Deterministic Langevin Monte Carlo with Normalizing Flows for Bayesian Inference
This addresses computational efficiency in Bayesian inference for practitioners dealing with expensive likelihoods, though it appears incremental as it builds on existing Langevin and Normalizing Flow techniques.
The authors tackled Bayesian inference for expensive likelihoods by proposing a deterministic Langevin Monte Carlo algorithm that replaces stochastic terms with deterministic density gradients evaluated via Normalizing Flows, showing it is competitive against state-of-the-art sampling methods.
We propose a general purpose Bayesian inference algorithm for expensive likelihoods, replacing the stochastic term in the Langevin equation with a deterministic density gradient term. The particle density is evaluated from the current particle positions using a Normalizing Flow (NF), which is differentiable and has good generalization properties in high dimensions. We take advantage of NF preconditioning and NF based Metropolis-Hastings updates for a faster convergence. We show on various examples that the method is competitive against state of the art sampling methods.