2020

Stochastic Normalizing Flows

Wu, Hao, Köhler, Jonas, Noé, Frank

Understand

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics.

While classical stochastic sampling methods such as Markov Chain Monte Carlo (MCMC) or Langevin Dynamics (LD) can suffer from slow mixing times there is a growing interest in using normalizing flows in order to learn the transformation of a simple prior distribution to the given target distribution.
Here we propose a generalized and combined approach to sample target densities: Stochastic Normalizing Flows (SNF) -- an arbitrary sequence of deterministic invertible functions and stochastic sampling blocks.
We show that stochasticity overcomes expressivity limitations of normalizing flows resulting from the invertibility constraint, whereas trainable transformations between sampling steps improve efficiency of pure MCMC/LD along the flow.

Built on

“Equilibrium electrostatic effects on the behavior of polyions in solution: polyion-mobile ion interaction”
D.. Ermak and Y. Yeh · 1974
Earlier work this paper cites.
“AMBER, a computer program for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to elucidate the structures and energies of molecules”
D.. Pearlman et al · 1995
Earlier work this paper cites.
“Gradient-based learning applied to document recognition”
Y. LeCun, L. Bottou, Y. Bengio and P. Haffner · 1998
Earlier work this paper cites.
“Annealed Importance Sampling”
Radford. Neal · 1998
Earlier work this paper cites.
“Understanding molecular simulation”
Daan Frenkel and Brerend Smit · 2001
Earlier work this paper cites.
“Density estimation by dual ascent of the log-likelihood”
Esteban Tabak and Eric Vanden-Eijnden · 2010
Earlier work this paper cites.
“Nonequilibrium candidate Monte Carlo is an efficient tool for equilibrium simulation”
Jerome. Nilmeier, Gavin. Crooks, David.. Minh and John. Chodera · 2011
Earlier work this paper cites.
“A family of nonparametric density estimation algorithms”
Esteban Tabak and Cristina Turner · 2013
Earlier work this paper cites.
“Nice: Non-linear independent components estimation”
Original
Laurent Dinh, David Krueger and Yoshua Bengio · 2014
Earlier work this paper cites.
“Adam: A Method for Stochastic Optimization”
Original
D.. Kingma and J. Ba · 2014
Earlier work this paper cites.
“Auto-Encoding Variational Bayes”
Original
D.. Kingma and M. Welling · 2014
Earlier work this paper cites.
“Variational inference with normalizing flows”
Original
Danilo Rezende and Shakir Mohamed · 2015
Earlier work this paper cites.
“Markov chain monte carlo and variational inference: Bridging the gap”
Tim Salimans, Diederik Kingma and Max Welling · 2015
Earlier work this paper cites.
“Deep unsupervised learning using nonequilibrium thermodynamics”
Original
Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan and Surya Ganguli · 2015
Earlier work this paper cites.
“Density estimation using Real NVP”
Original
Laurent Dinh, Jasha Sohl-Dickstein and Samy Bengio · 2016
Earlier work this paper cites.

Similar

“Continuous-time flows for efficient inference and density estimation”
Original
Changyou Chen et al · 2017
Cited alongside, same era.
“Learning deep latent Gaussian models with Markov chain Monte Carlo”
Matthew. Hoffman · 2017
Cited alongside, same era.
“Generalizing hamiltonian monte carlo with neural networks”
Original
Daniel Levy, Matthew Hoffman and Jascha Sohl-Dickstein · 2017
Cited alongside, same era.
“A-NICE-MC: Adversarial Training for MCMC”
J. Song, S. Zhao and S. Ermon · 2017
Cited alongside, same era.
“A-nice-mc: Adversarial training for mcmc”
Jiaming Song, Shengjia Zhao and Stefano Ermon · 2017
Cited alongside, same era.
“Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms”
Han Xiao, Kashif Rasul and Roland Vollgraf · 2017
Cited alongside, same era.
“Neural ordinary differential equations”
Tian Chen, Yulia Rubanova, Jesse Bettencourt and David Duvenaud · 2018
Cited alongside, same era.
“Explorations in homeomorphic variational auto-encoding”
Original
Luca Falorsi et al · 2018
Cited alongside, same era.
“Neural Network Renormalization Group”
Shuo-Hui Li and Lei Wang · 2018
Cited alongside, same era.
“Neural importance sampling”
Original
Thomas Müller et al · 2018
Cited alongside, same era.
“Flow-based generative models for Markov chain Monte Carlo in lattice field theory”
M.. Albergo, G. Kanwar and P.. Shanahan · 2019
Cited alongside, same era.
“Relaxing bijectivity constraints with continuously indexed normalising flows”
Original
Rob Cornish, Anthony Caterini, George Deligiannidis and Arnaud Doucet · 2019
Cited alongside, same era.

Then

“Reparameterizing Distributions on Lie Groups”
Original
Luca Falorsi, Pim de Haan, Tim Davidson and Patrick Forré · 2019
Later among the works it cites.
“Dynamical Sampling with Langevin Normalization Flows”
Minghao Gu, Shiliang Sun and Yan Liu · 2019
Later among the works it cites.
“NeuTra-lizing bad geometry in Hamiltonian Monte Carlo using neural transport”
Original
Matthew Hoffman et al · 2019
Later among the works it cites.
“Neural Jump Stochastic Differential Equations”
Original
Junteng Jia and Austin. Benson · 2019
Later among the works it cites.
“Equivariant Flows: sampling configurations for multi-body systems with symmetric energies”
Original
Jonas Köhler, Leon Klein and Frank Noé · 2019
Later among the works it cites.
“Neural SDE: Stabilizing neural ode networks with stochastic noise”
Original
Xuanqing Liu et al · 2019
Later among the works it cites.
“Asymptotically unbiased estimation of physical observables with neural samplers”
Original
Kim. Nicoli et al · 2019
Later among the works it cites.
“Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning”
Frank Noé, Simon Olsson, Jonas Köhler and Hao Wu · 2019
Later among the works it cites.
“Normalizing Flows for Probabilistic Modeling and Inference”
Original
George Papamakarios et al · 2019
Later among the works it cites.
“Hamiltonian Generative Networks”
Original
Peter Toth et al · 2019
Later among the works it cites.
“Neural stochastic differential equations: Deep latent Gausian models in the diffusion limit”
Original
Belinda Tzen and Maxim Raginsky · 2019
Later among the works it cites.
“Stochastic Normalizing Flows”
Original
Liam Hodgkinson, Chris van Heide, Fred Roosta and Michael Mahoney · 2020
Closest in time.
“Augmented normalizing flows: Bridging the gap between generative flows and latent variable models”
Original
Chin-Wei Huang, Laurent Dinh and Aaron Courville · 2020
Closest in time.
“Scalable Gradients for Stochastic Differential Equations”
Original
Xuechen Li, Ting-Kam Wong, Ricky.. Chen and David Duvenaud · 2020
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…