On the Quantitative Analysis of Decoder-Based Generative Models
The past several years have seen remarkable progress in generative models which produce convincing samples of images and other modalities. A shared component of some popular models such as generative adversarial networks and generative moment matching networks, is a decoder network, a parametric deep neural net that defines a generative distribution. Unfortunately, it can be difficult to quantify the performance of these models because of the intractability of log-likelihood estimation, and inspecting samples can be misleading. We propose to use Annealed Importance Sampling for evaluating log-likelihoods for decoder-based models and validate its accuracy using bidirectional Monte Carlo. Using this technique, we analyze the performance of decoder-based models, the effectiveness of existing log-likelihood estimators, the degree of overfitting, and the degree to which these models miss important modes of the data distribution.
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.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
On the Quantitative Analysis of Decoder-Based Generative Models
The past several years have seen remarkable progress in generative models which produce convincing samples of images and other modalities. A shared component of some popular models such as generative adversarial networks and generative moment matching networks, is a decoder network, a parametric deep neural net that defines a generative distribution. Unfortunately, it can be difficult to quantify the performance of these models because of the intractability of log-likelihood estimation, and inspecting samples can be misleading. We propose to use Annealed Importance Sampling for evaluating log-likelihoods for decoder-based models and validate its accuracy using bidirectional Monte Carlo. Using this technique, we analyze the performance of decoder-based models, the effectiveness of existing log-likelihood estimators, the degree of overfitting, and the degree to which these models miss important modes of the data distribution.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



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.
assistant
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.