Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methods
arXiv:2107.08001
Abstract
Normalizing flows can generate complex target distributions and thus show promise in many applications in Bayesian statistics as an alternative or complement to MCMC for sampling posteriors. Since no data set from the target posterior distribution is available beforehand, the flow is typically trained using the reverse Kullback-Leibler (KL) divergence that only requires samples from a base distribution. This strategy may perform poorly when the posterior is complicated and hard to sample with an untrained normalizing flow. Here we explore a distinct training strategy, using the direct KL divergence as loss, in which samples from the posterior are generated by (i) assisting a local MCMC algorithm on the posterior with a normalizing flow to accelerate its mixing rate and (ii) using the data generated this way to train the flow. The method only requires a limited amount of \textit{a~priori} input about the posterior, and can be used to estimate the evidence required for model validation, as we illustrate on examples.
References in corpus (7)
- Variational Inference with Normalizing Flows
- Solving Statistical Mechanics Using Variational Autoregressive Networks
- Asymptotically unbiased estimation of physical observables with neural samplers
- Learning Model Reparametrizations: Implicit Variational Inference by Fitting MCMC distributions
- Dynamical computation of the density of states and Bayes factors using nonequilibrium importance sampling
- Self-Supervised Learning of Generative Spin-Glasses with Normalizing Flows
- Adaptive Monte Carlo augmented with normalizing flows