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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 nonequilibrium statistical mechanics we derive an efficient training procedure by which both the sampler's and the flow's parameters can be optimized endtoend, 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.
Author Information
Hao Wu (Freie Universität Berlin)
Jonas Köhler (Freie Universität Berlin)
Frank Noe (FU Berlin)
Related Events (a corresponding poster, oral, or spotlight)

2020 Poster: Stochastic Normalizing Flows »
Thu. Dec 10th 05:00  07:00 PM Room Poster Session 5 #1367
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