Reviewer response for version 1
In this paper, the authors developed “space-log”, a new method to infer gene-gene network (GGN), by incorporating log penalty into the “space” method. 
The authors compared their method to the original “space” with LASSO penalty and the neighborhood selection (NS) methods, using simulation and real data. 
In general, the description of the proposed method is clear, and the simulation and real application settings made sense. 
However, I believe this paper needs to be revised to (1) provide the rationale for choosing the combination of “space” and log penalty, (2) compare with more state-of-the-art methods, and (3) improve the presentation and writing. 
Here are some specific comments.
- The authors need to discuss why they decided to combine “space” and log penalty for GGN detection. 
What is the benefit of using log penalty over other penalty choices, including concave penalties and other nonconcave penalties such as SCAD, MCP, and TLP? 
The introduction should be extended to include more state-of-the-art methods, such as adaptive LASSO or high-dimensional regression methods with sparse precision matrix estimation.
- Although briefly mentioned gLasso in the introduction, the authors did not talk about this class of methods in the rest of the paper. 
I am curious to see how space-log compares to gLasso and its extensions with nonconcave penalties in simulation and real application (see Fan et al. , 2009). 1
- Based on my understanding, the major benefit of using nonconcave penalties is to reduce the estimation bias of the correlation coefficients. 
I suggest the authors include comparisons based on the coefficient estimation. 
In addition, the authors should provide details about how the precision matrices are simulated. 
Currently, only the simulation methods for its bone structure are provided.
- In conclusion/discussion, the authors should provide more insights or heuristics about why the proposed method performed better than other methods. 
What aspects of the data makes the proposed method favorable? 
Is there any limitation that the users should pay attention to when applying this method in application?
Minor comments:
- The citations in this paper are apparently converted from an author-year citation format. 
The authors need to make changes to the writing to adapt to numbered citation format.
- Presentation and writing issues, for example:
- The authors need to decide if a comma is needed between two subscripts in the notation (e.g. \beta_{ij} or \beta_{i,j} on page 3 left column).
- On page 4, left column, third paragraph, the sentence “The initial paragraph …” only applies to BA model, but not ER model.
- Also, it should be “in the (t+1)th step” instead of “in the (k+1)th step”.
- In the last sentence of this paragraph, it should be “1/m” and “2/m”.
- This is not an exhaustive list of writing issues. 
I suggest the authors proofread carefully.
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