MixFlows: principled variational inference via mixed flows

TL;DR

MixFlows introduces a new variational inference method using mixtures of flow transformations, offering reliable posterior approximations with theoretical guarantees and practical algorithms, outperforming some existing methods in experiments.

Contribution

The paper proposes MixFlows, a novel variational family combining mixture models with flow transformations, along with efficient algorithms and theoretical convergence guarantees.

Findings

MixFlows provide more reliable posterior approximations than several normalizing flows.

MixFlows achieve sample quality comparable to state-of-the-art MCMC methods.

The method offers theoretical convergence guarantees under ergodic and measure-preserving conditions.

Abstract

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.