Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper proposes PLNet, a two-step approach to estimate the precision matrix of the latent normal distribution which represents the graph of count data. PLNet first considers the Poisson log-normal (PLN) graphical model and utilizes the maximum marginal likelihood estimator (MMLE) to estimate the latent covariance matrix. In the second step, PLNet estimates the sparse precision matrix by minimizing the lasso penalized D-trace loss. The authors also prove that the resulting estimator is a consistent estimator of the precision matrix in high dimensional settings under mild conditions. Extensive experiments, especially simulation experiments, demonstrate that PLNet outperforms baseline methods in both accuracy and efficiency.
strengths_and_weaknesses: Strengths:

1. Instead of using Gaussian distribution, the authors leverage multivariate Poisson log-normal (PLN) distribution to estimate the graphical models of count data, which handles the over-dispersion problem and is more likely to approximate the distribution of count data like scRNA-seq data. 

2. PLNet is computationally efficient as it avoids computing high-dimensional numeric integration when computing the log-likelihood of the multivariate PLN model, and applying the D-trace method to estimate the precision matrix is more efficient.

3. The authors provide the theoretical analysis of the estimator in the high-dimensional setting and prove that the estimator is a consistent estimator of the precision matrix under mild conditions.

Weaknesses:

1. It seems that the authors did not mention how to obtain the mean vector of the latent normal distribution in the PLNet. It would be great if the authors could discuss it.

2. Sometimes in scRNA-seq data, the number of genes (i.e., $p$) may be large, and thus the reviewer wonders if the estimator is still a consistent estimator of the precision matrix in this case?

3. Although extensive simulation results have been presented in this paper, it seems that the real-world experimental results are not very clear. The reviewer thinks that the authors may use some other criteria to quantify the results rather than just using the heatmap and within-between connection ratios. 

4. The presentation of experiment results should be improved, and it might be better to use tables to present the results.
questions: 1. The reviewer wonders if it is possible to incorporate the gene regulatory network information in the modeling process to improve the estimation performance?

2. In scRNA-seq data, sometimes gene expression of some genes is not detected. The reviewer wonders if the authors consider using a probability describing whether a gene's expression is detected to better approximate the real data.
limitations: Authors have discussed the Limitations and societal impacts in the Conclusion Section.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper introduces a consistent estimator for the sparse precision matrix of the Poisson log-normal (PLN) graphical model. The paper provides theoretical guarantees of the estimator's consistency and convergence rate. Using simulated data, the paper demonstrates that the proposed estimator is more accurate than competitive baselines across a variety of conditions. The paper also compares the proposed estimator to a recent baseline on inferring a gene regulatory network from RNA sequence data.
strengths_and_weaknesses: ## Clarity
This paper is very well-written and clear. It provides excellent coverage of prior work and situates the proposed approach well within the relevant literature. The technical exposition is cleanly structured and easy to follow. The experiments are reported with sufficient detail. I also appreciate that the proposed method is grounded in an applied problem, which provides strong motivation for the paper, and helps in understanding the method.

## Quality 
I found no flaws in the paper's logic or in the proofs for theorems 1-3 (which I only skimmed). The proposed method is simple and practical, while the theory guarantees root-n convergence of the estimator under mild conditions.

The experiments are thorough. The paper does a good job of simulating many synthetic data sets under varying conditions and performance to reasonable baselines. One drawback is that only the simple case of a banded covariance matrix is given as an example to compare visually the results of the proposed method to the baselines. Perhaps the authors can add more visual inspections to the appendix.

Minor comments/edits:
- "semi-positive definite" -> "positive semi-definite"
- line 69: "computational" -> "compuationally"
- line 104: "ditribution" -> "distribution"
- line 170 "convergency" -> "convergence"
- line 215 "tunned" -> "tuned"

## Originality
I've not worked in the area of Gaussian graphical models, nor in sparse estimation of precision/covariance matrices, so it's difficult for me to judge how original or novel the paper is. My sense is that the method itself is  built from standard pieces and is not very original, but the theory that establishes the method's consistency and convergence rates is non-trivial and new. 

## Significance
While this paper focuses on the particular applied setting of inferring gene networks from RNA sequence data, the method is fairly general to any setting in which multivariate count data arises. The method is simple, easy to understand, and seems easy to implement, so I expect it will be popular among practitioners. I would not be surprised if similar methods are already in use, and thus the new theoretic guarantees that this paper contributes will likely make the proposed method popular in practice.
questions: * In the experiments section there are 3 instances where PLNet and VPLN seem to achieve the same AUPR, but only PLNet is bolded. Is this just due to rounding?

* What is the relationship of the proposed method to the method given in section 2.4.2 of Fan, Liao, and Liu (2015) [1]?

[1] An Overview on the Estimation of Large Covariance and Precision Matrices. Jianqing Fan, Yuan Liao and Han Liu. 2015.
https://arxiv.org/pdf/1504.02995.pdf
limitations: Yes.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The authors propose a new algorithm (PLNet) for estimating the precision matrix of a Poisson log-normal (PLN) graphical model for count data. The authors evaluate their method on both simulated and real-world data and find improvements over baseline methods.
strengths_and_weaknesses: Overall I was quite happy with the paper and recommend acceptance.

Strengths:

1. The authors tackle a high-impact problem; rich scRNA-seq datasets are becoming more and more common, and methods for analyzing them are in high demand. Moreover, many works have found that analyzing scRNA-seq datasets after first normalizing and log-transforming the data leads to significant distortions. As such, methods that are able to operate on raw counts are crucial.
2. To my knowledge, the authors' proposed algorithm (as well as the theoretical analysis of it) is novel.
3. The authors demonstrate that their algorithm outperforms naive GGM approaches as well as a PLN approach that optimizes a lower bound to the log-likelihood (as opposed to directly optimizing the likelihood).
4. The writing in the manuscript was clear and I generally found the paper to be well-structured.

Weaknesses:

1. Ideally I would've liked to see another application on real-world data, though given space constraints I understand that may not have been possible to fit in.
questions: 1. Before reviewing this manuscript, I was not familiar with the VPLN model. As such, it wasn't clear to me why PLNet is computationally more efficient than VPLN. It would be great if the authors could provide more details on this.
limitations: The authors addressed the limitations of their work in a satisfactory manner. They did not discuss potential negative societal impact, which is fine for this work (I do not see any potential negative impacts here).
review_title: null

Meta-review: metareview: This paper addresses the problem of identifying a network of interacting entities with applications to genetic regulatory networks. The approach makes use of a Poisson log-normal graphical model structure for count data. The paper shows that the approach has desirable statistical properties such as consistency of the precision matrix estimate. The paper compares the performance to some other methods on various graph structures and presents results on a single-cell RNA sequencing data set.

The reviewers generally found merit in the approach. The clarity of the paper was judged by the reviewers to be good. The suggestion from one reviewer that prior information about the gene regulatory network may be incorporated was welcomed by the authors, though this addition may have an impact on the consistency results. The rate of convergence was found to be root-n and while the practical applicability of that rate for relatively expensive samples such as scRNA-seq is not clear, the method is applicable to a wide range of problems where a sample size that approaches the numbers simulation examples is more feasible. I would strongly encourage the authors to discuss potential limitations including: (1) the interaction between the expense of scRNA-seq data collection and the asymptotics of the consistency results, and (2) the degree to which model misspecification affect scientific conclusions based on parametric inference. 
confidence: Less certain
Decision: Accept