Reviewer response for version 1
The paper introduces an extension of the SPACE (Sparse Partial Correlation Estimation) method, which is used to estimate a gene-gene network (GNN). 
The proposed framework, space-log, relies on the log penalty, which delivers better variable selection performance than LASSO, especially for GGN with hubs. 
The authors also have created a very efficient R package for the proposed method. 
The paper is clearly written, and the proposed method showed promising results for real data analyses. 
I list my questions below:
- In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. 
Since log penalty can handle high dimension low sample size data, can you also include a real application with m larger than n?
- The numerical results are all based on the tuned model using extended BIC, which is one-shot of the result. 
It is better to also include ROC curves reflecting the whole spectrum of the results for a range of tuning parameters.
Minor comments:
- In formula (3), the ‘square root’ should not include Yj.
- In t page 3 section ‘Joint modeling space using lasso penalty: space-lasso’, it is better to include the relationship between \beta_{ij} and \simga_{ij} before making the conclusion that \rho_{i,j} = sign(\beta_{i,j}) \sqrt{\beta{ij}\beta_{ji}}.
- For the log penalty, please also cite ‘Enhancing sparsity by reweighted L1 minimization’.
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