Venue: ICLR 2017 workshop

Reviews:

final_score: rating: 7: Good paper, accept
review_content: The authors describe a simple and clear reinterpretation of importance
weighted autoencoders (Burda et al., 2016). I recommend this paper for
acceptance. It connects to much recent work on expressive variational
approximations, especially in those leveraging truncated Markov chains
as variational approximations. Further, it brings interesting ideas to
the table following this simple derivation.

A cool result is that this interpretation relaxes the idea of IWAEs to
be more broadly applicable to any divergence measure. Perhaps a key
experiment would not be so much comparing IWAEs with itself, but in
what this perspective allows, such as IWAE-based variational families
with alpha-divergences or operator variational objectives. Or alternatively,
combining the SIR approach with other rich posterior approximations.

With this perspective in mind, it's not necessarily clear if one
should even use IWAEs over other expressive variational
approximations. From my understanding of the field, most benchmarks
display IWAEs performing worse (in terms of held-out log-likelihood)
to others such as the variational Gaussian process (Tran et al.,
2016) and inverse autoregressive flows (Kingma et al., 2016).
This isn't a fault of this paper—it's great that the casting brings
these questions to bear—but I think it's something the paper should
certainly address if it aims to be more substantial in an extended
paper in the future.

The notation is not described in the paper; while experts in the field
can understand this, the work would benefit from properly laying out
definitions and properties.

References
+ Dinh, L., Sohl-Dickstein, J., & Bengio, S. (2017). Density estimation using Real NVP. Presented at the International Conference on Learning Representations.
+ Kingma, D. P., Salimans, T., & Welling, M. (2016). Improving Variational Inference with Inverse Autoregressive Flow. Presented at the Neural Information Processing Systems.
+ Li, Y., & Turner, R. E. (2016). Rényi Divergence Variational Inference. Presented at the Neural Information Processing Systems.
+ Ranganath, R., Altosaar, J., Tran, D., & Blei, D. M. (2016). Operator Variational Inference. Presented at the Neural Information Processing Systems.
+ Tran, D., Ranganath, R., & Blei, D. M. (2016). The Variational Gaussian Process. Presented at the International Conference on Learning Representations.
review_title: Simple and clear result, useful insights

final_score: rating: 8: Top 50% of accepted papers, clear accept
review_content: This paper introduces a new perspective on IWAE.
It is shown that the IWAE bound can be interpreted as a VAE bound with a particular implicit inference model q_IW. This implicit posterior distribution is a function of both the variational parameters, and the generative model parameters.

The derivation seems novel, and adds an interesting new link to IWAE and VAE objectives.

A potential drawback of the IWAE posterior, in comparison to alternative methods for building complex posteriors, is that it is relatively expensive; you may require a large number of samples to converge to the true distribution, probabily especially so in high dimensional space. However, that's besides the point of this paper, and I think it still proposes a valid and interesting perspective on IWAE.
review_title: IWAE bound derived as VAE bound with particular implicit distribution q_IW

Decision: Accept