From: ICLR.cc/2023/Conference/Paper217/Authors
title: Submission Withdrawn by the Authors

From: ICLR.cc/2023/Conference/Paper217/Authors
title: Late Response to the comments of Reviewer s8sJ on 4th Dec
comment: Sorry that this additional response is late,

### W2 More insights into the approximation in Algorithm 4 & Eq. (15)

We have completed the evaluation of BAO, SAVI-Accurate, SAVI-Approximate on general density estimation task, in order to better understand the consequence of SAVI-Approximate over SAVI Accurate. As evaluating SAVI accurate is intractable for NVC, we construct a small size 2-layer VAE following the architecture of [Burda et al., 2016] composed of 100 latent on first layer and 50 latent on second layer. The dataset is binary MNIST. The results are as follows:

|                    | NLL       | p-value                                        |
|--------------------|-----------|------------------------------------------------|
| FAVI (2-level VAE) | <=98.3113 |                                                |
| BAO                | <=91.5530 | <=0.001(t-test compared with FAVI)             |
| SAVI-Approximate   | <=91.5486 | <=0.001(t-test compared with BAO)              |
| SAVI-Accurate      | <=91.5482 | <=0.001(t-test compared with SAVI-Approximate) |

These results indicates that BAO has a significant advantage over FAVI; SAVI-Approximate has a significant advantage over BAO; and SAVI-Accurate has a significant advantage over SAVI-Approximate.

### Reference:
* Burda, Y., Grosse, R., & Salakhutdinov, R. (2015). Importance weighted autoencoders. arXiv preprint arXiv:1509.00519.

From: ICLR.cc/2023/Conference/Paper217/Authors
title: Late Response to the comments of Reviewer bAfb on 4th Dec
comment: Sorry that this additional response is late,

### W3 Additional experiments on generic data

We have completed the evaluation of BAO, SAVI-Accurate, SAVI-Approximate on general density estimation task, in order to better understand the consequence of SAVI-Approximate over SAVI Accurate. As evaluating SAVI accurate is intractable for NVC, we construct a small size 2-layer VAE following the architecture of [Burda et al., 2016] composed of 100 latent on first layer and 50 latent on second layer. The dataset is binary MNIST. The results are as follows:

|                    | NLL       | p-value                                        |
|--------------------|-----------|------------------------------------------------|
| FAVI (2-level VAE) | <=98.3113 |                                                |
| BAO                | <=91.5530 | <=0.001(t-test compared with FAVI)             |
| SAVI-Approximate   | <=91.5486 | <=0.001(t-test compared with BAO)              |
| SAVI-Accurate      | <=91.5482 | <=0.001(t-test compared with SAVI-Approximate) |

These results indicates that BAO has a significant advantage over FAVI; SAVI-Approximate has a significant advantage over BAO; and SAVI-Accurate has a significant advantage over SAVI-Approximate.

### Reference:
* Burda, Y., Grosse, R., & Salakhutdinov, R. (2015). Importance weighted autoencoders. arXiv preprint arXiv:1509.00519.

From: ICLR.cc/2023/Conference/Paper217/Reviewer_w52F
title: thanks for the feedback
comment: Thanks for your feedback, most of the concerns have been addressed.

From: ICLR.cc/2023/Conference/Paper217/Authors
title: Manuscript Revision Round I
comment: To all reviewers, thanks for your detailed review, and we have updated the manuscript accordingly. All the revision are marked in blue. Below is a summary of revisions:
* Revision on notations to separate DVC related symbols from SAVI related symbols, as suggested by bAfb.
* A new Section named Complexity and Scalability is added in Appendix, containing the new results on spatial temporal complexity, a new trick to speed up and improve scalibility, as suggested by s8sJ and w52F.
* A new Section named Impact on OEU is added in Appendix, containing the new results on applying our approach to OEU, as suggested by s8sJ.
* A new Section named Extending the Analysis Sec. 3 to general DAG case, containing the analysis of applying BAO to general SAVI problem, as suggested by bAfb.
* Minor editing to avoid misunderstanding, such as "practical" -> "tractable", as suggested by s8sJ.

From: ICLR.cc/2023/Conference/Paper217/Authors
title: Response to the comments of Reviewer bAfb
comment: Thanks for your detailed review. Below are our response to your questions and clarification to some minor misunderstandings:

### W1 Using notations  and  for bit allocation and  for all variables for general SAVI is confusing

Sorry for bring you confusion. Your intuitation is correct, the SAVI (Kim et al., 2018) is performed on both $y_i,w_i$, and Eq. 15 indicates that the approximation applies to both $y_i,w_i$. We agree that this is indeed confusing, and it is our bad to simplify notation. We will use $a_i,b_i$ to represent latent in general case, and make $y_i,w_i$ exclusive to bit allocation case.

__for revision__: we will revise this in revision.

### W2 A general idea of the DAG structures where the advantage over the BAO approach is significant

That is a very interesting point. As our startpoint is bit allocation, we have not thought about applying the generalized BAO (Xu et al., 2022) (Alg. 3) to general case. The theoratical disadvantage of the generalized BAO (Alg. 3) is obvious, as the gradient is incorrect as we described in Sec. 3. The analysis in Sec. 3 not only applies to bit allocation, but also the generalized DAG case, so long as we replace Fig. 1 into a generalized DAG. Again, while generalized BAO (Alg. 3) can not compute the gradient correctly, the SAVI on DAG latent (Alg. 2) can achieve this at the cost of intractibility, and the approximation SAVI on DAG (Alg. 4) statisfies one of 2 rules on gradient. We think it is benefical to provide a Sec. 3's analysis on generalized DAG, to highlight the problem in general case.

__for revision__: we will include those discussions in revision.

### W3 Additional experiments on generic data

We agree that it is very interesting to extend current approach to general scenario. We are considering extra experiments with linear model and Banana source. Although we can not secure providing the result during rebuttal (as it would be on a different codebase), we are glad to include them as soon as possible.

__for revision__: we will try our best to include the results and discussion in revision.

### Reference: 
* Yoon Kim, Sam Wiseman, Andrew Miller, David Sontag, and Alexander Rush. Semi-amortized 
variational autoencoders. In Int. Conf. on Machine Learning, pp. 2678–2687. PMLR, 2018. 
* Tongda Xu, Han Gao, Chenjian Gao, Jinyong Pi, Yanghao Li, Yuanyuan Wang, Ziyu Zhu, Dailan He, Mao Ye, Hongwei Qin, and Yan Wang. Bit allocation using optimization. arXiv preprint arXiv:2209.09422, 2022.

From: ICLR.cc/2023/Conference/Paper217/Authors
title: Response to the comments of Reviewer w52F
comment: Thanks for your detailed review. Below are our response to your questions and clarification to some minor misunderstandings:

### W1 Spatial and Temporal Complexity

We agree that the temporal complexity, memory cost should be presented and the scalability issue should be addressed. Below are additional results and a trick to address scalability.

We perform additional evaluation to compare current method with BAO (Xu et al., 2022) in terms of temporal complexity and memory cost. The evaluation result can be found in (Fig. temporal: https://ibb.co/9Zzm6kh ; Fig. memory: https://ibb.co/7kg9YpN). The general result is that our approach is $\approx 2.8$ times slower and cost $\approx 2.0$ times memory than BAO . We do agree that our current version is slower than BAO while performs better. Jointly consider RD performance, time and memory, our approach does not dominate BAO.

However, as our approach enables a sequential style semi-amortized variational inference (SAVI) (Kim et al., 2018) on latents, there exists a very simple trick to speed it up. Moreover, this trick also resolves the scalability issue. Specifically, to optimize the $i^{th}$ frame's latent, we do not compute the R-D cost of all the frames after it as we do now. Instead, we limit the R-D cost computation to a small fixed size of frames. Formally, we approximate the gradient as: $\frac{d\mathcal{L}(y_{i:T})}{d y_i} \approx \frac{d\mathcal{L}(y_{i:i+c})}{d y_i}$, where $c$ is a preset constant. With this trick, our approach cost only $\approx 50\\%$ of time and $\approx 60\\%$ of memory compared with BAO, while remains a superior performance ($\approx 5\\%$ better in BDBR) (See the Ours(fast) results in Fig. temporal and Fig. memory, the results are based on DVC Class D $c=2$). With this trick, jointly consider RD performance, time and memory, our approach clearly dominates BAO.

Furthermore, with this trick, the scalability issue of our approach is significantly ellivated. As shown in (Fig. scalability: https://ibb.co/cXCz9FY), the memory cost our approach with this trick is constant to GoP size, while that of BAO and our approach without this trick grows linearly with GoP size. This means that with this trick, our approach becomes scalable to any GoP, which is superior than BAO.

However, we still want to emphasis that both BAO and our approach aims at optimal performance. We frankly admit that we are not seeking a trade-off between resources and RD performance, we want the best RD performance. In general, our approach serves as a benchmark for other researchers in bit allocation community to test how far their fast algorithm are from best RD performance. That is also a reason why we opensource our code during submission. We believe that our work can inspire many faster, practical and scalable bit allocation algorithm in the future.

__for revision__: we will include those additional results and discussions in revision.

### Reference:
* Yoon Kim, Sam Wiseman, Andrew Miller, David Sontag, and Alexander Rush. Semi-amortized
variational autoencoders. In Int. Conf. on Machine Learning, pp. 2678–2687. PMLR, 2018.
* Tongda Xu, Han Gao, Chenjian Gao, Jinyong Pi, Yanghao Li, Yuanyuan Wang, Ziyu Zhu, Dailan
He, Mao Ye, Hongwei Qin, and Yan Wang. Bit allocation using optimization. arXiv preprint
arXiv:2209.09422, 2022.

From: ICLR.cc/2023/Conference/Paper217/Authors
title: Response to the comments of Reviewer s8sJ Part II
comment: ### W3 It is unclear whether the proposed idea can be extended to update the encoder rather than the latents
It should not be and is not benefical to encoder update. First, the Online Encoder Update (OEU) (Lu et al., 2020) is not SAVI and does not fit into SAVI framework. The base of our work is that we are optimizing the raw parameter of variational posterior, which can be described by a bayesian Network (the DAG in our paper). The OEU does not statisify this requirement, and the encoder parameter does not form a bayesian network according to the variational posterior structure. Empirically, we verify our argument in (Fig. COEU: https://ibb.co/q1F6SYC). As shown in the Fig. COEU, the progressive tuning of encoder parameter (COEU, green line) is not helpful.

__for revision__: we will include those additional results and discussions in revision.

### Clarity, Quality, Novelty And Reproducibility.
Sorry for the TYPOs, we will fix them. This paper is not an efficient version of BAO. It is an improved version of BAO with gradient issue fixed. The source code is available in the supplementary material as a zip file.

__for revision__: we will revise the TYPOs in revision.

### Reference:
* Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint
arXiv:1312.6114, 2013.
* Yoon Kim, Sam Wiseman, Andrew Miller, David Sontag, and Alexander Rush. Semi-amortized
variational autoencoders. In Int. Conf. on Machine Learning, pp. 2678–2687. PMLR, 2018.
* Tongda Xu, Han Gao, Chenjian Gao, Jinyong Pi, Yanghao Li, Yuanyuan Wang, Ziyu Zhu, Dailan He, Mao Ye, Hongwei Qin, and Yan Wang. Bit allocation using optimization. arXiv preprint arXiv:2209.09422, 2022.
* Guo Lu, Chunlei Cai, Xiaoyun Zhang, Li Chen, Wanli Ouyang, Dong Xu, and Zhiyong Gao. Content adaptive and error propagation aware deep video compression. In European Conference on Computer Vision, pp. 456–472. Springer, 2020.

From: ICLR.cc/2023/Conference/Paper217/Authors
title: Response to the comments of Reviewer s8sJ Part I
comment: Thanks for your detailed review. Below are our response to your questions and clarification to some minor misunderstandings:

### W1 Scalability and Temporal Complexity
First of all, we want to address that the merit of this paper is theoratical correctness and RD performance optimality, instead of practicality. We frankly admit that we are not seeking a trade-off between resources and RD performance, we want the best RD performance. In general, our approach serves as a benchmark for other researchers in bit allocation community to test how far their fast algorithm are from best RD performance. That is also a reason why we opensource our code during submission. We believe that our work can inspire many faster, practical and scalable bit allocation algorithm in the future. For an example in traditional codec, VTM is also very slow and far from practical. It takes several minutes to encode a single frame in VTM. However, its speed does not harm its value as a reference / benchmark, and does not stop its inspiration for other faster codecs.

We agree that the temporal complexity, memory cost should be presented and the scalability issue should be addressed. Below are additional results and a trick to address scalability.

We perform additional evaluation to compare current method with BAO (Xu et al., 2022) in terms of temporal complexity and memory cost. The evaluation result can be found in (Fig. temporal: https://ibb.co/9Zzm6kh ; Fig. memory: https://ibb.co/7kg9YpN). The general result is that our approach is $\approx 2.8$ times slower and cost $\approx 2.0$ times memory than BAO . We do agree that our current version is slower than BAO while performs better. Jointly consider RD performance, time and memory, our approach does not dominate BAO.

However, as our approach enables a sequential style semi-amortized variational inference (SAVI) (Kim et al., 2018) on latents, there exists a very simple trick to speed it up. Moreover, this trick also resolves the scalability issue. Specifically, to optimize the $i^{th}$ frame's latent, we do not compute the R-D cost of all the frames after it as we do now. Instead, we limit the R-D cost computation to a small fixed size of frames. Formally, we approximate the gradient as: $\frac{d\mathcal{L}(y_{i:T})}{d y_i} \approx \frac{d\mathcal{L}(y_{i:i+c})}{d y_i}$, where $c$ is a preset constant. With this trick, our approach cost only $\approx 50\\%$ of time and $\approx 60\\%$ of memory compared with BAO, while remains a superior performance ($\approx 5\\%$ better in BDBR) (See the Ours(fast) results in Fig. temporal and Fig. memory, the results are based on DVC Class D $c=2$). With this trick, jointly consider RD performance, time and memory, our approach clearly dominates BAO.

Furthermore, with this trick, the scalability issue of our approach is significantly ellivated. As shown in (Fig. scalability: https://ibb.co/cXCz9FY), the memory cost our approach with this trick is constant to GoP size, while that of BAO and our approach without this trick grows linearly with GoP size. This means that with this trick, our approach becomes scalable to any GoP, which is superior than BAO.

__for revision__: we will include those additional results and discussions in revision.

### W2 More insights into the approximation in Algorithm 4 & Eq. (15)
The accurate SAVI on DAG (Alg. 2) is based on 2 rules: 1. after the update of current latent $y_{i}$, all the future latent $y_{>i}$ are reinitialized by fully amortized variational inference (FAVI) (Kingma & Welling, 2013). 2. the gradient to update current latent $y_{i}$ requires the completion of update of all future latent $y_{>i}$. Our approximation in Alg. 4 keeps rule 1. while discard rule 2., and Eq. 15 describe the break of rule 2. And the line 4 in Alg. 4 corresponds to rule 1, which clearly differs our algorithm from BAO. In this sense, the current latent $y_i$ clearly impacts future latent $y_{>i}$ by initialization future latent $y_{>i}$ via FAVI, and thus clearly impacts the RD cost of future frames.

Furthermore, the source code with detailed annotation (See a snapshot: https://ibb.co/gFc7KxZ) explaining the code's correspondance to Algorithm 4 is provide in the supplementary material as a zip file (See the Readme file in supplementary). We hope that this explaination and code with annotation will lift your confusion.

__for revision__: we will include those discussions in revision.

From: ICLR.cc/2023/Conference/Paper217/Authors
title: Response to the comments of Reviewer rNPE
comment: We are sorry that we are not allowed to reveal our identity during submission / rebuttal phase. But to the best of our knowledge, our submission has no violation of ICLR policy:  
* First, it is fine to use an arxiv paper as baseline, no matter it is our own work or not. Further, we believe that ICLR does not include any constrain on the minimal time gap between previous arxiv paper and our submission. 
* Second, our submission is significantly different from BAO (Xu et al.).  Both of these two paper are around 20 pages, and have their own novel technical contribution. So they should not be merged.  
* Third, as we have addressed in the manuscript, this submission  is a follow up paper, not an errata. We agree the title of ‘Correct …' is somewhat misleading, we will change it to ‘Improving bit allocation with optimization’. 

We do not have research integrity issues (e.g., plagiarism, dual submission). This paper is neither a plagiarism nor a dual submission as it is a new paper. 

We hope this can address your concerns.

From: ICLR.cc/2023/Conference/Paper217/Reviewer_s8sJ
confidence: 5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.
summary_of_the_paper: This paper aims to address optimal bit allocation for learned video compression. Specifically, it points out the suboptimality of the arXiv publication "Bit Allocation using Optimization (BAO)", and proposes an improved version. The proposed method shows promising results as compared to BAO and Online Encoder Update (OEU). 
strength_and_weaknesses: Strengths:

(1) The idea of expending 1-level latent to 2-level non-factorized latent and using fixed w to optimize y to maximize ELBO by SAVI is interesting.

(2)  The experiment showcases the merits of the proposed method.

Weaknesses:

(1) The authors admit that the proposed method can NOT scale up to large GOP sizes (and likely high-resolution videos) and is not applicable to low-delay applications. In the current manuscript, there is no discussion and comparison on the encoding runtimes of different optimization techniques. The practicality of the proposed method is questionable.   

(2) More insights into the approximation in Algorithm 4 & Eq. (15) should be provided. The implications of the approximation should be highlighted too. It appears that the optimization of the current latent y_i has no impact on the RD cost of the future frames. 

(3) It is unclear whether the proposed idea can be extended to update the encoder rather than the latents. According to the OEU paper, this may have the advantages of reducing the number of iterations needed.  

clarity,_quality,_novelty_and_reproducibility: The readability is a bit low. There are also some TYPOs. This work appears to be an extended version of the arXiv publication "Bit Allocation using Optimization (BAO)". The idea of using GOP-based optimization is intuitively agreeable. But, how to achieve this efficiently is the major contribution of this paper. In this regard, the authors should be credited. There is no code available. But, the paper has enough implementation details. Reproducibility should be relatively less of a problem. 
summary_of_the_review: This work appears to be an extended version of the arXiv publication "Bit Allocation using Optimization (BAO)". The novelty is a bit low, although I believe the authors should be credited for proposing an efficient algorithm to achieve GOP-based optimization of latents. Currently, there is no comparison of encoding runtimes. As such, how practical the proposed method is questionable. Moreover, the implications of the approximation are missing. The scalability of the proposed method to large GOPs and high-resolution videos appears rather limited. 
correctness: 2: Several of the paper’s claims are incorrect or not well-supported.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
flag_for_ethics_review: NO.
recommendation: 3: reject, not good enough

From: ICLR.cc/2023/Conference/Paper217/Reviewer_w52F
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: The bit allocation issue in neural video compression is the main topic of this research. In order to arrive at the ideal bit allocation, the problem is defined as semi-amortized variational inference, and gradient-based optimization is used as a solution. They point out the source of the sub-optimal performance in another paper's implementation. According to a concrete analysis, they present the corrected version of the optimal algorithm. Moreover, a computationally efficient approximation is designed to balance performance and time complexity. The newly developed algorithm demonstrates a clear performance improvement.
strength_and_weaknesses: Strength:
1)	The paper is well organized with detailed analysis and theoretical derivation. Reasons behind sub-optimality are well explored. The consideration for preserving and fully exploiting inter-frame dependencies during optimization is convincing. The reference and extension of the SAVI optimization method also has certain theoretical innovations.
2)	The experiment performed well and successfully supported the theory. This reveals the significant impact of this optimization method on video compression performance.
3)	Clear writing.

Weakness:
1)	Even thought the complexity issue is taken into consideration in this paper, it’s still hard to get a clear impression on the time complexity in the actual codec implementation. The time consumption of the method and the comparison with that of baseline in the implementation can be briefly listed. More in-depth analysis on the codec complexity is necessary. 


clarity,_quality,_novelty_and_reproducibility: This paper is well-written and well-organized. Although the idea is not particularly original, the analysis work is thorough.
summary_of_the_review: Overall, the analytical concepts and theoretical derivation in this study are clear and extensive. It would be preferable to include further examination of the suggested scheme's novelty and superiority.
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 6: marginally above the acceptance threshold

From: ICLR.cc/2023/Conference/Paper217/Reviewer_rNPE
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: This paper provides a fix to a recent frame/region-level bit allocation method for neural video compression, called BAO. In particular, the paper finds that BAO does not properly perform semi-amortized variational inference for non-factorized latents, and provide a compute-efficient approximation to the proper SAVI. Empirically, the method outperforms the existing bit allocation methods for NVC.
strength_and_weaknesses: There is a significant issue with the paper, which I believe should be addressed before delving deep into the technical quality of the paper.

The first (as far as I know) publicly available version of BAO (Xu et al.) appears on the arXiv on September 20th of 2022 (https://arxiv.org/abs/2209.09422), which is only a day before the ICLR 2023 abstract submission deadline. From this fact, I could only guess that either (1) the authors of this paper have been extremely productive and GPU-rich that they could identify the error of the previous work in a day and perform all experiments in a week, or (2) this submission has been written by the BAO authors (or close collaborators), who caught and fixed their own errors.

If (2) is the case, I believe that the authors should retract the previous BAO submission and fix the manuscript directly. This is especially true because this paper is using (the unpublished) BAO as a main baseline, and the academic value of fixing an error of one's own, unpublished work is quite unclear.
clarity,_quality,_novelty_and_reproducibility: Please refer to the "Strength and Weakness" above.
summary_of_the_review: This submission should be retracted and merged with BAO.
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
flag_for_ethics_review: Yes, Research integrity issues (e.g., plagiarism, dual submission)
details_of_ethics_concerns: Please refer to the "Strength and Weakness" above.
recommendation: 1: strong reject

From: ICLR.cc/2023/Conference/Paper217/Reviewer_bAfb
confidence: 2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: This paper studies optimal bit allocation in a group of pictures for neural video compression. It begins by pointing out an algorithmic error in a previous work (BAO) that applied semi-amortized variational inference (SAVI) to this problem. The root of this problem is that the dependencies between variables were not considered during optimization, leading to incorrect derivative formula and incorrect evaluation points. The paper then derives the correct formula that exploit the factorization of the variables and, noting it is intractable for bit allocation, proposes to approximate the evaluation point but keeps the correct formula. Both the proposed relaxation and BOA are then evaluated and compare to other approaches using the HEVC Common Testing Conditions. The proposed relaxation is shown to be better than BOA in terms of BD-BR and bitrate error. BAO and the relaxation are then further analyzed by comparing the performance on successive frames of a Group of Picture.
strength_and_weaknesses: **Strength**
* This approach is an interesting contribution to the bit allocation problem in neural video compression.
* The SAVI algorithm on a DAG is interesting beyond this specific problem for the machine learning community.
* The experiments are well conducted, with multiple baselines, and clearly show the strength of the approach. Furthermore, the in-depth comparison with BAO is helpful to highlight how the proposed approach fix the problem.
* The source code is provided. 

**Weaknesses**
* Using notations $y$ and $w$ for bit allocation and $y$ for all variables for general SAVI confused me a little bit. It was fine until both are combined (Section 4.4). For example, it is not clear for me whether equation 15 indicates that the approximation applies only to the $y$ of the bit allocation problem or to both $y$ and $w$. I assumed it was the latter. 
* For a more general use of the approach, maybe it would be helpful to have a general idea of the DAG structures where the advantage over the BOA approach is significant.
* Similarly, maybe additional experiments on generic data could be interesting to better show the behavior of the approach.
clarity,_quality,_novelty_and_reproducibility: * I think the authors did a great job explaining their approach. It remains hard to understand for me, but the presentation helped a lot. Overall, the paper is well written and mostly clear, except for the minor point raised above.
* As far as I know, this approach is novel. Note that I am not familiar with recent literature on variational inference.
* The code is provided, so reproducibility is great. I did not try to run it.
* The idea presented is not trivial to me, application motivated and of interest to the machine learning community.

summary_of_the_review: I would recommend accepting this paper. It it well written, has both applicative and algorithmic contributions and experiments.
correctness: 4: All of the claims and statements are well-supported and correct.
technical_novelty_and_significance: 4: The contributions are significant, and do not exist in prior works.
empirical_novelty_and_significance: 4: The contributions are significant, and do not exist in prior works.
flag_for_ethics_review: NO.
recommendation: 8: accept, good paper