Stochastic Gradient Hamiltonian Monte Carlo
arXiv:1402.4102
Abstract
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard random-walk proposals. The popularity of such methods has grown significantly in recent years. However, a limitation of HMC methods is the required gradient computation for simulation of the Hamiltonian dynamical system-such computation is infeasible in problems involving a large sample size or streaming data. Instead, we must rely on a noisy gradient estimate computed from a subset of the data. In this paper, we explore the properties of such a stochastic gradient HMC approach. Surprisingly, the natural implementation of the stochastic approximation can be arbitrarily bad. To address this problem we introduce a variant that uses second-order Langevin dynamics with a friction term that counteracts the effects of the noisy gradient, maintaining the desired target distribution as the invariant distribution. Results on simulated data validate our theory. We also provide an application of our methods to a classification task using neural networks and to online Bayesian matrix factorization.
ICML 2014 version
References in corpus (1)
Cited by in corpus (202)
- A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges
- B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
- Generative Modeling by Estimating Gradients of the Data Distribution
- A Review and Comparative Study on Probabilistic Object Detection in Autonomous Driving
- Three Factors Influencing Minima in SGD
- Multiplicative Normalizing Flows for Variational Bayesian Neural Networks
- Bayesian Dark Knowledge
- Multi-fidelity Bayesian Neural Networks: Algorithms and Applications
- A Complete Recipe for Stochastic Gradient MCMC
- Sparse graphs using exchangeable random measures
- A Simple Baseline for Bayesian Uncertainty in Deep Learning
- Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks
- On the Random Batch Method for second order interacting particle systems
- On Markov chain Monte Carlo methods for tall data
- On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators
- Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning
- Stochastic Gradient Descent as Approximate Bayesian Inference
- Entropy-SGD: Biasing Gradient Descent Into Wide Valleys
- What Are Bayesian Neural Network Posteriors Really Like?
- Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo
- A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applications
- Quality of Uncertainty Quantification for Bayesian Neural Network Inference
- Piecewise-Deterministic Markov Chain Monte Carlo
- Bridging the Gap between Stochastic Gradient MCMC and Stochastic Optimization
- Implicit Weight Uncertainty in Neural Networks
- Learning Functional Priors and Posteriors from Data and Physics
- A Variational Analysis of Stochastic Gradient Algorithms
- A Survey of Optimization Methods from a Machine Learning Perspective
- On the Expressiveness of Approximate Inference in Bayesian Neural Networks
- Confidence Calibration for Convolutional Neural Networks Using Structured Dropout
- Scalable Bayes via Barycenter in Wasserstein Space
- Modified Hamiltonian Monte Carlo for Bayesian inference
- Ergodicity of Approximate MCMC Chains with Applications to Large Data Sets
- Calibration of Deep Probabilistic Models with Decoupled Bayesian Neural Networks
- How Good is the Bayes Posterior in Deep Neural Networks Really?
- Stochastic Quasi-Newton Langevin Monte Carlo
- The True Cost of Stochastic Gradient Langevin Dynamics
- Markov Chain Monte Carlo-Based Machine Unlearning: Unlearning What Needs to be Forgotten
- Adversarial Distillation of Bayesian Neural Network Posteriors
- Information Aware Max-Norm Dirichlet Networks for Predictive Uncertainty Estimation
- Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Acceleration
- Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families
- Uncertainty Quantification in Deep Learning for Safer Neuroimage Enhancement
- Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty
- Bayesian Autoencoders for Drift Detection in Industrial Environments
- On the Theory of Variance Reduction for Stochastic Gradient Monte Carlo
- A Survey of Bayesian Statistical Approaches for Big Data
- Stochastic Gradient MCMC with Repulsive Forces
- (Non-) asymptotic properties of Stochastic Gradient Langevin Dynamics
- Generalizing Hamiltonian Monte Carlo with Neural Networks
- Probabilistic Deep Learning to Quantify Uncertainty in Air Quality Forecasting
- Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlo
- All You Need is a Good Functional Prior for Bayesian Deep Learning
- Learning Scalable Deep Kernels with Recurrent Structure
- Recent advances in deep learning theory
- Mode jumping MCMC for Bayesian variable selection in GLMM
- TherML: Thermodynamics of Machine Learning
- Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models
- On Last-Layer Algorithms for Classification: Decoupling Representation from Uncertainty Estimation
- Scaling Hamiltonian Monte Carlo Inference for Bayesian Neural Networks with Symmetric Splitting
- Bayesian Variational Autoencoders for Unsupervised Out-of-Distribution Detection
- Attended Temperature Scaling: A Practical Approach for Calibrating Deep Neural Networks
- Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimization
- Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization
- Dirichlet belief networks for topic structure learning
- Sampling-Free Variational Inference of Bayesian Neural Networks by Variance Backpropagation
- Bayesian Inference for Large Scale Image Classification
- A Survey on Bayesian Deep Learning
- Bayesian Neural Ordinary Differential Equations
- Fast Threshold Tests for Detecting Discrimination
- Heavy Ball Neural Ordinary Differential Equations
- Confidence-Aware Learning for Camouflaged Object Detection
- Unbiased Bayes for Big Data: Paths of Partial Posteriors
- Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs
- Sliced Kernelized Stein Discrepancy
- Variance Networks: When Expectation Does Not Meet Your Expectations
- Deep Gaussian Processes: A Survey
- Covariance-Controlled Adaptive Langevin Thermostat for Large-Scale Bayesian Sampling
- Hamiltonian Monte Carlo with Energy Conserving Subsampling
- Big Learning with Bayesian Methods
- Error bounds for Approximations of Markov chains used in Bayesian Sampling
- Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization
- Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow
- Bayesian Learning of Parameterised Quantum Circuits
- Learning Gradient Fields for Shape Generation
- Bayesian Graph Neural Networks for Molecular Property Prediction
- Integrating Uncertainty into Neural Network-based Speech Enhancement
- HPOBench: A Collection of Reproducible Multi-Fidelity Benchmark Problems for HPO
- Parallel Stochastic Gradient Markov Chain Monte Carlo for Matrix Factorisation Models
- Sampling-based Bayesian Inference with gradient uncertainty
- Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents
- Learning Deep Generative Models with Doubly Stochastic MCMC
- On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method
- Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applications
- Scaling up Dynamic Topic Models
- A Contour Stochastic Gradient Langevin Dynamics Algorithm for Simulations of Multi-modal Distributions
- Stochastic Stein Discrepancies
- Data Augmentation for Bayesian Deep Learning
- Calibrating Bayesian Generative Machine Learning for Bayesiamplification
- Lifelong Bayesian Optimization
- Scalable Bayesian Learning of Recurrent Neural Networks for Language Modeling
- Bayesian Inference Forgetting
- Meta-Surrogate Benchmarking for Hyperparameter Optimization
- AMAGOLD: Amortized Metropolis Adjustment for Efficient Stochastic Gradient MCMC
- Spectral Subsampling MCMC for Stationary Time Series
- Remote sensing image fusion based on Bayesian GAN
- Stochastic Gradient Hamiltonian Monte Carlo with Variance Reduction for Bayesian Inference
- Distributed Computation for Marginal Likelihood based Model Choice
- Multi-variance replica exchange stochastic gradient MCMC for inverse and forward Bayesian physics-informed neural network
- Sparse Deep Learning: A New Framework Immune to Local Traps and Miscalibration
- Schr{ö}dinger-F{ö}llmer Sampler: Sampling without Ergodicity
- Average of Recentered Parallel MCMC for Big Data
- Quantifying the accuracy of approximate diffusions and Markov chains
- Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimation
- Federated Stochastic Gradient Langevin Dynamics
- Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics
- Stochastic Variance-Reduced Hamilton Monte Carlo Methods
- Quantum-Inspired Hamiltonian Monte Carlo for Bayesian Sampling
- Langevin Markov Chain Monte Carlo with stochastic gradients
- Gibbs Sampling the Posterior of Neural Networks
- URSABench: Comprehensive Benchmarking of Approximate Bayesian Inference Methods for Deep Neural Networks
- Stochastic Particle-Optimization Sampling and the Non-Asymptotic Convergence Theory
- CaMKII activation supports reward-based neural network optimization through Hamiltonian sampling
- An adaptive Hessian approximated stochastic gradient MCMC method
- Walsh-Hadamard Variational Inference for Bayesian Deep Learning
- De-randomizing MCMC dynamics with the diffusion Stein operator
- On the Effects of Quantisation on Model Uncertainty in Bayesian Neural Networks
- Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction
- HMC: avoiding rejections by not using leapfrog and some results on the acceptance rate
- Effect Handlers for Programmable Inference
- Mini-batch Metropolis-Hastings MCMC with Reversible SGLD Proposal
- Energy-Based Models with Applications to Speech and Language Processing
- Differentiable Visual Computing
- Distilled Thompson Sampling: Practical and Efficient Thompson Sampling via Imitation Learning
- Efficient Computation Reduction in Bayesian Neural Networks Through Feature Decomposition and Memorization
- Parallelising MCMC via Random Forests
- Adaptive Bayesian Linear Regression for Automated Machine Learning
- A deterministic and computable Bernstein-von Mises theorem
- Adaptively Preconditioned Stochastic Gradient Langevin Dynamics
- A Unifying and Canonical Description of Measure-Preserving Diffusions
- A Survey on Large-scale Machine Learning
- Introspective Generative Modeling: Decide Discriminatively
- Simulation-based Safety Assessment of High-level Reliability Models
- BORE: Bayesian Optimization by Density-Ratio Estimation
- Disentangling the Roles of Curation, Data-Augmentation and the Prior in the Cold Posterior Effect
- Batch Multi-Fidelity Bayesian Optimization with Deep Auto-Regressive Networks
- Subsampling MCMC - An introduction for the survey statistician
- MCMC Variational Inference via Uncorrected Hamiltonian Annealing
- Understanding MCMC Dynamics as Flows on the Wasserstein Space
- Bayesian Cycle-Consistent Generative Adversarial Networks via Marginalizing Latent Sampling
- High-Order Stochastic Gradient Thermostats for Bayesian Learning of Deep Models
- An Introduction to Hamiltonian Monte Carlo Method for Sampling
- Variational Transport: A Convergent Particle-BasedAlgorithm for Distributional Optimization
- Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo
- Variational Inference with Mixture Model Approximation: Robotic Applications
- Targeted stochastic gradient Markov chain Monte Carlo for hidden Markov models with rare latent states
- Differentiable Annealed Importance Sampling and the Perils of Gradient Noise
- A Record Linkage Model Incorporating Relational Data
- Generative Modeling by Inclusive Neural Random Fields with Applications in Image Generation and Anomaly Detection
- Precomputing Strategy for Hamiltonian Monte Carlo Method Based on Regularity in Parameter Space
- Geometry of Program Synthesis
- sgmcmc: An R Package for Stochastic Gradient Markov Chain Monte Carlo
- Fast Sampling for Bayesian Max-Margin Models
- Secure and Differentially Private Bayesian Learning on Distributed Data
- A Variational View on Bootstrap Ensembles as Bayesian Inference
- Bayesian neural networks and dimensionality reduction
- Real-Time Uncertainty Estimation in Computer Vision via Uncertainty-Aware Distribution Distillation
- A Decentralized Approach to Bayesian Learning
- A Langevinized Ensemble Kalman Filter for Large-Scale Static and Dynamic Learning
- Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimation
- A Markov Jump Process for More Efficient Hamiltonian Monte Carlo
- Chaining Meets Chain Rule: Multilevel Entropic Regularization and Training of Neural Nets
- Variational Langevin Hamiltonian Monte Carlo for Distant Multi-modal Sampling
- Differentially Private Hamiltonian Monte Carlo
- Structured Stochastic Gradient MCMC
- Generative Text Modeling through Short Run Inference
- Probabilistic Programs with Stochastic Conditioning
- TATi-Thermodynamic Analytics ToolkIt: TensorFlow-based software for posterior sampling in machine learning applications
- Contributions to Large Scale Bayesian Inference and Adversarial Machine Learning
- Data Subsampling for Bayesian Neural Networks
- Bayesian Eye Tracking
- Bayes-Adaptive Deep Model-Based Policy Optimisation
- Improving Predictive Uncertainty Estimation using Dropout -- Hamiltonian Monte Carlo
- A Novel Unsupervised Post-Processing Calibration Method for DNNS with Robustness to Domain Shift
- An Adaptive Empirical Bayesian Method for Sparse Deep Learning
- Stochastic Probabilistic Programs
- Stochastically Differentiable Probabilistic Programs
- On the Generative Utility of Cyclic Conditionals
- A New Framework for Variance-Reduced Hamiltonian Monte Carlo
- Non-asymptotic estimation of risk measures using stochastic gradient Langevin dynamics
- Variance reduction for Random Coordinate Descent-Langevin Monte Carlo
- Hamiltonian Monte-Carlo for Orthogonal Matrices
- Maximum conditional entropy Hamiltonian Monte Carlo sampler
- Mirrored Langevin Dynamics
- Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases
- Set Prediction without Imposing Structure as Conditional Density Estimation
- Generative Particle Variational Inference via Estimation of Functional Gradients
- Efficient MCMC Sampling for Bayesian Matrix Factorization by Breaking Posterior Symmetries
- Relative Entropy Gradient Sampler for Unnormalized Distributions
- Learning Sparse Structured Ensembles with SG-MCMC and Network Pruning
- Variance reduction for dependent sequences with applications to Stochastic Gradient MCMC
- Revisiting the Effects of Stochasticity for Hamiltonian Samplers