To Relieve Your Headache of Training an MRF, Take AdVIL
We propose a black-box algorithm called {it Adversarial Variational Inference and Learning} (AdVIL) to perform inference and learning on a general Markov random field (MRF). AdVIL employs two variational distributions to approximately infer the latent variables and estimate the partition function of an MRF, respectively. The two variational distributions provide an estimate of the negative log-likelihood of the MRF as a minimax optimization problem, which is solved by stochastic gradient descent. AdVIL is proven convergent under certain conditions. On one hand, compared with contrastive divergence, AdVIL requires a minimal assumption about the model structure and can deal with a broader family of MRFs. On the other hand, compared with existing black-box methods, AdVIL provides a tighter estimate of the log partition function and achieves much better empirical results.
This manuscript proposes a new approach to fitting Markov Random Fields (MRFs). The general structure of the algorithm is amenable to many MRF structures and can be fairly straightforwardly applied to learning on a wide variety of problems. The theoretical analysis supports that the algorithm is reasonable. Experimental results show strong results on several different MRF models, albeit on relatively small problems. I am giving this manuscript a weak accept. The approach, to me, seems novel in fitting MRFs. However, the theoretical claims and their limitations need to be more realistically discussed, and the empirical results need to be shown on larger and more complex datasets. First, on the empirical results, there is a large literature on fitting RBM models, including many on scaling to much larger models. Given that AdVIL actually diverges on the logZ estimation as the number of iterations goes up makes me worry about the efficacy of this approach on larger RBMs (Figure 2 uses v=64 and h=15 while a common RBM on MNIST is v=784 and h=500, a huge difference in scale). As a large literature shows that estimating partition functions or normalizing constants gets much harder as the dimensionality goes up, I worry about this strategy and I think the manuscript would be greatly enhanced by looking at more common model sizes from the ML literature. Also, to me, the classic MCMC+SGD is as much a black box as the proposed technique. I realize that many of the top performing MCMC adapt specifically to the problem, but much of this is transferable between systems and can be put in simple sampling schemes. Table 1 should be updated to include these typical techniques, because it is not clear that the proposed system actually outperforms the typical PCD-1 scheme (especially given in Figure 3). Or succinctly, it should be made clear why I should use this over an MCMC approach. To address these concerns, I would like the authors to answer how their proposed algorithm works in larger MRFs and do a more complete analysis compared to more traditional strategies. Second, the theoretical claims are nice, but the manuscript should be revised to address the limitations of the theory. In particular, Lemma 1 is extremely strong, and I disagree with the assessment that it is *much weaker* than the typical nonparametric assumption. It seems that as the optimization gets close to the solution, this is essentially the exact same condition. The authors need to clarify how exactly this is different, and dive into the practical implementations. This also seems like it would get increasingly difficult as the number of hidden and visible units increases, so they should address how this Lemma holds as the theory scales.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
To Relieve Your Headache of Training an MRF, Take AdVIL
We propose a black-box algorithm called {it Adversarial Variational Inference and Learning} (AdVIL) to perform inference and learning on a general Markov random field (MRF). AdVIL employs two variational distributions to approximately infer the latent variables and estimate the partition function of an MRF, respectively. The two variational distributions provide an estimate of the negative log-likelihood of the MRF as a minimax optimization problem, which is solved by stochastic gradient descent. AdVIL is proven convergent under certain conditions. On one hand, compared with contrastive divergence, AdVIL requires a minimal assumption about the model structure and can deal with a broader family of MRFs. On the other hand, compared with existing black-box methods, AdVIL provides a tighter estimate of the log partition function and achieves much better empirical results.
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 manuscript proposes a new approach to fitting Markov Random Fields (MRFs). The general structure of the algorithm is amenable to many MRF structures and can be fairly straightforwardly applied to learning on a wide variety of problems. The theoretical analysis supports that the algorithm is reasonable. Experimental results show strong results on several different MRF models, albeit on relatively small problems. I am giving this manuscript a weak accept. The approach, to me, seems novel in fitting MRFs. However, the theoretical claims and their limitations need to be more realistically discussed, and the empirical results need to be shown on larger and more complex datasets. First, on the empirical results, there is a large literature on fitting RBM models, including many on scaling to much larger models. Given that AdVIL actually diverges on the logZ estimation as the number of iterations goes up makes me worry about the efficacy of this approach on larger RBMs (Figure 2 uses v=64 and h=15 while a common RBM on MNIST is v=784 and h=500, a huge difference in scale). As a large literature shows that estimating partition functions or normalizing constants gets much harder as the dimensionality goes up, I worry about this strategy and I think the manuscript would be greatly enhanced by looking at more common model sizes from the ML literature. Also, to me, the classic MCMC+SGD is as much a black box as the proposed technique. I realize that many of the top performing MCMC adapt specifically to the problem, but much of this is transferable between systems and can be put in simple sampling schemes. Table 1 should be updated to include these typical techniques, because it is not clear that the proposed system actually outperforms the typical PCD-1 scheme (especially given in Figure 3). Or succinctly, it should be made clear why I should use this over an MCMC approach. To address these concerns, I would like the authors to answer how their proposed algorithm works in larger MRFs and do a more complete analysis compared to more traditional strategies. Second, the theoretical claims are nice, but the manuscript should be revised to address the limitations of the theory. In particular, Lemma 1 is extremely strong, and I disagree with the assessment that it is *much weaker* than the typical nonparametric assumption. It seems that as the optimization gets close to the solution, this is essentially the exact same condition. The authors need to clarify how exactly this is different, and dive into the practical implementations. This also seems like it would get increasingly difficult as the number of hidden and visible units increases, so they should address how this Lemma holds as the theory scales.
assistant
This manuscript proposes a new approach to fitting Markov Random Fields (MRFs). The general structure of the algorithm is amenable to many MRF structures and can be fairly straightforwardly applied to learning on a wide variety of problems. The theoretical analysis supports that the algorithm is reasonable. Experimental results show strong results on several different MRF models, albeit on relatively small problems. I am giving this manuscript a weak accept. The approach, to me, seems novel in fitting MRFs. However, the theoretical claims and their limitations need to be more realistically discussed, and the empirical results need to be shown on larger and more complex datasets. First, on the empirical results, there is a large literature on fitting RBM models, including many on scaling to much larger models. Given that AdVIL actually diverges on the logZ estimation as the number of iterations goes up makes me worry about the efficacy of this approach on larger RBMs (Figure 2 uses v=64 and h=15 while a common RBM on MNIST is v=784 and h=500, a huge difference in scale). As a large literature shows that estimating partition functions or normalizing constants gets much harder as the dimensionality goes up, I worry about this strategy and I think the manuscript would be greatly enhanced by looking at more common model sizes from the ML literature. Also, to me, the classic MCMC+SGD is as much a black box as the proposed technique. I realize that many of the top performing MCMC adapt specifically to the problem, but much of this is transferable between systems and can be put in simple sampling schemes. Table 1 should be updated to include these typical techniques, because it is not clear that the proposed system actually outperforms the typical PCD-1 scheme (especially given in Figure 3). Or succinctly, it should be made clear why I should use this over an MCMC approach. To address these concerns, I would like the authors to answer how their proposed algorithm works in larger MRFs and do a more complete analysis compared to more traditional strategies. Second, the theoretical claims are nice, but the manuscript should be revised to address the limitations of the theory. In particular, Lemma 1 is extremely strong, and I disagree with the assessment that it is *much weaker* than the typical nonparametric assumption. It seems that as the optimization gets close to the solution, this is essentially the exact same condition. The authors need to clarify how exactly this is different, and dive into the practical implementations. This also seems like it would get increasingly difficult as the number of hidden and visible units increases, so they should address how this Lemma holds as the theory scales.