We appreciate your time and the recognition of the strength of our work. We have marked the revision in the color **orange** on the paper.
**W1. What is the principal way of selecting the baseline methods?**
In the updated version of the paper, we have included the principles above in Appendix C.1: The Principle of Selecting Baseline Methods.
As introduced in the Related Work section, existing studies can be broadly categorized into two approaches: statistical methods and deep graph neural network (GNN)-based methods. We collected baselines from both categories.
For statistical methods, we first selected two classical and widely used techniques in the bio-network computing field: WGCNA and ARACNe. These methods have significantly contributed to bio-network studies over many years.
We also included more recently proposed methods, i.e., wTO and LEAP.
Our selection principles were as follows: (1) the method was recently published (and approximately a decade after the above classical methods), (2) it is user-friendly (with outputs compatible with popular analysis packages), and (3) it has been used as a baseline in related bio-network research [1,2].
For GNN-based methods, we applied the same selection principles and criteria.
Furthermore, as this interdisciplinary research represents a newly formulated machine learning task, there are only a few existing works in this area.
Based on these considerations, we selected three methods: GAERF, LR-GNN, and CSGNN.
[1] Davis-Marcisak E F, Deshpande A, et al. From bench to bedside: Single-cell analysis for cancer immunotherapy[J]. Cancer cell, 2021, 39(8): 1062-1080.
[2] Murrow L M, Weber R J, et al. Mapping hormone-regulated cell-cell interaction networks in the human breast at single-cell resolution[J]. Cell systems, 2022, 13(8): 644-664. e8.
**W2. Why did the authors not add or remove methods?**
We believe you may be referring to w/o ablation study of the Patient-M, Graph-M, and Infer-M learning modules. Due to space constraints, we have included the ablation study in Appendix I: Ablation Studies.
In this section, we evaluated and discussed the contributions of individual modules using four cancer datasets. Specifically, we analyzed three variants (GeSubNet-VAE, GeSubNet-VQVAE, and GeSubNet-GAN) based on the deep generative model for Patient-M, two GNN variants (GeSubNet-GCN and GeSubNet-GAT) for Graph-M, and two ablations (GeSubNet-OneStep and GeSubNet-Conca) based on the integration method for Infer-M. Detailed descriptions of these ablations are provided in the appendix.In summary, the results demonstrate that the proposed method consistently outperformed the baselines, achieving the best performance.
**W3. In table 2 how can we know if this is an outlier of the training process or a significant improvement?**
Thank you for your comment. We have performed repeated training to evaluate the methods regarding means with SD, and statistical tests show that this is a significant improvement. We have updated this result in Table 2.
**W4. In line 365 by which statistical measure was the importance ascertained?**
First, we used three graph metrics, CDV, GED, and DCS, to measure the structure differences of the generated network.
Their statistical measures are based on the fundamental properties of the generated network, such as the distinct nodes and edges.
Then, we used \#EBF (**line 370** in the updated paper) and shift rate ($\Delta_{\text{SR}}$, **line 397**) to measure the biological significance. Here we have included a more comprehensive introduction and definition of these measurements in Appendix E: Evaluation Metrics.
**W5. In line 416, could you cite why you can infer the "functional distinctions"?**
We added more citations below for the conclusion sentences in line 416 and its related content in Appendix E: Evaluation Metrics. These citations substantiate the idea that functional enrichment studies often use the number and uniqueness of enriched terms to infer the functional distinction or relevance of specific gene sets.
[1]Ashburner M, Ball C A, et al. Gene ontology: tool for the unification of biology[J]. Nature genetics, 2000, 25(1): 25-29.
[2] Wu T, Hu E, et al. clusterProfiler 4.0: A universal enrichment tool for interpreting omics data[J]. The innovation, 2021, 2(3).
**Q1. Can you expand on why you think your method outperformed the other methods?**
This paper investigates a method and a learning loss function that explicitly infers distinct networks tailored to different patient expression profiles. As noted in the Remark (**line 192**), the loss function in existing methods primarily focuses on common network reconstruction, which often includes irrelevant and noisy gene-gene links. This redundancy may diminish biological significance. In contrast, our proposed method emphasizes subtype-specific gene-gene links, effectively filtering out such redundancies and enhancing biological significance.