Task: Language Identification
Input (Spanish, English): This paper proposes a new kind of generative model based on an annealing process, where the transition probabilities are learned directly to maximize a variational lower bound on the log-likelihood. Overall, the idea is clever and appealing, but I think the paper needs more quantitative validation and better discussion of the relationship with prior work.  In terms of prior work, AIS and RAISE are both closely related algorithms, and share much of the mathematical structure with the proposed method. For this reason, it’s not sufficient to mention them in passing in the related work section; those methods and their relationship to variational walkback need to be discussed in detail. If I understand correctly, the proposed method is essentially an extension of RAISE where the transition probabilities are learned rather than fixed based on an existing MRF. I think this is an interesting and worthwhile extension, but the relationship to existing work needs to be clarified.  The analysis of Appendix D seems incorrect. It derives a formula for the ratios of prior and posterior probabilities, but this formula only holds under the assumption of constant temperature (in which case the ratio is very large). When the temperature is varied, the analysis of Neal (2001) applies, and the answer is different.   One of the main selling points of the method is that it optimizes a variational lower bound on the log-likelihood; even more accurate estimates can be obtained using importance sampling. It ought to be easy to report log-likelihood estimates for this method, so I wonder why such estimates aren’t reported. There are lots of prior results to compare against on MNIST. (In addition, a natural baseline would be RAISE, so that one can check if the ability to learn the transitions actually helps.)  I think the basic idea here is a sound one, so I would be willing to raise my score if the above issues are addressed in a revised version.   Minor comments:  “A recognized obstacle to training undirected graphical models… is that ML training requires sampling from MCMC chains in the inner loop of training, for each example.” This seems like an unfair characterization, since the standard algorithm is PCD, which usually takes only a single step per mini-batch.  Some of the methods discussed in the related work are missing citations.  The method is justified in terms of “carving the energy function in the right direction at each point”, but I’m not sure this is actually what’s happening. Isn’t the point of the method that it can optimize a lower bound on the log-likelihood, and therefore learn a globally correct allocation of probability mass?
Output (English): en