Venue: ICLR 2017 workshop

Reviews:

final_score: rating: 7: Good paper, accept
review_content: This extended abstract proposes an interesting method to learn a reference prior distribution using a variational formulation with the reparameterization trick. There is a need for this sort of work, since the generic prior distributions commonly used in VAEs and GANs are somewhat unsatisfying. The idea of learning a reference prior is interesting, and I haven’t seen it discussed in the context of deep generative models.

The contributions and experiments seem sufficient for a workshop paper, so I would recommend acceptance. 

I’m a little concerned about the variance of the estimates in Eqn. (3); this resembles the likelihood weighting based estimate of p(D), which can have extremely large, or even infinite variance. Are the estimates stable?

The VAE example is interesting. What can we learn from the shape of the learned prior?  Does the bimodal structure imply the distribution is multimodal?  Does the reference prior yield a better density model than the spherical Gaussian one?

In the VAE experiment, what keeps the prior from expanding to be infinitely broad?  Is the true reference prior guaranteed to be proper?  What happens if it is improper?


review_title: Interesting approach to learning priors for generative models

final_score: rating: 7: Good paper, accept
review_content: The paper is well written and presents a novel variational approach to find approximate reference priors for arbitrary models. The derivation of their method is clear and easy to follow. In the experimental section, the authors first show that their method recovers the well known Jeffreys prior for 1-dimensional toy models with high accuracy. They then show that they can also find an approximate reference prior for a VAE model with 2-dimensional latent space: This prior is significantly different from the widely used isotropic Gaussian, e.g., is is multimodal. This could be a significant result and might contribute important arguments for the discussion of how to choose priors and how to choose the model structure for deep generative models. Unfortunately, and probably due to the 3 page constraint for this workshop, I’m not convinced that these results are 100% trustworthy: The step from 1d models, where the proposed method works as expected, to VAE-style latent variable models seems rather big and I can imagine various ways how the optimization might fail and produce misleading results. Additional results for models of intermediate complexity and more details/diagnostics could greatly enhance this paper (but would probably break the 3 page limit). I’m also wondering whether there is a scale-invariance / degeneracy in the model: Scaling the mean/stddev. of the prior and posterior by a constant factor should result in an equivalent model.    



Nevertheless, I think this is very interesting work which has the potential to initiate a new discussion about priors for generative models.

Pro:
- original approach; well motivated 
- experiments show the method works on 1d toy models
- the result for the 2-dimensional VAE is surprising and might form some kind of argument for future work on latent variable models -> potential high impact. 

Con:
- weak experimental section: I’m not convinced that the result for the 2d VAE is trustworthy.  
review_title: An interesting and original proposal to bring (uninformative) reference priors to deep generative models. This work might contribute an important and original argument for the discussion of how to choose priors for deep generative models.

Decision: Accept