Traditional approaches to variational inference rely on parametric families of variational distributions, with the choice of family playing a critical role in determining the accuracy of the resulting posterior approximation. Simple mean-field families often lead to poor approximations, while rich families of distributions like normalizing flows can be difficult to optimize and usually do not incorporate the known structure of the target distribution due to their black-box nature. To expand the space of flexible variational families, we revisit Variational Rejection Sampling (VRS) [Grover et al., 2018], which combines a parametric proposal distribution with rejection sampling to define a rich non-parametric family of distributions that explicitly utilizes the known target distribution. By introducing a low-variance reparameterized gradient estimator for the parameters of the proposal distribution, we make VRS an attractive inference strategy for models with continuous latent variables. We argue theoretically and demonstrate empirically that the resulting method--Reparameterized Variational Rejection Sampling (RVRS)--offers an attractive trade-off between computational cost and inference fidelity. In experiments we show that our method performs well in practice and that it is well-suited for black-box inference, especially for models with local latent variables.

传统的变分推理方法依赖于变分分布的参数族，而变分分布的选择对后验概率近似的准确性起着关键作用。本文提出了一种基于Variational Rejection Sampling (VRS)的新策略，通过引入低方差的重新参数化梯度估计器，将VRS变为一个适用于具有连续潜在变量的模型的引人注目的推理策略。理论上的论证和实证实验表明，得到的方法 - Reparameterized Variational Rejection Sampling (RVRS)在计算成本和推理准确性之间提供了一个吸引人的折衷方案，特别适用于具有局部潜在变量的黑盒推理。

重新参数化的变分拒绝抽样