We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference in models where the prior and the posterior can be expressed as an intractable infinite mixture of some analytic density with a highly flexible implicit mixing distribution. We provide a sandwich bound on the evidence lower bound (ELBO) objective that can be made arbitrarily tight. Unlike discriminator-based and kernel-based approaches to implicit variational inference, DSIVI optimizes a proper lower bound on ELBO that is asymptotically exact. We evaluate DSIVI on a set of problems that benefit from implicit priors. In particular, we show that DSIVI gives rise to a simple modification of VampPrior, the current state-of-the-art prior for variational autoencoders, which improves its performance.

提出了一种名为DSIVI的新型半隐变分推断方法，可以在先验分布和后验分布均为半隐式分布的模型中工作，其优化的ELBO下界是渐进精确的，在某些对隐式分布有利的问题中超过了现有方法的性能。

双半隐式变分推断