Venue: ICLR 2017 conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: # Review
This paper proposes a quantitative evaluation for decoder-based generative models that use Annealed Importance Sampling (AIS) to estimate log-likelihoods. Quantitative evaluations are indeed much needed since for some models, like Generative Adversarial Networks (GANs) and Generative Moment Matching Networks (GMMNs), qualitative evaluation of samples is still frequently used to assess their generative capability. Even though, there exist quantitative evaluations like Kernel Density Estimation (KDE), the authors show how AIS is more accurate than KDE and how it can be used to perform fine-grained comparison between generative models (GAN, GMMs and Variational Autoencoders (VAE)).

The authors report empirical results comparing two different decoder architectures that were both trained, on the continuous MNIST dataset, using the VAE, GAN and GMMN objectives. They also trained an Importance Weighted Autoencoder (IWAE) on binarized MNIST and show that, in this case, the IWAE bound underestimates the true log-likelihoods by at least 1 nat (which is significant for this dataset) according to the AIS evaluation of the same model.


# Pros
Their evaluation framework is public and is definitely a nice contribution to the community.

This paper gives some insights about how GAN behaves from log-likelihood perspective. The authors disconfirm the commonly proposed hypothesis that GAN are memorizing training data. The authors also observed that GANs miss important modes of the data distribution.


# Cons/Questions
It is not clear for me why sometimes the experiments were done using different number of examples (100, 1000, 10000) coming from different sources (trainset, validset, testset or simulation/generated by the model). For instance, in Table 2 why results were not reported using all 10,000 examples of the testing set?

It is not clear why in Figure 2c, AIS is slower than AIS+encoder? Is the number of intermediate distributions the same in both?

16 independent chains for AIS seems a bit low from what I saw in the literature (e.g. in [Salakhutdinov & Murray, 2008] or [Desjardins etal., 2011], they used 100 chains). Could it be that increasing the number of chains helps tighten the confidence interval reported in Table 2?

I would have like the authors to give their intuitions as to why GAN50 has a BDMC gap of 10 nats, i.e. 1 order of magnitude compared to the others?


# Minor comments
Table 1 is not referenced in the text and lacks description of what the different columns represent.
Figure 2(a), are the reported values represents the average log-likelihood of 100 (each or total?) training and validation examples of MNIST (as described in Section 5.3.2).
Figure 2(c), I'm guessing it is on binarized MNIST? Also, why are there fewer points for AIS compared to IWAE and AIS+encoder?
Are the BDMC gaps mentioned in Section 5.3.1 the same as the ones reported in Table2 ?
Typo in caption of Figure 3: "(c) GMMN-10" but actually showing GMMN-50 according to the graph title and subcaption.
review_title: Interesting work, their evaluation framework is available online, good contribution to the community 

final_score: rating: null
review_content: Does "running the decoder on z" (page 9) refer to sampling from $p_\sigma(x | z)$  or deterministic reconstruction?
review_title: "Running the decoder"

final_score: rating: 7: Good paper, accept
review_content: Summary:
This paper describes how to estimate log-likelihoods of currently popular decoder-based generative models using annealed importance sampling (AIS) and HMC. It validates the method using bidirectional Monte Carlo on the example of MNIST, and compares the performance of GANs and VAEs.


Review:
Although this seems like a fairly straight-forward application of AIS to me (correct me if I missed an important trick to make this work), I very much appreciate the educational value and empirical contributions of this paper. It should lead to clarity in debates around the density estimation performance of GANs, and should enable more people to use AIS.

Space permitting, it might be a good idea to try to expand the description of AIS. All the components of AIS are mentioned and a basic description of the algorithm is given, but the paper doesn’t explain well “why” the algorithm does what it does/why it works.

I was initially confused by the widely different numbers in Figure 2. On first glance my expectation was that this Figure is comparing GAN, GMMN and IWAE (because of the labeling at the bottom and because of the leading words in the caption’s descriptions). Perhaps mention in the caption that (a) and (b) use continuous MNIST and (c) uses discrete MNIST. “GMMN-50” should probably be “GMMN-10”.


Using reconstructions for evaluation of models may be a necessary but is not sufficient condition for a good model. Depending on the likelihood, a posterior sample might have very low density under the prior, for example. It would be great if the authors could point out and discuss the limitations of this test a bit more.


Minor:

Perhaps add a reference to MacKay’s density networks (MacKay, 1995) for decoder-based generative models.

In Section 2.2, the authors write “the prior over z can be drastically different than the true posterior p(z|x), especially in high dimension”. I think the flow of the paper could be improved here, especially for people less familiar with importance sampling/AIS. I don’t think the relevance of the posterior for importance sampling is clear at this point in the paper.

In Section 2.3 the authors claim that is often more “meaningful” to estimate p(x) in log-space because of underflow problems. “Meaningful” seems like the wrong word here. Perhaps revise to say that it’s more practical to estimate log p(x) because of underflow problems, or to say that it’s more meaningful to estimate log p(x) because of its connection to compression/surprise/entropy.
review_title: Great empirical work

final_score: rating: 6: Marginally above acceptance threshold
review_content: The paper describes a method to evaluate generative models such as VAE, GAN and GMMN. This is very much needed in our community where we still eyeball generated images to judge the quality of a model. However, the technical increment over the NIPS 16 paper: “Measuring the reliability of MCMC inference with bidirectional Monte Carlo” is very small, or nonexistent (but please correct me if I am wrong!).  (Grosse et al). The relative contribution of this paper is the application of this method to generative models. 
In section 2.3 the authors seem to make a mistake. They write E[p’(x)] <= p(x) but I think they mean: E[log p’(x)] <= log E[p’(x)] = log p(x). Also,  for what value of x? If p(x) is normalized it can’t be true for all values of x. Anyways, I think there are typos here and there and the equations could be more precise.
On page 5 top of the page it is said that the AIS procedure can be initialized with q(z|x) instead of p(z). However, it is unclear what value of x is then picked? Is it perhaps Ep(x)[q(z|x)] ?
I am confused with the use of the term overfitting (p8 bottom). Does a model A overfit relative to a another model B if the test accuracy of A is higher than that of B even though the gap between train and test accuracy is also higher for B than for A. I think not. Perhaps the last sentence on page 8 should say that VAE-50 underfits less than GMMN-50?
The experimental results are interesting in that it exposes the fact that GANs and GMMNs seem to have much lover test accuracy than VAE despite the fact that their samples look great. 

review_title: Application of BDMCMC to generative models. Relative contribution small. 

final_score: rating: null
review_content: Regarding equations leading to Equation 5, does f_1(z) represents the unnormalized part of p_1(z)=p(z) (which is the prior p(z) in this case according to the text at the top of page 4)? I think f_1(z) = p(z) (or maybe Z_1=1 ?) is needed to obtain Equation 5.

For the Figure 1, have tried evaluating the images according to the image-quality measure (Salimans et al.)? If so, are the values similar between the three models?

When you report computation time, are the implementations of IWAE and KDE use GPU?

Also, in Figures 1, 2 and 3, what is LLD stands for?
review_title: Geometric average; GPU implementation of WAE and KDE

Meta-review: This paper describes a method to estimate likelihood scores for a range of models defined by a decoder.
 
 This work has some issues. The paper mainly applies existing ideas. As discussed on openreview, the isotropic Gaussian noise model used to create a model with a likelihood is questionable, and it's unclear how useful likelihoods are when models are obviously wrong. However, the results, lead to some interesting conclusions, and on balance this is a good paper.
Decision: Accept (Poster)