# Particle-based Online Bayesian Sampling

arXiv: https://arxiv.org/abs/2302.14796 · HTML: https://mlsanity.com/paper/2302.14796/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 57 references that are in the map.
- First posted on arXiv 28 Feb 2023.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Don't Decay the Learning Rate, Increase the Batch Size](https://mlsanity.com/paper/1711.00489/) (2017)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Bayesian Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.03836/) (2018)
- [Optimization, Learning, and Games with Predictable Sequences](https://mlsanity.com/paper/1311.1869/) (2013)
- [AdaGrad stepsizes: Sharp convergence over nonconvex landscapes](https://mlsanity.com/paper/1806.01811/) (2018)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [First-order Methods for Geodesically Convex Optimization](https://mlsanity.com/paper/1602.06053/) (2016)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Tracking Slowly Moving Clairvoyant: Optimal Dynamic Regret of Online Learning with True and Noisy Gradient](https://mlsanity.com/paper/1605.04638/) (2016)
- [Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds](https://mlsanity.com/paper/1605.07147/) (2016)
- [A Non-Asymptotic Analysis for Stein Variational Gradient Descent](https://mlsanity.com/paper/2006.09797/) (2020)
- [Streaming Variational Bayes](https://mlsanity.com/paper/1307.6769/) (2013)
- [A Unified Particle-Optimization Framework for Scalable Bayesian Sampling](https://mlsanity.com/paper/1805.11659/) (2018)
- [On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient](https://mlsanity.com/paper/1803.06573/) (2018)
- [Dropout Inference in Bayesian Neural Networks with Alpha-divergences](https://mlsanity.com/paper/1703.02914/) (2017)
- [A Generalization Bound for Online Variational Inference](https://mlsanity.com/paper/1904.03920/) (2019)
- [Stochastic Variational Inference for Hidden Markov Models](https://mlsanity.com/paper/1411.1670/) (2014)
- [A Theoretical Understanding of Gradient Bias in Meta-Reinforcement Learning](https://mlsanity.com/paper/2112.15400/) (2021)
- [Variance Reduction in Stochastic Particle-Optimization Sampling](https://mlsanity.com/paper/1811.08052/) (2018)
- [Probabilistic Programs with Stochastic Conditioning](https://mlsanity.com/paper/2010.00282/) (2020)
- [Kalman Bayesian Neural Networks for Closed-form Online Learning](https://mlsanity.com/paper/2110.00944/) (2021)
- [A Communication-efficient Algorithm with Linear Convergence for Federated Minimax Learning](https://mlsanity.com/paper/2206.01132/) (2022)
- [Tracking Moving Agents via Inexact Online Gradient Descent Algorithm](https://mlsanity.com/paper/1710.05133/) (2017)
- [Quantum-Inspired Hamiltonian Monte Carlo for Bayesian Sampling](https://mlsanity.com/paper/1912.01937/) (2019)

## Built on by (most cited first, 7 of 7)

- [Low-rank extended Kalman filtering for online learning of neural networks from streaming data](https://mlsanity.com/paper/2305.19535/) (2023)
- [Bayesian Optimization through Gaussian Cox Process Models for Spatio-temporal Data](https://mlsanity.com/paper/2401.14544/) (2024)
- [On-ramp and Off-ramp Traffic Flows Estimation Based on A Data-driven Transfer Learning Framework](https://mlsanity.com/paper/2308.03538/) (2023)
- [A Transfer Learning Framework for Proactive Ramp Metering Performance Assessment](https://mlsanity.com/paper/2308.03542/) (2023)
- [Electrostatics-based particle sampling and approximate inference](https://mlsanity.com/paper/2406.20044/) (2024)
- [A Gradient-based Approach for Online Robust Deep Neural Network Training with Noisy Labels](https://mlsanity.com/paper/2306.05046/) (2023)
- [Fast rates in Bayesian online learning with approximate posteriors](https://mlsanity.com/paper/2608.25706/) (2026)

## Abstract (arXiv)

Online optimization has gained increasing interest due to its capability of tracking real-world streaming data. Although online optimization methods have been widely studied in the setting of frequentist statistics, few works have considered online optimization with the Bayesian sampling problem. In this paper, we study an Online Particle-based Variational Inference (OPVI) algorithm that uses a set of particles to represent the approximating distribution. To reduce the gradient error caused by the use of stochastic approximation, we include a sublinear increasing batch-size method to reduce the variance. To track the performance of the OPVI algorithm with respect to a sequence of dynamically changing target posterior, we provide a detailed theoretical analysis from the perspective of Wasserstein gradient flow with a dynamic regret. Synthetic and Bayesian Neural Network experiments show that the proposed algorithm achieves better results than naively applying existing Bayesian sampling methods in the online setting.