The Variational Walkback Algorithm
A recognized obstacle to training undirected graphical models with latent variables such as Boltzmann machines is that the maximum likelihood training procedure requires sampling from Monte-Carlo Markov chains which may not mix well, in the inner loop of training, for each example. We first propose the idea that it is sufficient to locally carve the energy function everywhere so that its gradient points in the *right* direction (i.e., towards generating the data). Following on previous work on contrastive divergence, denoising autoencoders, generative stochastic networks and unsupervised learning using non-equilibrium dynamics, we propose a variational bound on the marginal log-likelihood of the data which corresponds to a new learning procedure that first walks away from data points by following the model transition operator and then trains that operator to walk backwards for each of these steps, back towards the training example. The tightness of the variational bound relies on gradually increasing temperature as we walk away from the data, at each step providing a gradient on the parameters to maximize the probability that the transition operator returns to its previous state. Interestingly, this algorithm admits a variant where there is no explicit energy function, i.e., the parameters are used to directly define the transition operator. This also eliminates the explicit need for symmetric weights which previous Boltzmann machine or Hopfield net models require, and which makes these models less biologically plausible.
The authors present a method for training probabilistic models by maximizing a stochastic variational-lower-bound-type objective. Training involves sampling and then learning a transition-based inference to *walk back* samples to the data. Because of its focus on transitions, it can be used to learn a raw transition operator rather than purely learning an energy-based model. The objective is intuitively appealing because of its similarity to previous successful but less principled training methods for MRFs like Contrastive Divergence. The idea for the algorithm is appealing, and it looks like it could find a nice place in the literature. However, the submission in its current form is not yet ready for publication. Experiments are qualitative and the generated samples are not obviously indicative of a high model quality. As pointed out elsewhere, the mathematical analysis does not currently demonstrate tightness of the variational bound in the case of a learned transition operator. More evaluation using e.g. annealed importance sampling to estimate held-out likelihoods is necessary. Assuming that the analysis can be repaired, the ability to directly parametrize a transition operator, an interesting strength of this method, should be explored in further experiments and contrasted with the more standard energy-based modeling. This looks like a promising idea, and other reviews and questions have already raised some important technical points which should help strengthen this paper for future submission.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
The Variational Walkback Algorithm
A recognized obstacle to training undirected graphical models with latent variables such as Boltzmann machines is that the maximum likelihood training procedure requires sampling from Monte-Carlo Markov chains which may not mix well, in the inner loop of training, for each example. We first propose the idea that it is sufficient to locally carve the energy function everywhere so that its gradient points in the *right* direction (i.e., towards generating the data). Following on previous work on contrastive divergence, denoising autoencoders, generative stochastic networks and unsupervised learning using non-equilibrium dynamics, we propose a variational bound on the marginal log-likelihood of the data which corresponds to a new learning procedure that first walks away from data points by following the model transition operator and then trains that operator to walk backwards for each of these steps, back towards the training example. The tightness of the variational bound relies on gradually increasing temperature as we walk away from the data, at each step providing a gradient on the parameters to maximize the probability that the transition operator returns to its previous state. Interestingly, this algorithm admits a variant where there is no explicit energy function, i.e., the parameters are used to directly define the transition operator. This also eliminates the explicit need for symmetric weights which previous Boltzmann machine or Hopfield net models require, and which makes these models less biologically plausible.
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>



The authors present a method for training probabilistic models by maximizing a stochastic variational-lower-bound-type objective. Training involves sampling and then learning a transition-based inference to *walk back* samples to the data. Because of its focus on transitions, it can be used to learn a raw transition operator rather than purely learning an energy-based model. The objective is intuitively appealing because of its similarity to previous successful but less principled training methods for MRFs like Contrastive Divergence. The idea for the algorithm is appealing, and it looks like it could find a nice place in the literature. However, the submission in its current form is not yet ready for publication. Experiments are qualitative and the generated samples are not obviously indicative of a high model quality. As pointed out elsewhere, the mathematical analysis does not currently demonstrate tightness of the variational bound in the case of a learned transition operator. More evaluation using e.g. annealed importance sampling to estimate held-out likelihoods is necessary. Assuming that the analysis can be repaired, the ability to directly parametrize a transition operator, an interesting strength of this method, should be explored in further experiments and contrasted with the more standard energy-based modeling. This looks like a promising idea, and other reviews and questions have already raised some important technical points which should help strengthen this paper for future submission.
assistant
The authors present a method for training probabilistic models by maximizing a stochastic variational-lower-bound-type objective. Training involves sampling and then learning a transition-based inference to *walk back* samples to the data. Because of its focus on transitions, it can be used to learn a raw transition operator rather than purely learning an energy-based model. The objective is intuitively appealing because of its similarity to previous successful but less principled training methods for MRFs like Contrastive Divergence. The idea for the algorithm is appealing, and it looks like it could find a nice place in the literature. However, the submission in its current form is not yet ready for publication. Experiments are qualitative and the generated samples are not obviously indicative of a high model quality. As pointed out elsewhere, the mathematical analysis does not currently demonstrate tightness of the variational bound in the case of a learned transition operator. More evaluation using e.g. annealed importance sampling to estimate held-out likelihoods is necessary. Assuming that the analysis can be repaired, the ability to directly parametrize a transition operator, an interesting strength of this method, should be explored in further experiments and contrasted with the more standard energy-based modeling. This looks like a promising idea, and other reviews and questions have already raised some important technical points which should help strengthen this paper for future submission.