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.

翻译：本文提出了混合变分流（MixFlows），一种新的变分族，由初始参考分布经过多次重复映射下的混合分布构成。首先，我们提供了独立同分布采样、密度评估以及无偏ELBO估计的高效算法。随后证明，当流映射是遍历且保测度时，MixFlows具有类似MCMC的收敛保证，并针对实际实现中流映射存在近似的情况，给出了误差累积的界。最后，我们基于未校正的离散哈密顿动力学结合确定性动量刷新开发了MixFlows的实现。模拟与真实数据实验表明，相比若干黑箱归一化流，MixFlows能提供更可靠的后验近似，且其生成样本质量可与最先进MCMC方法相媲美。