MixFlows: principled variational inference via mixed flows
This addresses the challenge of accurate posterior approximation in Bayesian inference for practitioners, though it is incremental as it builds on existing flow-based and MCMC methods.
The paper tackles the problem of improving variational inference by introducing MixFlows, a variational family using mixtures of repeated map applications, and shows it provides more reliable posterior approximations than black-box normalizing flows and samples comparable to state-of-the-art MCMC methods.
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show that MixFlows have MCMC-like convergence guarantees when the flow map is ergodic and measure-preserving, and provide bounds on the accumulation of error for practical implementations where the flow map is approximated. Finally, we develop an implementation of MixFlows based on uncorrected discretized Hamiltonian dynamics combined with deterministic momentum refreshment. Simulated and real data experiments show that MixFlows can provide more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.