Review for NeurIPS paper: Recursive Inference for Variational Autoencoders

Strengths: Soundness: The theoretical grounding and empirical evaluation are largely sound. The authors derive their technique in Section 3 and show how this naturally results in an objective for the current component that trades off between the ELBO and a KL from the current approximate posterior distribution. The authors compare their approach against a comprehensive set of baselines, including a standard VAE, semi-amortized VI (which also involves additional computation), normalizing flows (which uses a more expressive distribution), and a non-recursive mixture distribution (which has the same form of distribution). This comparison is performed across a range of image datasets and multiple model sizes using multiple runs. The authors also compare their approach with boosted VI, showing that the KL, rather than entropy, is useful for mixture estimation. Significance: The proposed approach outperforms more expressive VI techniques, particularly IAF.