Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy
We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD is applied to the setting of unsupervised learning by generative adversarial networks (GAN), in which a model attempts to generate realistic samples, and a discriminator attempts to tell these apart from data samples. In this context, the MMD may be used in two roles: first, as a discriminator, either directly on the samples, or on features of the samples. Second, the MMD can be used to evaluate the performance of a generative model, by testing the model’s samples against a reference data set. In the latter role, the optimized MMD is particularly helpful, as it gives an interpretable indication of how the model and data distributions differ, even in cases where individual model samples are not easily distinguished either by eye or by classifier.
This is an interesting paper containing three contributions: 1) An expression for the variance of the quadratic-time MMD estimate, which can be efficiently minimized for kernel selection. 2) Advanced computational optimizations for permutation tests for the quadratic MMD statistic. 3) Crystal-clear examples on the importance of reducing the variance in two-sample testing (Figure 2) Regarding my criticisms, 1) The conceptual advances in this submission are modest: the use of MMD to train generative models, as well as the importance of variance-reduction in MMD were already known. 2) The quadratic-time MMD test may lead to a discriminator that is *too good* in practical applications. Since MMD quickly picks up on pixel-level artifacts, I wonder if its use would be possible to train generators properly on realistic (non-binarized) data. This of course could be addressed by regularizing (smoothing) the kernel bandwidths, and for sure raises an interesting question/trade-off in generative modeling. Overall, the submission is technically sound and well-written: I recommend it for publication in ICLR 2017.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy
We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD is applied to the setting of unsupervised learning by generative adversarial networks (GAN), in which a model attempts to generate realistic samples, and a discriminator attempts to tell these apart from data samples. In this context, the MMD may be used in two roles: first, as a discriminator, either directly on the samples, or on features of the samples. Second, the MMD can be used to evaluate the performance of a generative model, by testing the model’s samples against a reference data set. In the latter role, the optimized MMD is particularly helpful, as it gives an interpretable indication of how the model and data distributions differ, even in cases where individual model samples are not easily distinguished either by eye or by classifier.
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>



This is an interesting paper containing three contributions: 1) An expression for the variance of the quadratic-time MMD estimate, which can be efficiently minimized for kernel selection. 2) Advanced computational optimizations for permutation tests for the quadratic MMD statistic. 3) Crystal-clear examples on the importance of reducing the variance in two-sample testing (Figure 2) Regarding my criticisms, 1) The conceptual advances in this submission are modest: the use of MMD to train generative models, as well as the importance of variance-reduction in MMD were already known. 2) The quadratic-time MMD test may lead to a discriminator that is *too good* in practical applications. Since MMD quickly picks up on pixel-level artifacts, I wonder if its use would be possible to train generators properly on realistic (non-binarized) data. This of course could be addressed by regularizing (smoothing) the kernel bandwidths, and for sure raises an interesting question/trade-off in generative modeling. Overall, the submission is technically sound and well-written: I recommend it for publication in ICLR 2017.
assistant
This is an interesting paper containing three contributions: 1) An expression for the variance of the quadratic-time MMD estimate, which can be efficiently minimized for kernel selection. 2) Advanced computational optimizations for permutation tests for the quadratic MMD statistic. 3) Crystal-clear examples on the importance of reducing the variance in two-sample testing (Figure 2) Regarding my criticisms, 1) The conceptual advances in this submission are modest: the use of MMD to train generative models, as well as the importance of variance-reduction in MMD were already known. 2) The quadratic-time MMD test may lead to a discriminator that is *too good* in practical applications. Since MMD quickly picks up on pixel-level artifacts, I wonder if its use would be possible to train generators properly on realistic (non-binarized) data. This of course could be addressed by regularizing (smoothing) the kernel bandwidths, and for sure raises an interesting question/trade-off in generative modeling. Overall, the submission is technically sound and well-written: I recommend it for publication in ICLR 2017.