GeSubNet: Gene Interaction Inference for Disease Subtype Network Generation
Authors: Ziwei Yang
Zheng Chen
Xin Liu
Rikuto Kotoge
Peng Chen
Yasuko Matsubara
Yasushi Sakurai
Jimeng Sun
Venue: ICLR 2025 Oral (2025)
Keywords: Gene Functional Networks
Disease Subtypes
Bioinformatics
Primary area: learning on graphs and other geometries & topologies
TL;DR: Gene interaction inference for disease subtype network generation

Abstract: Retrieving gene functional networks from knowledge databases presents a challenge due to the mismatch between disease networks and subtype-specific variations. Current solutions, including statistical and deep learning methods, often fail to effectively integrate gene interaction knowledge from databases or explicitly learn subtype-specific interactions. To address this mismatch, we propose GeSubNet, which learns a unified representation capable of predicting gene interactions while distinguishing between different disease subtypes. Graphs generated by such representations can be considered subtype-specific networks. GeSubNet is a multi-step representation learning framework with three modules: First, a deep generative model learns distinct disease subtypes from patient gene expression profiles. Second, a graph neural network captures representations of prior gene networks from knowledge databases, ensuring accurate physical gene interactions. Finally, we integrate these two representations using an inference loss that leverages graph generation capabilities, conditioned on the patient separation loss, to refine subtype-specific information in the learned representation. GeSubNet consistently outperforms traditional methods, with average improvements of 30.6%, 21.0%, 20.1%, and 56.6% across four graph evaluation metrics, averaged over four cancer datasets. Particularly, we conduct a biological simulation experiment to assess how the behavior of selected genes from over 11,000 candidates affects subtypes or patient distributions. The results show that the generated network has the potential to identify subtype-specific genes with an 83% likelihood of impacting patient distribution shifts.

Published as a conference paper at ICLR 2025
GESUBNET: GENE INTERACTION INFERENCE FOR DISEASE SUBTYPE NETWORK GENERATION
Ziwei Yang! Zheng Chen': Xin Liu" Rikuto Kotoge,, Peng Chen', Yasuko Matsubara', Yasushi Sakurai', Jimeng Sun
Bioinformatics Center, Kyoto University, Japan 2SANKEN, Osaka University, Japan NNational Institute of Advanced Industrial Science and Technology (AIST), Japan
*RIKEN Center for Computational Science, Japan
Department of Computer Science, University of Illinois Urbana-Champaige USA yang. ziwei. w 3 kyoto-u. ac. ip {chenz, rikuto88, yasuko, yasssaayyssnssss........ (asusshhssssneennn.o Jsakken, o osaka u...c xin. lin.iiuaisst.. go jp, peng. chen@ jp, jimeng0 wwwiiiinnnni..........i
ABSTRACT
Retrieving gene functional networks from knowledge databases presents chal- lenge due to the mismatch between disease networks and subtype-specific vari- ations. Current solutions, including statistical and deep learning methods, of- ten fail to effectively integrate gene interaction knowledge from databases or ex- plicitly learn subtype-specific interactions. To address this mismatch, we pro- pose GeSubNet, which learns a unified representation capable of predicting gene interactions while distinguishing between different discase subtypes. Graphs generated by such representations can be considered subtype-specific networks. GeSubNet is multi-step representation learning framework with three modules: First, deep generative model learns distinct disease subtypes from patient gene expression profiles. Second, a graph neural network captures representations of prior gene networks from knowledge databases, ensuring accurate physical gene interactions. Finally, we integrate these two representations using an inference loss that leverages graph generation capabilities, conditioned on the patient sep- aration loss, to refine subtype-specine GeSubNet consistently outperforms traditional methods, with average improve- ments of 30.6%, 21. 310%, 20. 1 and 56.6% across four graph evaluation metries, averaged over four cancer datasets. Particularly, conduct biological simu- lation experiment to assess how the behavior selected genes from over 11,000 candidates affects subtypes or patient distributions. The results show that the gen- erated network has the potential to identify subtype-specific genes with an 83% likelihood of impacting patient distribution shifts.
information in the learned representation.
INTRODUCTION
Biological knowledge bases such as STRING (Szklarezyk et al., 2023) and KEGG (Kanehisa et al,, 2024). and wet-lab experimental datasets such as gene expression data are crucial for understanding disease-gens association. While the knowledge bases are comprehensive, they often lack specificity for disease subtypes. This work introduces a deep learning method integrate general knowledge bases with disease-subtype-see sppcie- experimental data to create more targeted knowledge graphs.
Decades of research have generated extensive disease-gen gene association data, compiled into various biological knowledge databases (Goh et al.) [20076] Szklarczyk et al. 22033 Kanehisa & Goto 2000). These databases integrate known and predicted gene interactions, forming gene functional networks that describe how gene behaviors relate to disease processes. They support disease research by interpreting experimental results (Vella et al. (017). facilitating biomarker discovery (Yang et al. 2023), and enabling personalized treatment (Goossens et al. 2015).
"Corresponding authors.

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Breast cancer gene network from STRING database
A mismatch issue between general network and patient group-specific network
Subtype (Luminal A)
8 Sublype (Luminal B)
Subtype C (Basai-Ilke)
Genes of interest (upxdown-regulated)
Other common genes
Disease network
Functional interaction
Potential sub-network
Gene set with consistent behaviors
Unknown relationship
Figure I:
An example illustrating the mismatch issue in cancer gene networks. The BRCA gene network from the STRING database shows general interactions across various subtypes. Although a gene set with consistent behavior leads the discovery of sub-network, this sub-network cannot be directly linked to specific subtypes, such as Luminal A, Luminal B, or Basal-like.
Besides general knowledge bases, there are also in-lab experimental data, such patient gene pression profiles. These experiments filter candidate genes, and the interactions in databases sup- ported by these candidates are considered more relevant to subtypes. However, mismatch exists between generic knowledge bases and experimental data when studying disease subtypes. For in- stance, shown in Figure T, breast cancer comprises multiple subtypes (luminal A, luminal B, and Basal-like), but databases like STRING provide only general gene network for all subtypes. This generalization can lead to misinterpretations of gene behaviors across subtypes.
While bio-researchers have proposed data generation approaches to construct meaningful subtype- specific networks (Zaman al. 2013), they often require extensive in-lab analyses such as pair-wise gene examination among hundreds to thousands of gene candidates. This paper introduces a novel data-driven approach to address this mismatch, automating the integration of gene expression data and knowledge databases to directly generate gene functional networks for various disease subtypes.
Related Work. Existing methods for generating subtype gene networks can be categorized into two groups: statistical and deep learning-based methods. Statistical methods focus on speeding up gene filtering by mining experimental data. These methods employ similarity metrics measure the correlation between genes. High correlations, such as co-expressed genes (Zhang & Horvath, 2005]. are marked as functional interactions. For example, ARACNe (Margolin et al. (2066) uses mutual information to measure expression similarity and removes indirect links with low similar- ity. WGCNA (Langfelder & Horvath 2008) calculates Pearson correlation to support large-scale comparisons, while wTO (Gysi et al. 2018) transforms the correlations into probabilistic measures. However, gene interaction retrieval still prioritizes genes of interest.
few deep learning methods leverage both knowledge databases and experimental datasets. They form disease networks as graphs and embed gene expression data, containing different patient infor- mation, as node embeddings. They set up link prediction and reconstruction using graph neural net- works (GNNs). The newly reconstructed graphs can be viewed as specific networks. Representative methods include GAERF (Wu al. 2021a), which learns node features with a graph auto-encoder and then uses a random forest to predict links. CSGNN (Zhao et al. (2021) predicts gene interactions using both mix-hop aggregator and a self-supervised GNN. LR-GNN (Kang et al., (022) proposes dynamic graph method to gradually reconstruct graph structure, mitigating the constraints of prior general disease network information. Recent works focus on improving the accuracy of gene-gene link prediction (Li et al. 2024 Pang al.) 2024). However, their objective is only to reconstruct general disease-gemt -ene associations, including irrelevant interactions. This approach does not explic- itly learn the distinct gene interactions unique disease subtypes.
Contributions and Novelty. We present new solution for leveraging distinct subtype information from experimental data, i.e., gene expression profiles, to directly infer Gene interactions specific to
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disease Subtype Networks. This leads to GeSubNet, which learns unified representation that can accurately predict prior gene interactions while being able to distinguish different subtypes of disease. Graphs generated by such representations can be considered subtype-specie networks. GeSubNet is a multi-step learning framework with independent data representation learning and integration. The first step uses deep generative model to learn gene expression representations. These representations capture distinct data distributions and can distinguish subtypes in a latent fea- ture space. The second step employs GNN to learn graph representations of prior gene networks. This step ensures GeSubNet captures true gene-gent functional interactions collected in knowl- edge databases. Finally, we integrate the two representations, updating graph representations and inferring subtype-specific gene interactions using reconstruction loss on the gene expression data. Our experiments confirm that GeSubNet can simultaneously generate different subtype networks within a general cancer. The contributions lie in:
Formulating New Gene Problem. We first frame this problem as how to infer gene interactions can help models distinguish subtypes in experimental datasets. We investigate method that automates the integration of gene expression data and knowledge databases, explicitly generating discase subtype networks.
Proposing Automated Data Integration Methodology. GeSubNet is an effective architecture that combines a VQ- VAE and Neo-GNN, achieving average improvements of 30.6%, 21.0%, 20.1%, and 56.6% across three metrics on four cancer datasets. More advanced models can be easily integrated into GeSubNet.
Impacting Broad Biological Relevance. We propose impactful biological evaluations and a new metrie. The experiments involving 11,327 gene evaluations demonstrate that genes selected by GeSubNet are highly related to specific subtypes. We are the first to conduct a simulated exper- iment, termed Knock-out (Bergman & Siegal 2003), to assess how the behavior of genes affects different subtypes. The proposed metric evaluates the reliability of selected gene interactions. The results show that GeSubNet t effectively narrows down key genes.
Integrated Datasets for Cancer Subtyping. We collect physical cancer-gene networks across four knowledge databases and construct machine-learmin learning-ready datasets for experiments and evaluation. We release our datasets with this paper to support continued investigation. The code and data resources are available at:
com/ ChenzRG/GeSualle
2 PRELIMINARY AND PROBLEM SETTING
2.1 BACKGROUND: CANCER SUBTYPE
Cancer is a major public health concern with increasing incidence and leading to mortality. The Na- tional Cancer Institute (NCI) reports that the high costs of cancer care have been projected to grow to $246.6 billion by 2030 (COS) 2023). A key driver of these high costs and morbidity is cancer's inherent heterogeneity. Each cancer type is made up of multiple subtypes, characterized by distinct biochemical mechanisms, requiring specific therapeutic approaches (Balmain et al., 2003). While these subtypes may differ biochemically, they often share similar morphological traits, such as the physical structure and form of the organism (Yang et al.] 2023), complicating precise diagnosis and treatment responses. This complexity highlights the need for deeper research into gene networks specific to cancer subtypes. However, as shown in Figure D current knowledge bases like STRING provide only broad cancer gene networks without distinguishing between subtypes. This limitation in specificity creates gap in effectively targeting treatments based on unique subtype characteris- tics. Our paper addresses this problem by focusing on advancing research and tools that differentiate these subtypes at more granular level.
2.2 PROBLEM SETTING
Definition 1 (Gene expression data). The fundamental entity in gene expression profile data is the individual patient. Each patient profile comprises tens of thousands of genes with measured features.
Let X far (m) m= denote dataset of M patients. Each patient can be represented as N sequence (m)
of gene measures x (m) = {z( _ subtypes for cancer. Each (m) is associated with label y.
(m)) (m)) EN }. Let Y = {y1, U2, ) denotes the set of
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Stepl. Patient-M
Step2. Graph-M
Eq.(1) (1) x();x)
Encoder
Decoder
Link prediction
Dooele
Input network
A
Eq. (2) [(0;w)
Knowledge datahase (e.g. STRING)
Reconstructed expression data
2 T Add
Gene expression data with subtype information
Zp
Parient representaion
Eq (3) x()
negative links
2g
Gene representation
i
Intergration
Updare gene representation and infer gene interactions
nafe
Eineoder
Re-train
Subtype-specifie networks
Discrete larent feature space
Reconstruction
Decoder
update GNN encoder
Step3. Infer-M
Figure 2: Overview: Step Patient-M sets up an unsupervised learning task to generate the patient sample representation (Z,p) from the input gene expression data (X), which can distinguish subtypes. Step 2: Graph-M sets up a link prediction task to train the GNN encoder and decoder, learning the graph representation (Zg) from the input gene graph (9) and expression data (X). Step 3: Infer-M uses an objective function that integrates representations to generate subtype-specific networks. The reconstruction from Patient-M, conditioned the GNN training in Graph-M (go (Zg (9)), refines the graph structure, while ensuring accurate patient profile reconstruction (x((x)
Definition 2 (Knowledge gene nefworks). A gene network, as compiled in knowledge databases, can be represented as general graph G = (V, cross all M patients, where V denotes the set of vertices, corresponding to the genes and & the set of edges representing the gene interactions/links. Here, a link can be represented as Cij (r;, 1y), where i, N.
Problem (Subtype-specific gene network inference). Given a general disease-gent network we assume that it can be decomposed into set of sub-graphs G, = (9) ...... . }, corresponding to Y subtypes. The links, as defined in knowledge databases, are directly transformed into set of edges {0. 1)N 4 Ctj E [0, 1|M, where K.I. denotes knowledge- based initialization for graph struction. We aim to integrate the gene expression profile X identify specific link sets relevant to a given subtype, formalized as F(.) et + {0, 1)((), Notably, these sub sub-graphs are not independent.
Remark. The function F(-) designed by existing methods focusing reconstructing the general graph G. The learned representations only carry information for accurate reconstruction. In contrast, investigate how learn representation from both data sources, one that captures essential information from gene interactions while distinguishing different subtypes. Our investigation is based on the following observation: the onset of complex diseases typically attributed to changes (e.g., perturbations or disruptions) within a limited subset of genes (Goh et al. 2007a).
Formally, given X and knowledge graph G, have (91; G2, .,....,,9yy1. learn unified representation Z with two properties: (i) encode high-quality Z from gene expres- sion profiles X. that is, any (1m)) and (m) should correspond the same patient group ys (ii) enable Z to predict gene-gene interactions in E. For the sub-graphs, we have two hypotheses:
F(X:9), We aim to
Hypothesis-1. The size of the sub- sub-graph should be 19), << |g], in terms of both the node set V and the link set E, while having large margin differences with other sub- uub-graphs.
Hypothesis-2. Gy must maintain physical and biological meaningfulness. This an important metric evaluated in experiments.
3 GESUBNET
3.1 FRAMEWORK
GeSubNet consists of three modules: patient sample representation learning module (Patient-M), graph representation learning module (Graph-M), and network inference module (Infer-M).
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This module sets up cancer subtyping task, aiming to project patient gene expression profiles into a latent representation Zp. which can distinguish subtypes. This is typically an un-
Patient-M:
supervised learning task (Withnell et al. 2021: Yang et al. 2021b 2023). GeSubNes employs a Vector Quantized-Variationall AutoEncoder (VQ-VAE) Van Den Oord et al. 2017) for two pur-
poses: (i) model this discriminative latent space using flexible categorical distribution (Chen
ct al. 2023a), and (ii) to use the decoder as a key component of Infer-M.
Graph-M: This module forms a link prediction task, leveraging both knowledge databases and gene expression data to learn Zg. The goal is to train a well-performed GNN autorencoder, where the encoder learns holistic gene interactions, and the decoder is used generate new graphs. Since we focus on interactions, GeSubNeet employs Neo-GNN (Yun et al.) 2021). which combines structural information with node representations to prevent over-smoothing of node features.
This module involves a novel objective function that integrates Zp and Zg. GeSubNet uses the information from Patient-M,, the decoder, and the reconstruction loss optimize the prior knowledge in the gene network, i.c., the GNN encoder, for generating subtype-specife networks.
Infer-M:
3.2 SUBTYPE GENE NETWORK INFERENCE
Gene Expression Representation Learning Patient-M. Given a gene expression dataset X E RMXN, first encode the gene expression profile to low-dimensional embedding Ze R R D through linear layers with ReLU activation function: Z = (Linarri)a)((X)) where D is the di- mension of Ze We apply Batch Normalization operation prevent overfitting the limited patient gene expression samples. The Z. is then projected along the D-axis into a set of feature vectors Ze E x where S denotes the vector dimension. Then, we project Ze into discrete code- book (Van Den Oord et al. 2017 Chen et al.) 20236). This involves encoding each dimension of gene features into code, resulting in Zp The codebook consists of K latent vectors PI.k. which defines K-way categorical distribution. The projection is conducted using the nearest neighbor search. Then, decoder, consisting of linear layers with ReLU activations, reconstructs the original gene expression profiles, X E R TRMx N
Gene Interactions Representation Learning Graph-M. Given general graphs G represented by an adjacency matrix A and gene expression data X, we learn structural feature representations
X' E ig==a using two MLPs: X' = MLP ( MLP (A.g) X), where the first MLP handles edges and the second handles nodes. Next, we encode X' with A to obtain graph representations Zg E R N DD The GNN decoder computes similarity scores between paired node embeddings by
first computing the clement-wise product of Zg (f) and ZiÍ") The resulting D-dimensional product is then aggregated into single value as the similarity score. Finally, we train a binary classification
where 1 indicates MLP to perform the link prediction task: E. = 1, Similarity Score 2 0.5
0. Otherwise
the presence of a link between node vi and vj. and O indicates the absence of a link. We use the predicted result E. to guide Graph-M in learning prior gene interaction knowledge.
Subtype Network Inference Infer-M. This module integrates information from both Patient-M and Graph-M to optimize the prior cancer network and generate subtype-specific networks. We propose an objective function that uses Graph-M's graph generation capabilities, conditioned on the patient separation loss in Patient-M. GeSubNet follows three independent training phases.
Recall that we first train a well-initialized Patient-M to learn Zp using gene expression profiles X. This captures distinct subtype information through the following loss function:
L( x) = Exg. [log P k
where @ represents the parameters of the encoder and decoder. Then, we implement Graph-M to map predefined gene interactions for given cancer into Zg:
E Σ the log (0))) + (1- he) log(1 - he (w; Z (0)))
C(0:w) = 1
(2)
where 0 and the parameters of the encoder and decoder in the GNNs, and he represents the ground truth for the presence of a gene interaction. After training L(Ø; x) and ((# we first fix the model parameters ø and w, and reconstruct new gene expression profile via matrix multiplication:
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X = Zp Zg" _ The reconstruction error between the integrated X and the original patient gene expression profile is used to optimize the parameters 9 of the graph encoder by:
[( x) Eo (0) log (x
(3)
Here, the graph encoder conditions the reconstruction of patient or subtype-specific gene expression profiles. This ensures that graph representations capture the subtle characteristics each patient's gene expression profile, inferring the newly generated links/interactions more relevant subtypes.
EXPERIMENTS
4.1 DATASET AND PREPROCESSING
Cancer gene expression dataset. We collected the gene expression datasets from the world's largest cancer gene information database, The Cancer Genome Atlas (TCGA) (The Cancer Genome Atlas Research Network 2013), across four cancer types: breast invasive carcinoma (BRCA) (Sharma et 2010), glioblastoma multiforme (GBM) (Urbańska et al.] (014), brain lower grade glioma (LGG) (Forst et al., 2014), and ovarian serous cystadenocarcinoma (OV) (Jayson et al. 2014). De- tailed information can be found in Table and Appendix [B.]
Preprocessing: TCGA collected cancer samples from various experimental platforms with differ- ent patient information, such as gene sequencing results, and lacked alignments. First, removed the unmatched gene IDs across cancer samples to ensure platform independence. Then, we identified and eliminated genes with zero expression (based threshold of more than 10% of samples) or missing values. Finally, we converted the scaled estimates in the original gene-level RSEM (RNA- Seq by expectation maximization) files to FPKM (fragments per kilo-million base) mapped reads data. The detailed data preprocessing pipeline can be found in Appendix B.2
Gene network dataset. We collected gene functional networks corresponding these four cancer types from four well-used knowledge databases, including KEGG (KE) (Kanehisa & Goto 2000), STRING (ST) (Szklarczyk al. 2015), InterPro (Int) Paysan-Lafosse et al. 2023). and Monarch
(Mona) (Mungall et al. 2017).
We searched and downloaded raw network data through website APIs We mapped the gene IDs in the expression dataset to the standard format of Entrez Gene IDs (Maglott et al.) 2010 in the networks. We stored gene interactions with the shared gene IDs across both datasets. Finally, we reconstructed the raw data binary matrix to initialize the gene graph construction. More details of the datasets and preprocessing can found Appendix B.3 and B.4
Preprocessing:
Table 1: Summary of gene expression profile data and gene network data for four cancer types.
Gene Exprcssion Matrix
Gene Network
Knowledge Databases
Cancer
#Subtypes
#Teeatures
#Patients
#Nodes
#Edges
KE
ST
Int
Mona
BRCA GBM
11327
638
146
868
11273
416
102
LGG
3
11124
451
103
345
OV
11324
291
109
159
v
Baselines. We collected baselines from both the statistical methods and GNN-based methods. (1) The statistical methods include WGCNA (Langfelder Horvath 2008). which identifies mod- ules of highly correlated genes using Pearson correlation; wTO (Gysi et al. 2018). which normal- izes correlation by all other correlations and calculates probabilities for each edge in the network; ARACNe (Margolin et al., (206)), which calculates mutual information between pairs of nodes and removes indirect relationships; and LEAP (Specht & Li 2017), which utilizes pseudotime order- ing to infer directional relationships. (2) The GNN-based methods include GAERF (Wu et al.) 2021a), which learns node features with a graph auto auto-encoder and a random forest classifie;; LR- GNN (Kang al., 2022), which generates node embeddings with GCN encoder and applies the propagation rule to create links; and CSGNN (Zhao et al.) 202T), which predicts node interactions using a mix-hop aggregator and self-supervised GNN. More details are provided in Appendix C

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Table 2: Bascline comparison results on GED, DCS, and CDV for the proposed and baselines. GED, DCS, and CDV are subjected to min-max normalization. The best-performing results are highlighted in bold. The second-best results are highlighted in underline.
Method
CT)
BRCA GID
DCS (1)
CDV (T)
GBM (T)
DCS (1)
CDV (T)
LGG
DCS (1)
CDV (1)
ON
DXCS
WOCNA
0.2
20.0
0.03
a.002
0.00
0.822
0.00
ARACNe
0.420002
0.550.00
0.73
0.332
0.7000.0
0.57
0.76 0..44
0.2
0.05
0.00
LEAP
0.491:00
0.4
0.78
0.46 1005
0.45 1001
0.78 0.0
0.46 0.05
0.55 1062
0.27 0.04
0.2 0.00
0.36 1005
0.41004
GABRE
0.5
0..0
0:05
000
0.05
0.05
0:05
0.50
0
0.3
0.36
0
LIGGNN
0.54..085
0:59 0..6
0.82 0.06
0.57 1005
061.1.000
0.75 0.06
0.56 1.066
0:66 1.077
0.22 10.05
0.54 0.06
0:37
082 082.1000
CSGNN
0.6.1...6
0.6 0.00
0.52 1:06
0.65 0.007
0.6.
0.00
0.591.0.6
0.68 10.07
0.33 0.05
0.30.1003
codubee:
0.7
1UN
6.87
073
8MM
9.7
0.7
0.4
0.7
4.2 EXPERIMENT-I: NETWORK INFERENCE
Objective. This experiment evaluates the effectiveness of subtype-specific networks, following our Hypothesis-1: (1) [gly < [g], ensuring the generated network is sparse compared to the original; (2) each subtype network exhibits structural differences from the others.
Setup and Metries. We train GeSubNet for each cancer (the parameter settings can be found in Appendix D) and then evaluate the generated graphs for subtypes on two factors:
Sparsity Assessment: utilize the Coefficient of Degree Variation (CDV) (Pržulj. 2007) to mea- sure the variability in gene nodes within a network. A higher CDV value indicates that most genes have very few interactions (edges). Thus, GeSubNet infers that the network becomes sparser because only few active genes dominate the interactions in this subtype network.
Graph Structural Differences: we employ the Graph Edit Distance (GED) (Gao et al. 2010) and the DeltCon Similarity (DCS) (Koutra et al. 2013 to measure structural differences in gene net- works. GED captures local changes in gene interactions, while DCS evaluates global structural similarities. A high GED value indicates significant differences in gene interactions. Conversely, a high DCS implies high similarity.
Results. Table 2 presents GeSubNet significantly outperforms all baseline methods in terms of GED, DCS, and CDV metries across four cancer types. Compared with the second-best base- line, CSGNN, GuSubNet achieves improvements of
22342....43.... 1% in terms of GED across all four tasks. Additionally, it delivers relative reduction of 29.8% 190.8%/133.55 13.5% 3.5%%/1166%/999..... .6%//193%% in terms of DCS. For CDV, the improvements are 33.4%%/13.7%/11799%% mary, when evaluating BRCA, GBM, LGG, and OV, GeSubNet consistently achieves lower DCS scores and higher GED and CDV scores. This indicates that the generated subtype-specific gene net- works are sparse but structurally unique, i.e they are significantly different from each other. The OV results are apparently unsatisfactory, but this aligns with existing knowledge (Lawler et al., 2017) that OV is challenging cancer type due to the limited available samples (only 291 patients in Table I and the lack of information on their pathogenic mechanisms in existing knowledge databases.
respectively.
sum-
4.3 EXPERIMENT-II: BIOLOGICAL MEANINGFULNESS
Objective. While three graph metrics show the statistical significance of the generated network, this experiment further evaluates their biological relevance, following our Hypothesis-2. (1) Instead of structural differences, we further assess whether each network shows biologically functional differ- ences from other networks. (2) We examine whether the generated networks have the potential to narrow down key genes that contribute more specifically to their respective subtypes.
Setup and Metrics. We hence conduct two experiments as follows:
Gene Ontology (GO) Analyses (Ashburner et al. 2000a): This method counts the number of unique GO terms (under the category Biological Process (Desmedt et al., 2008) associated with the genes in each network. GO terms describe gene functions across biological processes, molec- ular functions, and cellular components, enabling comparisons between gene networks. For ex- ample, if GO(G)) = {A, B, C} and GO(G)) = (A, D, E}. where G and G2 represent two generated subtype gene networks. GO(-) denotes the sets of GO terms for two networks. Here the number of Enriched Biological Functions (#EBF) is 4. i.e.. [B,C, D, E}, since A is the shared GO term. We evaluate GO for each cancer dataset across all baselines. high #EBF value indi- cates greater functional diversity and biological differences between subtypes.
Simulated Gene Knockout (Bergman & Siegal 2003): This is a computational technique that mimics the effects of gene knockout experiments without physically altering the genome. In this
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WGGNA
L2-GNN
CSGNN
GeSub/Net
BRCA
GBM
LGG
OV
Shared
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Cull cgcle smus.
INNA damace renponen. Apoptoric signaling pothway.
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Oermur Jastins Cell oyde anrest Turnr nacros fetto sigraling)
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(DNA damage checkpoint signaling)
Figure 3: The Venn diagrams illustrate the overlap in GO terms resulting from different methods (WGCNA, CSGNN, LR-GNN, and GeSubNet) across four cancers. Shared and unique function items are listed here. A full list is provided in Appendix[Gi We highlight some unique function items that are well-supported by biological evidence in bold.
simulation, gene is either deleted or deactivated to study its role within specific subtype by observing changes in the patient sample distribution. As we described in an observation See. 2 the key genes with significant expression differences form small, limited set (Goh et al. 2007a). which leads to a distribution shift in patient samples during simulation experiments.
Our experiments follow three steps: (I) Rank all genes based on node degree disparities between the generated networks. (2) Group the genes into two sets: a high-ranking gene set and low- ranking gene set, based on a threshold.
(3) Individually simulate the knockout for high-ranking and low-ranking gene sets by transforming their expression values non non-expression level.
To evaluate the results, this paper proposes new metric Shift Rate (AsR) to measure the likelihood of distributional shifts in subtype after set of genes is knocked out. It calculates the average distance between the sample distributions before and after the knockout. We set a threshold (o,) based on the sample spread assess the significance of distance. The ASR is defined by
1 T
ASR
before
k- oi
(4)
n
where I' the total number of knockout tests, n is the number of patient samples within subtype, T; represents an individual patient sample, is a scaling factor (e.g., 1. or L.5) used to adjust the threshold, and oy is the standard deviation of sample distances. Notably, this metric is only used after model training and cannot be involved in modeling training. More details on the simulated
Gene Knockout can be found in Appendix H
Results. Table presents the results of the GO analysis, where our method consistently achieves the highest #EBF value across all datasets. These higher values indicate that the generated networks not only exhibit structural differences but also show functional distinctions from others from a biological perspective (Ashburner et al.) 2000b Wu et al.) (0211b)
Figure presents Venn diagrams of detailed GO analysis for four cancer datasets, highlighting overlaps and unique in biological functions among three selected baselines and our method. We can consistently identify several unique functions across all datasets, while other methods rarely uncover unique functions, even when they achieve a com- parable #EBF. For instance, in the LGG cancer dataset. CSGNN identifies 4 #EBF but finds no unique functions, whereas our method identifies #EBF with 3 unique fune- tions. From biological perspective, our method demon- strates a robust array of enriched GO terms across differ- ent cancers, including pathways like Apoptotic signaling, Wnt signaling, Tumor necrosis factor signaling. and Cell proliferation. These terms represent critical cancer-related biological functions common to many cancers (Aktipis & Nesse 2013), shown in Table 9 in Appendix G For
Table 3: The comparison results on #EBF between GeSubNet and the basclines. Only biological functions with high statistical significance (p-
value < 0.05) are reported.
WEBF(T)
Method
BRCA
GBM
LGG
OV
WGCNA
3
2
2
wTO
4
2
ARACNe
LEAP
3
3
GAERF
3
3
2
IR-GNNN
4
3
3
CSGNN
5
4
GeSubbet
5
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The patient group before simulating gene knockout The patient group after simulating gene knockout
Table: Shift rates (Aua) on knocking out high- and low-ranking genes across different methods
(b)
Metric: Ase
obvious shift
Method
High-ranking genes (t)
Low-ranking genes ())
WGCNA
0.24
0.22
Shilt to other patient groups
wTO
0.24
0.24
ARACNe
0.23
0.25
LEAP
0.28
0.24
GAERE
0.32
0.28
LR-GNN
0.23
0.23
CSGNN
0.34
0.29
GeSubNet
0.88
0.12
Low-ranking genes
High-ranking genes
Figure 4: (a) UMAP visualization of an example showing patient distribution before and after the simulated gene knockout for target subtype. The gray points in the main figure represent the negative control groups (subtypes). The small figures at the bottom left represent the original distri- butions of different subtypes. In the right subfigure, high-ranking genes are knocked out, while in the left, low-ranking genes are knocked out. (b) Table: shift rates (ASR) on knocking out high- and low-ranking genes, found by different baselines. The best results are highlighted in bold.
unique functions, method identifies the "Immune diseases" function in BRCA, which has ident support as being related to breast cancer (MeAlpine et al.] 2012), and the "DNA damage checkpoint signaling" pathway, which is specific to GBM (Cheng et al. 201T).
Figure 4 shows the results of the simulated gene knockout experiments. The subfigure (a) visualizes an example of patient distribution before (red-marked points) and after (green-marked points) the Simulated Gene Knockout in both target and control groups (subtypes). In the left subfigure, there are almost no differences between the before and after distributions for the low-ranking gene set. In contrast, the right subfigure shows significant shift in patient distribution, indicating that the suppression of high-ranking genes has a greater impact.
Figure b)) further provides a quantitative table across 11.327 genes in BRCA. our method achieves the highest ASR for high-ranking genes, with an 83% likelihood of significantly shifting sample distributions. Meanwhile, the 12% AsR for low-ranking genes suggests that our method effectively filters out common genes. Other baselines exhibit substantially lower ASr values for high-ranking genes, ranging from 20%-30%, nearly matching those for low-ranking genes. Notably, while GNN- based methods like LR- GNN and CSGNN achieve comparable results in graph statistical metrics, their biological relevance is lower. This discrepancy arises because their objective functions aim only to reconstruct general disease networks, including irrelevant gene interactions, for all subtype sam- ples. Although gene expression data embeddings result in different graph structures, these methods do not explicitly learn the distinct gene interactions unique to disease subtypes. However, learning a representation that incorporates prior knowledge while explicitly distinguishing patient samples in different subtypes is the key focus of this paper. This simulation experiment further validates the effectiveness of our method and demonstrates that GeSubNet maintains biological significance.
4.4
CASE STUDY
The case study BRCA cancer follows established protocols in bioinformatics gene function stud-
ies (Huang et al. 2009). The analysis workflow is available in Appendix [.] [ and 1.2
Figure shows the gene networks A and B obtained for two BRCA subtypes. We observe that our method can generate gene networks with more distinct gene nodes. The networks show significant differences between the two subtypes, whereas the baselines produce more similar networks.
Tigure[[1) 1) shows the gene expression distribution for the high-ranking and low-ranking gene sets. Different patient groups are marked in various colors to represent the ground truth. In the first col- umn, we observe minimal differences in the expression distribution of low-ranking genes across patient groups. However, significant differences are evident in the high-ranking gene sets, as shown by the noticeable shift in distribution peaks.
Figure ([2) presents expression heatmaps for the top three genes in both the high- and low-ranking gene sets. For the high-ranking set, the genes are ERBB2, CCNA2, and CCNEI, while the low- ranking set includes HHIP, MAPKI, and STK4. The high high-ranking genes exhibit large differences in expression across subtypes, reflected by distinct color variations corresponding to the labels.

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GeSubNet
CSGNN
WGCNA
Network
less differences
larger differences
Network
GED (t): 0.79 DCS (L):
GED (1): 0.66
GED (t): 0.38
DCS (1): 0.52
(L):
CDV (1): 0.75
CDV (1): 0.64
CDV (1): 0.44
Figure The obtained gene networks for two BRCA patient groups (subtypes).
(1)
HHIP
MAPK1
STK4
100
Expression distributions of low-ranking genes
Patient group ground truth
Expression heatmaps of the top-3 low-ranking genes
ERBB2
CCNA2
CCNE1
-44
00
Expression distributions of high-ranking genes
Patient group ground fruth
Expression heatmaps the top-3 high-ranking genes
Figure 6: (1) expression level distributions and (2) the expression heatmaps the top-3 genes from the high-ranking and low-ranking gene sets among different patient groups.
CONCLUSIONS
This paper introduced GeSubNet, a framework for inferring discase subtype-specific gene net- works. GeSubNet includes sample and gene embedding learning modules that capture the charac- teristics of both patients and the prior gene graph. These embeddings then utilized to reconstruct the input gene profile in the network inference module. This approach incorporates patient group information into the updated gene embeddings, enabling more accurate gene network inference spe- cific to patient groups. In general, we explored method for group-specifir gene network inference on real-world clinical data. Importantly, we demonstrated the reliability of SubuNet through series of biological validations. We believe that continued investigation will bridge computational and biological sciences, advancing the understanding of diseases and foundational gene roles.
ACKNOWLEDGMENT
This work supported by JSPS KAKENHI Grants-in-Aid for Scientific Research Number 24K20778 and 25K03231, JST CREST JPMICR23M3, NSF award SCH-2205289, SCH-2014438, IIS- IIS-2034479, and AIST pasec budget projects of "Research DX Platforms". This paper is based on results obtained from the project, "Research and Development Project of the Enhanced infrastructures for Post 5G Information and Communication Systems" (JPNP20017), commissioned by the New Energy and Industrial Technology Development Organization (NEDO).
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Appendix
CONTENTS
Notations
16
Dataset
16
B.
Gene Expression Data
16
B.2
Preprocessing of Gene Expression data
16
B 3
Gene Network Data
17
B.4
Preprocessing of Gene Network Data
17
Baselines
18
The Principle of Selecting Baseline Methods
18
Baseline Methods
18
Hy Hyperparameter Setting
19
Computational Requirements
19
Evaluation Metries
19
GO Function Enrichment Analysis
20
G.1
GO (Gene Ontology) and Biological Process
20
G.2
GO Function Enrichment Analysis Results
H
Simulated Gene Knockout Experiment
23
Workflow
23
H.2 Shift Rate
23
Case Study
24
Breast Invasive Carcinomal
24
1.2 Experiments and Analysis Protocols
24
J Ablation Studies
25
K Prior Graph V.S. Newly Generated Graph
26
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A
NOTATIONS
All the mathematical notations and explanations used in the paper are summarized Table
Table 4: Mathematical notations and explanations.
Notations
Explanations
M
Number patients
N
Number of genes
X
Longitudinal gene expression data for patient m Set of patient groups
Y
9(V. 8)
Gene network represented as graph Vertex (or node) representing genes in G Set of edges representing associations between genes in G Sub-graph for patient group y Reconstructed gene network
Oy Eny G
F(-)
Function to generate sub-graphs from edge information Function representing the model with parameters
fo
Cjj Z. Zp. Zg
Edge between gene and gene
Lower-dimensional feature representation
B DATASET
B.1 GENE EXPRESSION DATA
Gene expression refers to the process by which information from a gene is used to synthesize func- tional gene products, typically proteins. This process is tightly regulated and varies between cell types, tissues, and environmental conditions, such as the tumor microenvironment (Brazma & Vilo, 2000). By measuring gene expression levels, researchers can determine the activity of specific genes within a cell or tissue at any given moment.
Gene expression data has a long history been used in cancer research (Zhang et al., 1997) because cancer is driven by the dysregulation of cellular processes, which often manifests in abnormal gene expression patterns. High-throughput technologies, such as RNA sequencing (RNA-Seq) and mi- croarryys, gather patient gene expression profiles and simultancously enable large-scale measure- ment of gene expression across thousands of genes (Liang Pardee (003). Gene expression data allows researchers to study the molecular mechanisms hidden deeply in tumor development and progression.
The gene expression data used in this study collected from The Cancer Genome Atlas (TCGA) (The Cancer Genome Atlas Research Network 2013). obtained through the world's ' largest cancer gene information database Genomic Data Commons (GDC) portal (Grossman et al.) 2016). All candidate patient samples were generated across various experimental platforms from cancer samples before treatment. For the cancer research community, is common for available data be contributed from various cancer study projects and institutions. As a result, the data are typically generated from different assay platforms. This non-uniformity of assay platforms introduces tech- nical variations, such as differences in experimental protocols. These inherent batch effects pose challenge as they can significantly impact downstream model training and any further analysis.
B.2 PREPROCESSING OF GENE EXPRESSION DATA
To ensure platform independence, we initially removed the cross-platform lost genes. For the gene expression (transcriptomics) data generated from the Hi-Seq platform, we converted the scaled es- timates in the original gene-level RSEM (RNA-Seq by expectation maximization) files to FPKM (fragments per kilo-million base) mapped reads data. We initially identified and removed all non- human expression features for the remaining data generated from the Illumina GA and Agilent array platforms. Subsequently, we applied a logarithmic transformation to the converted data. To elimi- nate potential noise, identified and eliminated features with expression levels (based
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threshold of more than 10% of samples) missing values (designated as N/A). Table 5 describes the details of all experimental cancer gene expression datasets.
Preprocessing pipeline in R (Ver.4..1)::
(1) Data Import: Gene expression data were loaded after download.
data <-
read.
seeneeeeprression.dattt csv")
(2) Filtering Low-Quality Samples: Samples with a low number of expressed genes were removed using default cutoff based counts per million (CPM) values calculated with the edgeR pack- age Robinson et al. 2010).
keep <- rowSums (cpm (data) 1) >= 10 filtered.data <- data [keep, ]
(3) Normalization: To account differences sequencing depth across samples, normalization was performed using the TMM (Trimmed Mean of M-values) method from the edgeR package.
norm_factors <- calcNormFactors (filtatt (filtered.data)
normalized.data <- cpm (filtereddddaa, 1og=FALSE,
normalized. lib. siweii.ssiieiiaes. sizes=TRUE)
(4) Batch Effeet Correction: To minimize batch effects arising from non-uniform experimental protocols, the 'ComBat' function from the SVA package (Leek et al. 2012) was applied to remove unwanted variation across different platforms and projects.
corrected data <- ConBat (dat-normal wet.mmaaiidddddddee bat btw.hh-aaacciifo.f........
(5) Log Transformation: The gene expression data were log-transformed to stabilize variance across genes.
log_data <- 1og2 (normalized.data 1)
(6) Missing Data Imputation: Missing expression values were imputed using the 'impute' function from the impute package (T et al. 2022
imputed.data <- impute. knn (log.data) $data
B.3 GENE NETWORK DATA
To obtain refined and coherent prior gene networks, we curated comprehensive dataset by amalgamating information from diverse sources, including KEGG (Kanehisa & Goto 2000).
STRING (Szklarczyk et al. 2015), InterPro (Paysan-Lafosse et al., 2023). and Monarch (Mungall al. 2017). These repositories collectively provide information on a broad spectrum gene teraction corroborated by evidence from high-throughput lab experiments, co-expression analyses, genomic context predictions, disease-related gene pathways, and previously published knowledge.
B.4 PREPROCESSING OF GENE NETWORK DATA
Our detailed preprocessing follows: We initiated the network construction process by retrieving re- lated gene information through database APIs for a specified target cancer entry available in the databases above. To ensure uniformity in gene identifiers across disparate datasets, we harmonized gene IDs to the standard format of Entrez Gene IDs (Maglott et al. 2210)). Subsequently, fied and included common genes across all database sources as candidate nodes for constructing the prior network. Next, we retained common gene-gene associations obtained from multiple databases for each candidate node pair as the final edges to be preserved. Concurrently, isolated nodes were systematically removed from the network. During this curation of edges, we implemented two distinct screening strategies to elucidate two types of networks with edges embodying distinct cor- relation properties: (1) we identified edges denoting that the proteins are integral components physical complex, denoted edges of Type I; and (2) retained edges indicative of functional and physical protein associations, denoted as edges of Type II. This approach enhances our prior gene network by capturing diverse aspects of gene relationships and interactions. Table 6 describes the details of all experimental cancer gene network datasets. KEGG, STRING, InterPro, and Monarch abbreviated as KE, ST, Int, and Mona, respectively.
identi-
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Table 5: Descriptions of four cancer gene expression datasets.
Raw Transcriptomics
Gene Expression Matrix
Cancer
#Gene
#Patient
#Group
Sample size
Feature size
BRCA
19537
638
5
{320, 124, 119, 54, 21
11327
GBM
17455
416
5
(125, 111, 80, 68, 32)
11273
LGG
16245
451
{213. 151, 87)
11124
OV
17226
291
4
(81, 76, 68. 66)
11324
Table 6: Descriptions of the four cancer gene network datasets.
Data Source
#Edge (Type I)
#Edge
Cancer
#Node
(Type II)
KE
ST
Int
Mona
BRCA
V
146
289
579
GBM
102
75
128
LGG
V
V
103
206
139
OV
109
46
95
C BASELINES
C.I THE PRINCIPLE OF SELECTING BASELINE METHODS
We collected baselines from both statistical methods and GNN-based methods. For statistical meth- ods that do not involve neural networks, first included two of the most classical and widely used methods in the bio-network computing field: WGCNA (Langfelder & Horvath] 2008) and ARACNe (Margolin et 2006). These methods have continually contributed bio-netwon stud- ies for many years.
In addition, we want include more recently proposed methods in this category. Our selection principles were as follows: (1) the method was recently published (and approximately decade after the above classical methods), (2) provides open-source code (available on platforms such as GitHub), (3) it is easy use (with outputs compatible with popular analysis packages), and (4) it has been used as a baseline in related bio-network research. Based on these criteria, we selected two methods, wTO Gysi et al. 2018) and LEAP (Specht & Li 2017).
For the GNN-based methods, our principles aligned with the above five lines for selecting newly proposed statistical methods. We selected three methods (i.e., GAERF (Wu et al., (021a). LR- GNN (Kang et al. (022). and CSGNN (Zhao et al. 202I)) that meet these principles.
C.2 BASELINE METHODS
(1) Weighted Gene Co-expression Network Analysis (WGCNA) [Lanffelder & Horvath, 2008
utilizes Pearson correlation to identify modules of highly correlated genes, where genes within the same module are likely be functionally related involved in similar biological processes. (2) Weighted Topological Overlap (wTO) (Gysi et al. 2018) normalizes the chosen correlation by all other correlations and calculates a probability for each edge in the network. (3) Algorithm for the Reconstruction of Accurate Cellular Networks (ARACNe) (Margolin et al. (2006) calculates the mutual information between pairs of nodes and then removes indirect relationships during network building. (4) Lag-based Expression Association for Pseudotime-series (LEAP) (Specht & Li) 2017) utilizes pseudotime ordering to infer the directionality between genes the network. (5) Graph Auto-encoder and Random Forest (GAERF) (Wu et al., 2021a learns features of nodes by a graph auto-encoder and concatenates features two nodes as input for the random forest clas- sifier. (6) Link Representation-Gree
Neural Network (LR-GNN) (Kang et al. 2022) generates embeddings using a GCN encoder and then applies a propagation rule to create link representations for predicting associations in networks. (7) Contrastive Self-supervised Graph Neural Network
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Table 7: Hyperparameter sensitivity experiment. The best-performing results are highlighted in bold, and the checkmark indicates our choice of the optimal settings.
Hyperparameters etrics
GED (1)
DCS (L)
CDV (1)
Latent Dim 16
0.76
0.49
0.74
Latent Dim 32 (V)
0.78
0.47
0.75
Latent Dim 64
0.79
0.48
0.73
#Code Book 16
0.72
0.51
0.68
#Code Book = 32 (V)
0.78
0.47
0.75
#Code Book 64
0.75
0.54
0.63
Batch Size 16
0.76
0.48
0.73
Batch Size 32 (V)
0.78
0.47
0.75
Batch Size = 64
0.77
0.49
0.68
(CSGNN) (Zhao et al. 2021) predicts node interactions in networks by employing a mix-hop aggre- gator and contrastive self-supervised GNN. WGCNA, wTO, ARACNe, and LEAP are well-used traditional methods that use only non-graph gene expression data as input, while GAERF, LR-GN LR-GNN, and CSGNN are deep learning-basse
methods that use known paired integrations or networks as input. These methods are reported to have competitive performance for similar tasks like molecu- lar interaction prediction. supplementary data, such sequence data, is available.
also worth noting that these methods tend perform better when
D HYPERPARAMETER SETTING
We conducted parameter sensitivity experiments to determine the optimal hyperparameters. The results are presented in Table 7 Overall, the findings indicate that the model's performance is not significantly affected by changes in the hyperparameters.
E COMPUTATIONAL REQUIREMENTS
Table 8: The computational requirements of the proposed method, including both runtime (training and inference time) and memory usage, across different cancer datasets.
Dataset
Training Time (sec)
Inference Time (sec)
GPU Memory Usage (MB)
BRCA
6.23 0.03
2.21
0.05
4393
152
GBM
3.64 : 0.04
1.44 0.07
2764
117
LGG
5.96 0.03
0.04
3834 122
3.45 0.04
1.25 0.04
2583 108
Pan-cancer
454.47 12.2
142.86 5.2
15893 733
We evaluated the computational requirements of the proposed method, including runtime (training and inference time) and memory usage, across four cancer datasets. While cancer patient gene expression datasets typically contain hundreds of patients for each cancer type, we assessed the method's ''s scalability by conducting additional test using the TCGA Pan-Cancer expression dataset based on the BRCA graph. This dataset includes 8,314 patient samples and is one of the largest pan- cancer datasets. The results summarized in the Table g We find that the computational require- ments of the proposed method are manageable for real-world cancer datasets and scale effectively larger datasets with more patient samples.
F EVALUATION METRICS
(1) Graph Edit Distance (GED). GED (Goo et al. 2010) measures dissimilarity between graphs by quantifying the minimum cost required to transform one graph into another through a series edit operations, such adding deleting nodes and edges and modifying node edge attributes. GED
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between two gene networks N1 and N₂ is defined as: NE) min, D(a,)eer c(u, e). Here иT a set of edit operations. typically represented as a set of pairs (u, where u is node in N1 and v is a node in N2. This set represents the optimal alignment or correspon- dence between nodes in the two networks. c(u,v) is the cost associated with aligning nodes and depending
factors such as node attributes, edge attributes, or the type of edit opera- tion. We calculate the overall GED among n inferenced networks as: N2, N,) - w[n-I] DE= GED(N,,
(2) DeltCon Similarity (DCS). It is similarity score calculated through the DeltCon algo- rithm (Koutra et al. (2013). DCS quantifies the structural similarity between two graphs by com- paring the influence of nodes across these graphs. It relies on the computation of the influence matrix derived from the graph Laplacian. The similarity is based on how the node influences the change in values between the two graphs. DCS mathematically defined as: G2)
(V* (Ta, (i.5) Ic, (i.)))) where N is the number of nodes in the graphs, and Ia, (i, and Ta (i,5) represent the influence of node i on node j in graphs G1 and G2 respectively.
1 1- Ei=1
(3) Coefficient of Degree Variation (CDV). The degree distribution of gene network represents the frequency distribution of node degrees, indicating the number of interactions with each gene. In other words, this variation in connectivity suggests that the network's degree distribution implies that certain genes are more central or connected than others, and these central genes may have crucial roles in defining or influencing specific cancer subtypes. CDV (Pržulj 2007) also decreases as the
average degree (k) of the network increases. CDV defined as: CDV
+ EE (k.
AVN
R-
Here, N is the total number of nodes, k; is the degree of node and i is the average degree.
(4) Number of enriched biological functions (#EBF). Corresponding to the differences in graph properties of gene networks, we also explore their biological significance. A commonly used method for this is functional enrichment analysis, which identifies biological functions, pathways, and molecular activities that are overrepresented within gene set when compared a random selection of genes with a similar size and degree distribution from the genome. In our study, we performed Gene Ontology (GO) enrichment analysis using the R package clusterProf ler (Ashburner et al., 2000a), which leverages data from databases such as KEGG and GO to identify enriched biological terms. greater degree of enrichment suggests that the network exhibits more meaning- ful gene interactions than would be expected by chance. This unique enrichment across subtypes implies that the gene networks represent biologically significant interactions, where genes within specific cancer subtype networks are functionally connected tional diversity between two gene networks, we conducted an experiment using GO to count the number of unique GO terms associated with the genes in each network. Specifically, we used the enrichGo () function from clusterProfiles to map the genes from both networks to their corresponding GO terms. The compareCluse csstarrellltrerrre () function was applied to compare the sets of GO terms associated with each network and to identify differences, focusing on the number of enriched biological functions. To quantify the differences, we calculated the number of enriched biological functions (#EBF) using the symmetric difference between the sets of GO terms. Math- ematically, this is represented as: #EBF = (GO(S)) GO()2)) U (GO(G2) GO(G))). This operation captures the unique functions present in one network but not another. Enrichment was evaluated based on statistical significance, where the biological functions with a p-value < 0.05 were reported. A higher #EBF indicates that the networks capture different biological processes or molecular functions, potentially reflecting the underlying biological differences between the net- works' contexts.
a group. To evaluate the func-
G GO FUNCTION ENRICHMENT ANALYSIS
G.1 GO (GENE ONTOLOGY) AND BIOLOGICAL PROCESS
Gene Ontology (GO) Ashhurner et al. 2000a is comprehensive and standardized framework for annotating genes based on their functions in biological contexts. It provides a structured vocabulary to describe the roles of genes in three broad categories:
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Biological Process (BP): This category defines the biological objectives events that the gene products are involved in. BP terms focus on cellular functions that go awry in diseases like cancer. It includes essential processes such "signal transduction", "cell cycle regulation", "immune response", and "metabolic processes".
This category defines the cellular locations where the gene products carry out their functions. CC terms focus on the spatial aspect of gene activity. Examples include terms like "cytosol", "nucleus", "mitochondrion", and "plasma membrane".
Cellular Component (CC):
Molecular Function (MF): This category outlines the biochemical activities of the gene product. MF terms focus on how genes contribute to cellular machinery on a molecular level. Examples include terms like "ATP binding", "enzyme activity", and "protein binding".
The Biological Process (BP) category is of particular relevance to cancer research because it di- rectly reflects the underlying mechanisms that drive cancer development and progression and, there- fore, serves as a suitable representative class for cancer-related GO terms (Desmedt et al. (008).
Identifying disruptions in BP terms related to cancer mechanisms can also help guide therapeutic strategies. For instance, drugs targeting cell cycle checkpoints, such as Dyclin-dependent kinase inhibitors, those promoting apoptosis, like Bel-2 family inhibitors, are being developed specif- ically correct or mitigate BP-related dysfunctions (Shapiro 2006 Ashkenazi et al.) 2017).
G.2 GO FUNCTION ENRICHMENT ANALYSIS RESULTS
Table 9 presents the enriched Gene Ontology (GO) terms associated with various biological func- tions across four cancer types (BRCA, GBM, LGG, and OV), as identified using different methods in the GO analysis of Experiment II. The Venn diagrams in Figure illlstratee the overlaps among the results from the different methods. Due to the complexity of comparing multiple methods, we present four-way Venn diagram focusing on four selected methods (WGCNA, CSGNN, LR-GNN, and GeSubNet) for clarity.
GeSubNet findings:
GeSubNet shows robust array of enriched GO terms across different
cers, including:
Apoptotic signaling pathway: series of biochemical events leading to programmed cell death, which is essential for eliminating damaged unwanted cells and maintaining tissue homeostasis. Dysregulation of apoptosis is a hallmark of cancer.
Wnt signaling pathway: A network of proteins involved in cell signaling that regulates important processes such as cell proliferation, migration, and differentiation. Aberrant Wnt signaling is often implicated in cancer development.
Tumor necrosis factor signaling: A signaling pathway that can induce inflammation, apoptosis, or cell survival, depending on the context. involved in various aspects of cancer biology, including tumorigenesis and immune response.
Cell proliferation: The process by which cells divide and multiply, essential for growth and tissue repair. In cancer, deregulated cell proliferation leads to tumor growth and cancer progression.
This set of terms encompasses a range of crucial cancer-related biological functions shared by most cancers. This indicates that the resulting gene network maintains physical and biological meaning- fulness, i.e,, the backbone consists of genes involving the main cancer progression.
The proposed method identifies a broader range of distinct GO terms compared to other methods, and the GO term set identified by GeSubNet constitutes a superset of the terms determined by different methods.
Comparison:
For instance, in BRCA, WGCNA and CSGNN identify terms primarily focusing cell cycle reg- ulation, DNA repair, and apoptosis. wTO and ARACNe report similar functionalities with notable overlaps. GAERF and LR-GNN overlap more with the proposed method but still do not capture as many terms as the proposed method. The proposed method's 's overlap with other approaches sig- nificant, particularly regarding Cell cycle arrest (common in most methods), and Apoptotic signaling pathways (reported by several methods). However, the proposed method finds unique terms, such as immune diseases in BRCA,
cancer pathways such as DNA repair (present in all methods),
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Wnt signaling pathway. Tumor necrosis factor signaling. Cell proliferation
DNA repuir. Apuptotic signaingg pullway
Regulation cell migration.
DNA repair, Apoptotic signaing pathway
Apoptotic signaling pathway. Cell proliferation
Apuptotic signaing puthway
Apoptotic signaling pathway, Cell proliferation
DNA repuir. Apoptotic signaling pathway, Wnt signaling sallng pathway, Cell proliferation
Apuptotic signaling pathway,
DNA repair
DNA repair.
DNA repair.
DNA repair.
DNA repair.
OV
Table 9: Detailed enriched GO terms across four cancer tasks resulting from different methods.
Wnt signaling pathway. Notch signaling pathway. Tumor necrosis factor signaling. Cell proliferation
Wnt signaling pathway, Regulation cell migration
Regulation of migration, Wnt signaling pathway
Cell cycle arrest, Wnt signaling puttway, Regulation of cell migration
Call cycle arrest. Apoptotic signaling pathway, Wnt signaling pathway, DNA repair
Call cycle arrest, Apoptotic signaling puthway,
Wht signaling pathway, DNA repair
Wht signaling pathway
Cell cycle arrest, Wnt signaling pathway, DNA repair
LGG
DNA damage check opoint signaling
DNA damuge response, Apoptotic signaling pathway
DNA damage response, Apoptotic signaling pathway, Tumor necrosis factor signaling,
Wnt signaling pathway DNA damage response. Tumor necrosis factor Signliin,
DNA damage response, Apoptotic signaling pathway, Wnt signaling pathway
Wnl signaling palhway, DNA damage response, Apoptotic signaling pathway, Cell proliferation
DNA damage response, Apoptotic signaling pathway, Wnt Wit signaling patwway, Cell proliferation, Tumor mecrosis factor signaling
DNA damage response. Apoptotic signaling pathwuy;
W signaling pathway. Tumor necrosis factor signaling, Cell protiferation.
Wnt signaling pathway.
DNA damage response, Wnt signaling pathway, Cell proliferation
Cell cycle arrest,
Cell proliferation
GBM
Tumoor necrosis factor signaling. Cell proliferation
Apoplotic signaling pathway, Regulation of cell mi migration, Wat signaling pathway
Apoptotic signaling pathway, Regulation cell migration
Apoptotic signaling pathway, Regulation of cell migration
Wnt signaling pathway, Apoptotic signaling pathway,
Regulation cell migration
Wnt signaling pathway, Apoptotic signaling pathway, Regulation of cell migration. DNA damage ge response
DNA repair. Cell cycle arrest, Apoptotic signaling pathway
Cell arrest. Apoptotic signaligg pathway, Wnt signaling pathway.
Regulation of cell migration, Immune discases,
Wat signaling pathway
Cell Call cycle arrest, DNA repair,
Cell cycle arrest.
Cell cycle arrest,
Call cycle arrest,
Cell cycle arrest
Call cycle arrest,
DNA repair,
DNA repair,
DNA repair.
DNA repairs
DNA repair,
DNA repair,
BRCA
Method
WGCNA
ARACNe
LEAP
GABRF
LR GN-
CSGNN
Proposed
WTO
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DNA damage checkpoint signaling in GBM, and the Notch signaling pathway in LGG. They absent in other method's 's results, yet evidence has proven their relevance to cancers.
H SIMULATED GENE KNOCKOUT EXPERIMENT
H.1 WORKFLOW
Step 1: The simulation begins by ranking all genes based on node degree disparities calculated from the connectivity matrices of the sub-networks. Node degree is quantified as the number of direct connections each gene has to other genes within the network, serving as a measure of its centrality and influence across different cancer subtypes. To derive the connectivity matrices, we analyze the interactions between genes, where each gene is represented as node and each interaction as an edge. The degree of each node is then computed to identify highly interconnected genes.
Step 2: After ranking, we categorize the genes into two sets: a high-ramking gene set, which includes genes exhibiting the largest degree disparities (above defined threshold based on node degree vari- ance), and low-ranking gene set, composed of genes with minimal degree differences (below the same threshold). Using node degree variance as threshold ensures our classification is statistically grounded. This method isolates genes that play critical roles in the network dynamics.
Next, we individually simulate the knockout of genes within the high-ranking and low- ranking gene sets. This process involves transforming their expression values to a baseline non- expression level, which is defined as either zero or predefined low expression value (such as the mean expression level of the lowest 10% of genes). This transformation mimics the functional loss of these genes. For each gene target in the selected sets, we systematically replace its expression value in the patient samples with the baseline non-expression level.
Step 3:
To ensure robustness and statistical validity, we repeat the simulations multiple times, typically run- ning each simulation for predetermined number of iterations (e.g.. 100 or 1000). Each simulation involves the random selection of a subset genes from the respective gene set. For the random selection, define the number of genes be included in each subset based total genes in the gene set. For instance, we set p(select) to 10%, which means we select 10% each itera-
fraction of the
of the genes from the high-ranking gene set and 10% from the low-ranking gene tion. This approach allows us to assess the impact of knocking out varying combinations of genes while maintaining consistent sample size across runs. The random selection is performed using a uniform sampling technique to ensure that each gene has an equal chance of being included in the knockout simulation for that run. After each knockout simulation, we record the changes patient distributions regarding the Shift Rate (SR).
H.2
SHIFT RATE
The shift rate measures the likelihood of sample groups shifting significantly after set of genes is knocked out. It accounts for the average distance between samples within a patient group before and after the knockout and compares this distance to adaptive threshold based on the spread (standard deviation) of samples. Let the distance between a sample within given group before gene knockout, denoted as 2 a.before, and after gene knockout, denoted as xalter be expressed as ||zchefiee ..ffer]l. The spread of samples within the group before knockout in knockout test is quantified by the standard deviation σ, of their distances to the centroid of the before group. The shift rate (SR) is defined as: ASR = 1 m Σ ( E ||z.before - = > k (-a))) Where m the total number of knockout tests, n is the number of samples within the group. σ, is the standard deviation of the distances between the samples before knockout and the centroid of the group in knockout test j. and & is a scaling factor (c.g., 1.0 or 1.5) used to determine the threshold for considering a shift.
Shift Rate:
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1 CASE STUDY
1.1 BREAST INVASIVE CARCINOMA
Breast Invasive Carcinoma, commonly called BRCA, holds significant position in cancer research due to its prevalence and clinical importance (Sharma et al.) 2010). BRCA represents the most common form of breast cancer, accounting for substantial portion of cancer-related morbidity and mortality worldwide. Moreover, it is a heterogeneous disease with diverse molecular subtypes, each with distinet clinical behaviors and therapeutic responses. This molecular complexity and clinical diversity make it an ideal candidate for investigating gene networks and deciphering the intricacies of cancer biology. Therefore, in cancer studies, BRCA serves a cornerstone. Insights gained from BRCA research have huge implications for cancer biology and precision oncology, extending beyond breast cancer to other malignancies.
BRCA Subtypes. Within the used BRCA dataset are various molecular subtypes (patient groups). They are identified based on distinct genetic alterations and clinical features. These subtypes include luminal A, luminal B, HERZ-enriched, basal-like, and normal-like subtypes, each characterized by specific gene expression patterns and clinical behaviors (Orrantia-Borunda et al. 2022). We give brief overview of these subtypes:
Luminal A: This subtype is characterized by the expression of estrogen receptor (ER) and/or progesterone receptor (PR) and low levels of the HER2 protein. Luminal A tumors typically have a favorable prognosis and are often responsive to hormone-bese based therapies.
Luminal B: Luminal B tumors also express ER and/or PR but may have higher proliferation markers such as Ki-67 levels (Sobecki et al., 2017). They can divided into luminal B HER2- positive SER/PR-positive HER2- (RER--positive) and luminal B HER2-negativ (ER/PR- -positive,, HER2- negative) subtypes. Luminal B tumors generally have a poorer prognosis compared to luminal A tumors.
HER2-enriched: HER2-enriched tumors overexpress the HER2 protein without expressing hor- mone receptors neg/avee HER2-positive). They are typically aggressive and associated with higher risk of recurrence. Targeted therapies directed against HER2, such as trastuzumab (Herceptin), are often effective in treating HER2-enriched tumors.
Basal-like: Basal-like tumors are characterized by the absence of hormone receptors (ER/PR- negative) and HER2 amplification (HER2-negative). They often display features similar to basal/myyoepithelial cells of the mammary gland and associated with poor prognosis. Basal- like tumors are frequently referred to as "triple-negative" (Chacón & Costanzo 2010) breast cancers due the lack of expression of ER, PR, and HER2.
Normal-like: Normal-like tumors have gene expression profiles resembling normal breast tissue. They are less common and less well-defined than other subtypes, and their clinical significance is not fully understood.
1.2 EXPERIMENTS AND ANALYSIS PROTOCOLS
We briefly introduce the background and application cases of the experiments and analysis protocols in the biological validation.
Gene Expression Distribution Analysis. This analysis involves examining the distribution of gene expression levels across different experimental conditions or patient groups to visualize the dis- tribution of expression levels for genes. This analysis has been extensively used in cancer research to explore the expression patterns of key oncogenes and tumor suppressor genes across different cancer types and stages. In studies of cancer patients, researchers may compare the expression distributions of oncogenes and tumor suppressor genes between tumor samples and adjacent normal tissue sam- ples. Differences in expression distributions may indicate dysregulation of these genes in cancer. For instance, gene expression distribution analysis was employed to investigate the expression levels of TP53, well-known tumor suppressor gene, in various cancer types (Olivier et al. 2010). This analysis revealed significant alterations in the distribution of TP53 expression in different cancer cohorts, showing its potential role diagnostic or prognostic marker in malignancies.
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Differential Gene Expression Analysis. Differential gene expression analysis has been stone of transcriptomic studies. This analysis compares gene expression levels between different experimental conditions sample groups to identify significantly upregulated or downregulated genes. Statistical tests such as t-tests or non-parametric tests are commonly used. For example, cancer patients' and healthy controls' gene expression profiles be compared to identify dys- regulated genes in cancer. Genes with significant differences in expression levels may be further investigated as potential biomarkers or therapeutic targets. For example, researchers performed dif- ferential gene expression analysis on RNA-seq data from Alzheimer's s disease patients and healthy controls (Twine al., 2011]. This analysis identified panel of differentially expressed genes im- plicated in neuroinflammation and synaptic dysfunction, showing molecular pathways associated with Alzheimer's disease progression.
J ABLATION STUDIES
In this section, we introduce the ablation studies. We designed the ablations and model variants for each module. This to verify the effectiveness of the proposed method's core concepts across a diverse set of deep structures and training strategies.
Firstly, we executed experiments utilizing various deep generative models to learn sample embed- dings in the sample embedding learning module. The experiment comprised the following model variants:
-VSu: It uses basic VAE to learn sample embeddings by performing clustering tasks on patient samples.
GeSubNet- BorbbiNet-QVASS V It uses VQ-VAE to learn sample embeddings by performing clustering tasks on patient samples.
GeSubNet Gonet-GAAN GAN: It incorporates a GAN structure on top of basic AE. This model performs sample augmentation while performing clustering tasks on patient samples.
Next, in the gene embedding learning module, we conducted experiments using various graph neural network models to learn gene embeddings. The experiment included the following model variants:
GeSubNet-GGN: A variant utilizes GCN to learn gene embeddings through the link prediction task.
GeSubNet-GAT: variant utilizes GAT to learn gene embeddings through the link prediction task.
Finally, in the ablation study on the gene network inference module, we experimented and included the following model variants:
GeSubNet-One model.
variant removes the entire module and substitutes it with a one-step
GeSubNet-Cond : Another one-step variant contains additional neural layer that uses catenated sample embeddings and gene embeddings for network classification tasks.
Ablation. We conduct three detailed ablation studies to evaluate the impact of each module in GeSubNet. More details can be found in Appendix [ Figure 7 presents the results of the three ablation studies across all variant models. For Patient-M, the proposed sample encoder sig- nificantly outperforms all other DGM models across the four network inference tasks (BRCA, GBM, LGG, and OV). For instance, the proposed method achieves average improvement of 32.3% 3..%%/3...%//........... 1.22 %/32.3% in terms of GED. The Graph-M ablations show that the method using Neo-GNN consistently performs best, while the other GNN models yield comparable results. For Infer-M M ablation, GeSubNet significantly outperforms the other objective functions, achieving ap- proximately twice the metric values of its counterparts.
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Tripaei
0.8
BRCA
0.6
0.5
GBM
0.8
0.6
0.4
004
0.4
0.4
604
0.2
0.0
0.0
0.0
0.0
0.0
0.
0.6
LGG
0.3
0.6
0.3
0.4
8 0.4
0.2
3.44
8 0.2
0.2
0.2
0.2
0.1
0.0
Mertod
0.0
Matrod
0.0
Metood
Mahhod
0.0
Methed
0.0
Manhod
Figure Ablation Study results on GED, DCS, and CDV for the proposed method and all compared methods. GED, DCS, and CDV are subjected to Min-Max normalization.
Potentt
Pattent
Posient
UMAP Dim3
UMAP Din
UMAP Dim2
UIMPP Dim2
UMAP Dimn
UMAP .Dim1
Samole Latent Space Based on General Disease Gene Network
Samp e Latenn Space Based on Patients-Grea Specific Gene Network
Figure 8: Compare GNN model learning results based general and patient group-specific gene networks. The latent sample space was gained via training the GNN model based on the general and patient group-specific gene networks.
K PRIOR GRAPH V.S. NEWLY GENERATED GRAPH
We evaluated the performance of patient group learning by inputting the newly generated graph from the GeSubNet into plain GCN and comparing the results. Figure&ppeeeentss UMAP visualization of the learned latent sample spaces, with the prior graph initialization (Left) and the generated graph GCN initialization (Right). The left sub-figure shows that different patient groups appear mixed in the latent sample space derived from the prior gene network. However, there are clearer boundaries between various patient groups, shown on the right side. Such results confirm the redundancy of information in the common prior gene networks. It demonstrates that the GeSubNet provides more structured information and potential for cancer studies.
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Reviews:
[{"review_id": "VYZGfp59cW", "reviewer": "Reviewer_ezgh", "summary": "The authors present a novel algorithm that identifies gene-to-gene interactions and disease subtypes. It has three components: A disease subtype from gene expression detection, second a gene network deep learning, and thirdly a part that combines both representations. This approach has out perform several SOTA algorithms.", "questions": "Can you expand on why you think your method outperformed the other methods? Maybe such an addition could be an excellent addition to the discussion.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "The authors present a novel method for creating gene-gene interactions that are aware of disease subtypes. They also present a new combination architecture and a novel method for integrating knowledge graphs and gene expression data, as well as a shared integrated dataset. \nThe paper is very clear and presents the underlying biological problem concisely. The mathematical formulation of the problem is well presented as well. \nThe different experiments conducted are very well displayed and designed.", "weaknesses": "The authors did not explain the principal way they selected the baseline methods; in other words, why was this method selected and not others? Why did the authors not add or remove methods?\nIn table two, while the GeneSubNet is significantly better, how can we know if this is an outlier of the training process or a significant improvement? This can be attained by repeated training and presenting the mean with SD or maybe other statistical insight. Specifically, in line 365, by which statistical measure was the importance ascertained? \nLine 416: could you cite why you can infer the \"functional distinctions...\" this might belong to the conclusions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HhlGKSLfA8", "reviewer": "Reviewer_k9TA", "summary": "The manuscript introduces a novel method, GeSubNet, for generating disease subtype-specific networks from general gene-gene interaction networks. The approach combines a deep generative model to learn distinct disease subtypes from patient gene expression profiles and a graph neural network to capture representations of prior gene networks from knowledge databases. By integrating these two representations, GeSubNet generates subtype-specific gene networks. The experimental results demonstrate that GeSubNet outperforms traditional methods across four cancer datasets.", "questions": "see above", "limitations": "", "rating": 8, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. Generating disease subtype-specific networks from general gene-gene interaction networks is a critical challenge in the field of precision medicine. \n\n2. The manuscript introduces the concept of geometric subnetworks (GeSubNet), with detailed descriptions of the algorithms used and the validation process.\n\n3. The paper is well-written and structured.", "weaknesses": "1. The baseline methods used in the comparative analysis are limited. Most of the current baselines are not specifically designed for subtype network generation. \n\n2. The ablation study is limited. A more comprehensive ablation study that evaluates the contributions of individual components (e.g., the \ndeep generative model and the graph neural network), and the databases, would provide deeper insights into the effectiveness of the model.\n\n3. What are the computational requirements of the GeSubNet algorithm, particularly in terms of runtime and memory usage? How scalable is the method for very large datasets?\n\n4. Figure 1 is hard to understand, particularly the flow of how expression data is integrated into the knowledge graph, as described in Section 3.2.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "0KsqQFPF8H", "reviewer": "Reviewer_X4R1", "summary": "The work presented introduces a novel methodology for gene interaction detection and disease subtype network generation. The topics addressed are of extreme importance in bioinformatics and biomedical machine learning since current methodologies fall short in determining disease subtype networks and limit themselves to the identification of broader networks related to a disease without a fine-grained differentiation between subtypes. The authors present GeSubNet, an architecture composed of three parts. Block 1 is endued with the encoding of gene expression data describing patients. Block 2 deals with the ending of the gene-gene interactions. Block 3 is tasked with determining disease subtype networks. The experiments confirm the biological relevance of the networks obtained and outperform other inference methods also in terms of enrichment analysis, in which GeSubNet is able to detect more enricher terms with respect to its compared counterparts. In the cancer use case presented, the enricher terms are confirmed to be associated with cancer by previous clinical studies.", "questions": "Overall, I find the paper really interesting. I would simply ask the authors to deal with the \"weak points\" I described. Moreover, did the authors test the methodology also on different diseases? it would be interesting to see the method applied to detect other disease subtypes. This would further prove the validity and efficacy of the method. However, this would be a \"plus\" since the work presented, in my opinion, contains enough scientific content for publication.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "The main strengths of the paper are the following:\n\n1) The work presented is novel. It proposed a new and effective architecture for the task of interest.\n\n2) The methodology is clearly presented, and the experiments are carried out carefully and described thoroughly. In particular, the analysis of the biological relevance of the network further validates the results and highlights the relevance of the methodology for this non-trivial bioinformatics task.\n\n3) The gene knockout simulation is really interesting and seems effective. \n\n4) The method presented outperforms the compared methodologies both quantitatively and qualitatively.\n\n5) Code is provided by the authors allowing for inspection and reproduction of the results.\n\nI believe the points I highlighted make it a good paper. Despite the strong bioinformatics focus, I believe the paper is relevant to the broader machine-learning community, given its substantial methodological contribution.", "weaknesses": "Some weaknesses are the following:\n\n1) There are some language inconsistencies in the paper. The authors refer to their method both as GeSubNet and GenSubNet. I believe those are typos.\n\n2) In Figures 1 and 2 the authors seem to have used the \"comic sans\" font. Please refrain from using that in scientific writing. Moreover, some parts of the text are in bold, italics, or colored. I would suggest writing those parts with no particular font style or color. Also, in lines 103-104, when the authors introduced the name of their methodology, I suggest the authors don't use different fonts to highlight the letters in the words that form the name; bold or capital letters, in this case, work fine.\n\n3) In line 299, introducing abbreviations with a phrase, which is not a clause (so with no verb), sounds not correct. I suggest the authors introduce the abbreviations together with the methods or in the caption of Table 1.\n\n4) There are some misunderstandings about GO terms. The authors refer to \"biological functions,\" but GOs (gene ontologies) are divided into \"biological processes,\" \"cellular components,\" and \"molecular function.\" I guess the authors are referring to \"biological processes,\" but this should be clarified.\n\nAdditional typos:\n\nLine 38: \"web lab\". I guess this should be \"wet lab\".\nTable1: I think that the names that follow #, which stands for \"number\", should be written in plural.\nLine 414: cannot involved -> cannot be involved.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Oral)