# Toward Unlimited Self-Learning MCMC with Parallel Adaptive Annealing

arXiv: https://arxiv.org/abs/2211.14024 · HTML: https://mlsanity.com/paper/2211.14024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Variational Autoencoders Pursue PCA Directions (by Accident)](https://mlsanity.com/paper/1812.06775/) (2018)
- [Generalizing Hamiltonian Monte Carlo with Neural Networks](https://mlsanity.com/paper/1711.09268/) (2017)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines](https://mlsanity.com/paper/1610.02746/) (2016)
- [Barriers and Dynamical Paths in Alternating Gibbs Sampling of Restricted Boltzmann Machines](https://mlsanity.com/paper/2107.06013/) (2021)
- [Hamiltonian Monte Carlo Without Detailed Balance](https://mlsanity.com/paper/1409.5191/) (2014)
- [Towards reduction of autocorrelation in HMC by machine learning](https://mlsanity.com/paper/1712.03893/) (2017)
- [Quantitative Understanding of VAE as a Non-linearly Scaled Isometric Embedding](https://mlsanity.com/paper/2007.15190/) (2020)

## Abstract (arXiv)

Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate Markov chain Monte Carlo (MCMC) methods using a machine learning model. With latent generative models, SLMC methods realize efficient Monte Carlo updates with less autocorrelation. However, SLMC methods are difficult to directly apply to multimodal distributions for which training data are difficult to obtain. To solve the limitation, we propose parallel adaptive annealing, which makes SLMC methods directly apply to multimodal distributions with a gradually trained proposal while annealing target distribution. Parallel adaptive annealing is based on (i) sequential learning with annealing to inherit and update the model parameters, (ii) adaptive annealing to automatically detect under-learning, and (iii) parallel annealing to mitigate mode collapse of proposal models. We also propose VAE-SLMC method which utilizes a variational autoencoder (VAE) as a proposal of SLMC to make efficient parallel proposals independent of any previous state using recently clarified quantitative properties of VAE. Experiments validate that our method can proficiently obtain accurate samples from multiple multimodal toy distributions and practical multimodal posterior distributions, which is difficult to achieve with the existing SLMC methods.