Annealed Flow Transport Monte Carlo
arXiv:2102.07501
Abstract
Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow Transport (AFT), that builds upon AIS and SMC and combines them with normalizing flows (NFs) for improved performance. This method transports a set of particles using not only importance sampling (IS), Markov chain Monte Carlo (MCMC) and resampling steps - as in SMC, but also relies on NFs which are learned sequentially to push particles towards the successive annealed targets. We provide limit theorems for the resulting Monte Carlo estimates of the normalizing constant and expectations with respect to the target distribution. Additionally, we show that a continuous-time scaling limit of the population version of AFT is given by a Feynman--Kac measure which simplifies to the law of a controlled diffusion for expressive NFs. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications.
References in corpus (25)
- Adam: A Method for Stochastic Optimization
- Auto-Encoding Variational Bayes
- A nonequilibrium equality for free energy differences
- Stochastic Backpropagation and Approximate Inference in Deep Generative Models
- Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference
- Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
- Normalizing Flows for Probabilistic Modeling and Inference
- MADE: Masked Autoencoder for Distribution Estimation
- Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm
- Bayesian Inference with Optimal Maps
- TensorFlow Distributions
- On adaptive resampling strategies for sequential Monte Carlo methods
- Variational inference for Monte Carlo objectives
- Escorted Free Energy Simulations: Improving Convergence by Reducing Dissipation
- Asymptotically unbiased estimation of physical observables with neural samplers
- i-flow: High-dimensional Integration and Sampling with Normalizing Flows
- Adaptive importance sampling for control and inference
- Auto-Encoding Sequential Monte Carlo
- GPU accelerated population annealing algorithm
- Understanding and Accelerating Particle-Based Variational Inference
- Gibbs flow for approximate transport with applications to Bayesian computation
- Sequential Monte Carlo with transformations
- Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net
- Deep FPF: Gain function approximation in high-dimensional setting
- Universality of the Langevin diffusion as scaling limit of a family of Metropolis-Hastings processes I: fixed dimension