method effectively tunes SGMCMC hyperparameters for various applications.
This paper introduces a scalable benchmark for evaluating local posterior sampling in neural networks.
problem Degeneracy in neural network loss landscapes and its impact on SGMCMC algorithms.
method Development of a scalable benchmark for local posterior sampling.
result RMSProp-preconditioned SGLD is most effective at representing the local geometry of the posterior distribution.
Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space the time-discret…
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…
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.
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.
A new method reduces variance in SGMCMC by preferentially subsampling data.
problem High variance in stochastic gradient estimates impacts sampler performance.
method Use a non-uniform probability distribution to preferentially subsample data points and adaptively adjust subsample size.
result Maintains accuracy while substantially reducing average subsample size.
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.
Adaptive stepsizing improves sampling in Bayesian neural networks.
problem Scalable sampling of posterior distributions in Bayesian neural networks.
method SA-SGLD, employing time rescaling to adapt stepsize dynamically.
result SA-SGLD achieves more accurate posterior sampling than SGLD.
New algorithm tracks deep RL value functions with uncertainty.
problem Static RL algorithms ignore uncertainty in agent-environment interactions.
method Langevinized Kalman Temporal-Difference (LKTD) algorithm using SGMCMC.
result LKTD algorithm converges to posterior distribution of deep RL parameters.
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…
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.
Bayesian neural networks show complex posterior distributions that HMC can capture effectively.
problem Understanding and approximating the high-dimensional, non-convex posterior of Bayesian neural networks.
method Full-batch Hamiltonian Monte Carlo (HMC) on modern architectures.
result HMC provides a robust and comparable representation of the BNN posterior, with significant performance gains over standard training and deep ensembles.
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…
Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an SGMCMC algorithm. Furthermore, we extend recent SG-MCMC methods with two key co…
Global inducing points improve Bayesian neural network performance.
problem Improving Bayesian neural network performance.
method Adapting correlated approximate posterior to all layers in a Bayesian neural network and deep Gaussian processes using learned global inducing points.
result State-of-the-art performance on CIFAR-10 (86.7%) without data augmentation or tempering.
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.