Annealed Importance Sampling with q-Paths

Brekelmans, Rob; Masrani, Vaden; Bui, Thang; Wood, Frank; Galstyan, Aram; Steeg, Greg Ver; Nielsen, Frank

doi:10.48550/arxiv.2012.07823

Cited by 2 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Within the MCMC/AIS literature, significant work has focused on improving transition kernels (Levy et al, 2018;Gabrié et al, 2022), intermediate distributions (Brekelmans et al, 2020) and the target distribution of AIS. In this paper, we have opted to use relatively simple versions of AIS.…”

Section: Discussion and Related Workmentioning

confidence: 99%

Flow Annealed Importance Sampling Bootstrap

Midgley¹,

Stimper²,

Schölkopf³

et al. 2022

Preprint

View full text Add to dashboard Cite

Normalizing flows are tractable density models that can approximate complicated target distributions, e.g. Boltzmann distributions of physical systems. However, current methods for training flows either suffer from mode-seeking behavior, use samples from the target generated beforehand by expensive MCMC simulations, or use stochastic losses that have very high variance. To avoid these problems, we augment flows with annealed importance sampling (AIS) and minimize the mass covering α-divergence with α = 2, which minimizes importance weight variance. Our method, Flow AIS Bootstrap (FAB), uses AIS to generate samples in regions where the flow is a poor approximation of the target, facilitating the discovery of new modes. We target with AIS the minimum variance distribution for the estimation of the α-divergence via importance sampling. We also use a prioritized buffer to store and reuse AIS samples. These two features significantly improve FAB's performance. We apply FAB to complex multimodal targets and show that we can approximate them very accurately where previous methods fail. To the best of our knowledge, we are the first to learn the Boltzmann distribution of the alanine dipeptide molecule using only the unnormalized target density and without access to samples generated via Molecular Dynamics (MD) simulations: FAB produces better results than training via maximum likelihood on MD samples while using 100 times fewer target evaluations. After reweighting samples with importance weights, we obtain unbiased histograms of dihedral angles that are almost identical to the ground truth ones.

show abstract

Section: Discussion and Related Workmentioning

confidence: 99%

Flow Annealed Importance Sampling Bootstrap

Midgley¹,

Stimper²,

Schölkopf³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In particular the link between M β for averaging in the minimization and M ′ α the mean for generating abstract mixtures. More generally, Brekelmans et al [12] considered the α-divergences extended to positive measures…”

Section: Js-symmetrization Based On Generalized Information Radiusmentioning

confidence: 99%

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances based on the Information Radius

Nielsen

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We generalize the Jensen-Shannon divergence by considering a variational definition with respect to a generic mean extending thereby the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and yields another way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to probability measure families, we get relative Jensen-Shannon divergences and symmetrizations which generalize information projections. Finally, we discuss applications of these divergences and diversity indices to clustering and quantization tasks of probability measures including statistical mixtures.

show abstract

Annealed Importance Sampling with q-Paths

Cited by 2 publications

References 8 publications

Flow Annealed Importance Sampling Bootstrap

Flow Annealed Importance Sampling Bootstrap

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances based on the Information Radius

Contact Info

Product

Resources

About