Annealed Flow Transport Monte Carlo
- URL: http://arxiv.org/abs/2102.07501v1
- Date: Mon, 15 Feb 2021 12:05:56 GMT
- Title: Annealed Flow Transport Monte Carlo
- Authors: Michael Arbel, Alexander G. D. G. Matthews, Arnaud Doucet
- Abstract summary: Annealed Flow Transport (AFT) builds upon Annealed Importance Sampling (AIS) and Sequential Monte Carlo (SMC)
AFT relies on NF which is learned sequentially to push particles towards the successive targets.
We show that a continuous-time scaling limit of the population version of AFT is given by a Feynman--Kac measure.
- Score: 91.20263039913912
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 (NF) 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 NF 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 NF. We demonstrate experimentally the
benefits and limitations of our methodology on a variety of applications.
Related papers
- Sequential Kalman Monte Carlo for gradient-free inference in Bayesian inverse problems [1.3654846342364308]
We introduce Sequential Kalman Monte Carlo samplers to perform gradient-free inference in inverse problems.
FAKI employs normalizing flows to relax the Gaussian ansatz of the target measures in EKI.
FAKI alone is not able to correct for the model linearity assumptions in EKI.
arXiv Detail & Related papers (2024-07-10T15:56:30Z) - Convergence Bounds for Sequential Monte Carlo on Multimodal Distributions using Soft Decomposition [6.872242798058046]
We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm.
We show that bounds can be obtained in the truly multi-modal setting, with mixing times that depend on local MCMC dynamics.
arXiv Detail & Related papers (2024-05-29T22:43:45Z) - Combining Normalizing Flows and Quasi-Monte Carlo [0.0]
Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods.
We demonstrate through numerical experiments that this combination can lead to an estimator with significantly lower variance than if the flow was sampled with a classic Monte Carlo.
arXiv Detail & Related papers (2024-01-11T14:17:06Z) - Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution.
We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
arXiv Detail & Related papers (2023-06-27T08:15:28Z) - Mitigating Out-of-Distribution Data Density Overestimation in
Energy-Based Models [54.06799491319278]
Deep energy-based models (EBMs) are receiving increasing attention due to their ability to learn complex distributions.
To train deep EBMs, the maximum likelihood estimation (MLE) with short-run Langevin Monte Carlo (LMC) is often used.
We investigate why the MLE with short-run LMC can converge to EBMs with wrong density estimates.
arXiv Detail & Related papers (2022-05-30T02:49:17Z) - Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region.
Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
arXiv Detail & Related papers (2022-02-23T06:11:49Z) - Continual Repeated Annealed Flow Transport Monte Carlo [93.98285297760671]
We propose Continual Repeated Annealed Flow Transport Monte Carlo (CRAFT)
It combines a sequential Monte Carlo sampler with variational inference using normalizing flows.
We show that CRAFT can achieve impressively accurate results on a lattice field example.
arXiv Detail & Related papers (2022-01-31T10:58:31Z) - Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions.
We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions.
We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
arXiv Detail & Related papers (2021-02-04T02:21:08Z) - Projected Latent Markov Chain Monte Carlo: Conditional Sampling of
Normalizing Flows [37.87437571724747]
Projected Latent Markov Chain Monte Carlo (PL-MCMC) is a technique for sampling from the high-dimensional conditional distributions learned by a normalizing flow.
As a conditional sampling method, PL-MCMC enables Monte Carlo Expectation Maximization (MC-EM) training of normalizing flows from incomplete data.
arXiv Detail & Related papers (2020-07-13T00:47:39Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.