Stochastic Normalizing Flows

Abstract

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. By invoking ideas from non-equilibrium statistical mechanics we derive an efficient training procedure by which both the sampler's and the flow's parameters can be optimized end-to-end, and by which we can compute exact importance weights without having to marginalize out the randomness of the stochastic blocks. We illustrate the representational power, sampling efficiency and asymptotic correctness of SNFs on several benchmarks including applications to sampling molecular systems in equilibrium.

References in corpus (32)

• Adam: A Method for Stochastic Optimization
• Auto-Encoding Variational Bayes
• Deep Unsupervised Learning using Nonequilibrium Thermodynamics
• NICE: Non-linear Independent Components Estimation
• Density estimation using Real NVP
• Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
• Normalizing Flows for Probabilistic Modeling and Inference
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Invertible Residual Networks
• Neural Network Renormalization Group
• Scalable Gradients for Stochastic Differential Equations
• FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models
• Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation
• Asymptotically unbiased estimation of physical observables with neural samplers
• Sylvester Normalizing Flows for Variational Inference
• Neural Jump Stochastic Differential Equations
• Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise
• Improving Variational Auto-Encoders using Householder Flow
• A-NICE-MC: Adversarial Training for MCMC
• NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
• Explorations in Homeomorphic Variational Auto-Encoding
• Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit
• Equivariant Flows: sampling configurations for multi-body systems with symmetric energies
• Stochastic Normalizing Flows
• Monge-Ampère Flow for Generative Modeling
• Continuous-Time Flows for Efficient Inference and Density Estimation
• Hamiltonian Generative Networks
• Generalizing Hamiltonian Monte Carlo with Neural Networks
• Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Models
• Block Neural Autoregressive Flow
• Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows
• A RAD approach to deep mixture models

Cited by in corpus (7)

• Denoising Diffusion Probabilistic Models
• Eryn : A multi-purpose sampler for Bayesian inference
• STEER: Simple Temporal Regularization For Neural ODEs
• Introduction to Normalizing Flows for Lattice Field Theory
• AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning
• Training Invertible Linear Layers through Rank-One Perturbations
• Latent Transformations for Discrete-Data Normalising Flows