Customized Subgraph Selection and Encoding for Drug-drug Interaction Prediction
Authors: Haotong Du
Quanming Yao
Juzheng Zhang
Yang Liu
Zhen Wang
Venue: NeurIPS 2024 poster (2024)
Keywords: Drug-drug Interaction Prediction
Neural Architecture Search
Graph Neural Networks
Primary area: machine_learning_for_healthcare
TL;DR: We propose to efficiently and robustly search for data-specific subgraph-based pipeline components for drug-drug interaction prediction.

Abstract: Subgraph-based methods have proven to be effective and interpretable in predicting drug-drug interactions (DDIs),
which are essential for medical practice and drug development. 
Subgraph selection and encoding are critical stages in these methods, 
yet customizing these components remains underexplored due to the high cost of manual adjustments. 
In this study, 
inspired by the success of neural architecture search (NAS), 
we propose a method to search for data-specific components within subgraph-based frameworks. 
Specifically, 
we introduce extensive subgraph selection and encoding spaces that account for the diverse contexts of drug interactions in DDI prediction. 
To address the challenge of large search spaces and high sampling costs, 
we design a relaxation mechanism that uses an approximation strategy to efficiently explore optimal subgraph configurations. This approach allows for robust exploration of the search space. 
Extensive experiments demonstrate the effectiveness and superiority of the proposed method, 
with the discovered subgraphs and encoding functions highlighting the model’s adaptability.

Customized Subgraph Selection and Encoding for Drug-drug Interaction Prediction
Haotong Du
Quamming Yao² Juzheng Zhang? Yang Liu'
Zhen Wang"t
werttwwettern Polytechnical University TTsnnguaa University duhaotong@mail nwpu. awpu.edu. gyaoaa@tsinghua edu. (juzhengzh00, wwwgluyyhl/oomalll.oooo
edu. en w-zhen@nupu, edu en
Abstract
Subgraph-based methods have proven to he effective and interpretable in predict- ing drug-drug interactions (DDIs), which are essential for medical practice and drug development. Subgraph selection and encoding are critical stages in these methods, yet customizing these components remains underexplored due the high cost of manual adjustments. In this study, inspired by the success of neural architecture search (NAS), we propose a method search for data-specifie com- ponents within subgraph- based frameworks. Specifically, we introduce extensive subgraph selection and encoding spaces that account for the diverse contexts of drug interactions in DDI prediction. To address the challenge of large search spaces and high sampling costs, we design a relaxation mechanism that uses an approximation strategy to efficiently explore optimal subgraph configurations This approach allows for robust exploration the search space. Extensive experiments demonstrate the effectiveness and superiority of the proposed method, with the discovered subgraphs and encoding functions highlighting the model's adaptability.
1 Introduction
Precise prediction of drug-drug interactions (DDIs) is essential in biomedicine and healthcare research [1]. Drug combination therapy [2] can enhance treatment effectiveness for certain diseases; however, it also increases the risk of adverse drug reactions, potentially threatening patient safety [3]. Identifying DDIs through laboratory experiments both costly and time-consuming [4, 5J. With the success of deep learning, researchers have increasingly explored computational methods for DDI prediction. Early approaches primarily relied on molecular fingerprint information [6] or hand-engineered features [7], often neglecting the pre-existing interaction properties between drugs.
Considering drugs as nodes and their interactions as edges, DDI prediction can be framed as a multi-relational link prediction problem within the constructed drug interaction network. Recent advancements in graph neural networks (GNNs) [8, 9, 10, 11] have consistently achieved superior per- formance in this task. Specifically, subgraph- based methods, such SumGNN [12], EmerGNN [13], and KnowDDI [14], have shown promising results by selecting subgraphs around query edges and applying sophisticated encoding functions (message passing functions) to represent these sub- graphs, Such methods transform the multi-relational link prediction task into a multi-type subgraph classification problem. Figure illustrates the pipeline of subgraph-based methods.
However, due the dense nature [15. 16] of drug interaction networks and their complex in- teraction semantics [17], existing hand-designed subgraph methods often fail to capture the nu- anced but crucial information across different data inputs. the initial phase of the reasoning pipeline, the subgraph sampler must have the capability to customize the selection of drug sub- graphs for different queries, thereby ensuring precise contextualization of the reasoning evidence.
1 *Corresoondng author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Subgraph Selection
Subgraph Encoding
Predicted
Yur
Query nodes
GDDI
9 U,V
Query edges
Figure The pipeline subgraph-basee methods includes subgraph selection and subgraph encoding. In this work, we focus specifically on searching for components within the red-dotted lines. Without customized subgraph selection, SumGNN samples subgraphs using a fixed subgraph range k. selecting the k-hop neighbors of each drug associ- ated subgraphs for predicting drug-drug interactions (DDIs). This coarse grainned approach is straightfor- ward and easy to implement, but it may introduce noise omit valuable information needed to reason about diverse drug pair interactions.
Table I: Comparing with existing methods."-
represents not applicable.
Fine Fine-grained Subgraph Selection
Data Data-specific Encoding Function
Method
SEAL [18]
Grall. [19]
XX
XXP
XX
In terms of encoding process, the encoding function must be capable modeling a wide variety of drug in- teractions within the drug interaction network. Real- world drug interactions exhibit complex mechanisms, for instance, sttabolissmbbased interactions display asymmetric semantic patterns, whereas phenotype- based interactions are symmetric. Manually designed encoding functions are limited in their ability to ac- commodate both types of distinct semantic patterns simultaneously [23]. Therefore, designing customized and data-adaptive subgraph-basee pipeline is essential for effective DDI prediction.
SumGNN [12]
SNRI [20]
X
x
KnowDDI [14]
MR MR-GNAS [21]
AutoGEL [22]
CSSE-DDI
Neural architecture search (NAS) [24, 25] has achieved remarkable success in designing data-specific models, often surpassing architectures crafted by human experts in various fields, such as computer vision [26], graph neural network [27], and knowledge graph learning [23]. However, effectively selecting suitable subgraphs from the vast space of candidates and efficiently optimizing the joint search process of subgraph selection and encoding remain open challenges.
In this paper, we leverage NAS to search for data-specific components in the subgraph-based pipeline. Specifically, design search spaces for pipeline components, including subgraph selection and encoding spaces, to capture various drug interaction patterns. To enable efficient exploration of the extensive subgraph selection space, introduce relaxation mechanism that continuously selects subgraphs in structured manner. Additionally, we propose a subgraph representation approximation strategy to reduce the high cost of explicit subgraph sampling, enabling efficient and robust search. Compared with existing methods Table 1, our proposed Customized Subgraph Selection and Encoding for Drug-Dou -oug-Drgg Interaction prediction (CSSE-DDI) achieves fine- grained subgrpah selection and data-specific encoding functions, providing an efficient and precise method for drug interaction prediction. Our main contributions are summarized follows:
We present CSSE-DDI, a searchable framework for DDI prediction that adaptively customizes the subgraph selection and encoding processes. To the best of our knowledge, this is the first application NAS techniques to tailor an adaptive subgraph-basee pipeline for the DDI prediction task.
We construct expressive search spaces to ensure precise capture of evidence for drug interaction prediction. Additionally, we devise relaxation mechanism transform the discrete subgraph selection space into a continuous form, enabling differentiable search. Simultaneously, we apply a subgraph representation approximation strategy mitigate the inefficiencies of explicit subgraph sampling, thereby accelerating the search process.
Extensive experiments on benchmark datasets demonstrate that our method, which searches for customized pipelines, achieves superior performance compared to hand-designed methods. Additionally, our approach effectively captures the underlying biological mechanisms of drug-drug interactions.

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2 Related Works
Subgraph-based Link Prediction Recently, subgraph-based methods [18, 19, 28] have emerged as a promising approach, showing superior performance link prediction tasks. Different from canonical GNNs, subgraph-based method extracts a subgraph patch for each training and test query, learning a representation of the extracted patch for final prediction, as illustrated in Figure
Existing works has primarily focused on designing more informative subgraphs and more expressive encoding functions. However, they do not take into account eustomizing these components to deal with various data. Specifically, in terms of subgraph sampler, current approaches lack fine-grained and adaptive extraction for different query subgraphs. While PS2 [29] demonstrates the effectiveness of identifying optimal subgraphs for each edge in homogeneous graph link prediction, there is no comparable work in multi-relational graph link prediction. In dense DDI networks, fine-grained identification of subgraph for different queries is even more crucial.
As for the encoding function, existing works overlook the importance of data-specific encoding, which has been emphasized in recent literature [30, 27]. Customized encoding functions are especially advantageous for drug interaction networks with complex and diverse interactions.
GNN-based DDI Prediction Recently, there has been growing interest in applying GNNs for DDI prediction [8, 9]. However, these works execute peessage-aassing functions over the entire graph, which limits their ability to capture explicit local evidence for specific query drug pairs and lack interpretability. In contrast, subgraph-base DDI prediction methods [12, 63, 13, 14] transform the multi-relational link prediction problem into subgraph classification problem by extracting subgraphs around query nodes, achieving strong performance. Nevertheless, these works use the same subgraph extraction strategy for all queries and rely a fixed message-passingg function to handle complex DDIs, which limits their flexibility and adaptivity in dense DDI networks.
Graph Neural Architecture Search Graph neural architecture search (GNAS) [31] aims to find high-performing GNN architectures using NAS techniques. Recent studies [30, 27] have explored GNAS to create more expressive GNN models across various tasks. AutoDDI [32], for instance, automatically designs GNN architectures learn molecular graph representations of drugs for DDI prediction. However, research on optimizing graph sampling for GNAS remains limited due to the diversity of graph-structured data.
Regarding search strategy, early approaches explores the search space using reinforcement learn- ing [33] or evolutionary algorithms [34], which is highly inefficient. One-shot approaches [35] instead construct an over-parameterized network (supernet) and optimize it using gradient descent, leveraging continuous relaxation of the search space to improve search efficiency. The recently pro- posed few-shot NAS paradigm [36] further enhances supernet evaluation consistency by generating multiple sub-supernets
Proposed Method
3.1 Problem Formulation
Given a set of drugs V and interaction relations R among them, the drug interaction network is denoted as GDDI = {u, D) u, E V,r E R], with each tuple (u, r, v) describes an interaction between drug u and drug Consequently, drug-drug interaction (DDI) prediction can be framed a multi-relational link prediction task within the drug interaction network GDDI- The objective is to predict the types of interactions between two given drug nodes, which can be denoted query (u, ?, v), i.e. given the query drug-pair entities u and v, to determine the interaction r that makes (u, v) valid.
Moreover, instead of directly predicting on the entire graph GDDI, subgraph-based methods decouple the prediction process into two stages: (1) selecting query-specific subgraph and (2) encoding the subgraph to predict interactions, as shown in Figure 1. The prediction pipeline then becomes
Selection.(u.v) G,.
Encoding
GDDI
Y
(1)
a,
where the sampler selects a subgraph G.,, conditioned on the given query (u, v). Using this subgraph Gu,,, the encoding function produces the final predictions Y....
Building on previous analysis and existing research, and inspired by NAS, we propose to search for data- data-adaptive subgraph selection and encoding components to obtain customized subgraph
3

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pipeline. In Section 3.2, we first introduce the well-designed subgraph selection and encoding spaces to ensure comprehensive coverage of cricual information various drug interaction networks. Further, in Section 3.3 we present subgraph relaxation strategy and approximation mechanisms for subgraph representations to facilitate efficient differentiable search. Finally, we develop a robust search algorithm to address the customized search problem with stability and precision.
3.2 Search Space
3.2.1
Subgraph Selection Space
In practice, subgraph- baasap methods define the drug-pair subgraph between drug pairs as the union or interaction of k-hop ego-network of query drugs. Here, is a key hyperparameter that determines the range of message propagation aggregated by the central node. Selecting k is crucial to model performance, as it dictates whether the model has access to high-quality evidence context for accurate prediction.
Prior works [12, 37] typically utilize a fixed hyperparameter for all drug pairs, i.c., selecting the union of fixed k-hop ego-network for arbitrary queries. Nevertheless, this approach can lead to imprecise collection of evidence for interaction reasoning, potentially undermining the reasoning process due missing critical information the inclusion of excessive irreeevnn information.
Based on the above analysis, we define a drug-pair subgraph selction space containing a range of subgraphs of different sizes for a given query (u, v):
S.,
(9% iiijj n))
where G:.d is generated by taking the union of the i-hop ego-network of node u and the j-hop ego-network of node v. i.e., Gid fz E V E (u ( U (()))) where Mi(u) and (v) are the i-hop and the j-hop neighbors of and v, respectively. The threshold vy constrains the maximum subgraph range.
Since each drug-pain pair has a specific subgraph selection space, the overall size of space in the entire graph is s7 22 where |&'] represents the number of edges in the drug interaction network. larger [E] result in subgraph selection space that grows exponentially with the number of edges. Therefore, efficiently searching for the optimal subgraph configurations for different queries challenging.
3.2.2 Subgraph Encoding Space
For the automated design of the subgraph encoding function, we first adopt unified message passing framework [21, 38] comprising several key modules: the message-computing function MES, the aggregation function AGG, the combination function COM, and the activation function ACT, as follows:
step 1: +- AGG(MES( (oa he(..))
(3)
step 2: h, + ACT(CCM(h...... m.)),
where h, E Id and h, E Rd represent the embeddings of node u and interaction respectively, and m,, is the intermediate message representation of u aggregated from its neighborhood. Ni (u).
A substantial amount of literature [39, 40, 41] has focused on manually designing these modules to improve performance. However, such encoding functions are inflexible for handling diverse interac- tion patterns across different drug interaction network. For example, interactions in DrugBank [42] describe how one drug affects the metabolism another one. The excretion of Acamprosate, for in- stance, may be decreased when combined with Acetylsalicylic acid (Aspirin). Such interaction pattern asymmetric, meaning r(z, y) * r(y, .r.. Conversely, interactions the TWOSIDES dataset [43] are primarily at the phenotypic level, such as headache or pain in throat, representing symmetric patterns where r(x, y) = r(y, .r). These two relational semantics are distinctly different, and existing hand-designed encoding functions struggle to capture such diverse semantics effectively [44, 23].
Here, we aim to perform an adaptive searching for the encoding function in the context of drug interaction prediction. Based on the framework presented in Eq. (3), we design an expressive subgraph encoding space with a set of candidate operations. Detailed explanations of these modules can be found in the Appendix A.
A hop netwokk of node consists of the node and its h-hop neighbors.

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After encoding the subgraph Gu,v. we obtain the representation Zu,v of the input subgraph Gu. The predictor then maps the representation zu to the probability logits for different interactions between drug pairs, i.c., Vu,e = predkuuvv where W Wpedd pred E |2dx|R] the parameter of the predictor.
3.3
Search Strategy
3.3.1 Search Problem
Based on the well-designed search space described above, we formulate a bi-level optimization problem to adaptively search for the optimal configuration of subgraph-based pipelines.
Definition 1 (Customized Subgraph-basd based Pipeline Search Problem). Let A denote the subgraph encoding space, S..v represent the subgraph selection space for the query (u, v), be candi- date encoding function in A. W represent the parameters of model from the search space, and W9 a) denote the trained operation parameters. Let Dura and D denote the training and validation sets, respectively. The search problem is formulated as follows:
arg AA E (urs))DD.. (C(W"(Gu, (
(4)
S.T. W (G arg minw Σ (u, C(Wguu,i o<),
(5)
where the classification loss is minimized for all interactions, while the performance measurement M is expected be maximized.
In this work, we adopt the differentiable search paradigm [45] to solve the bi-level optimization problem, which widely used in recent NAS literature [46] and enables efficient exploration of the search space. Nevertheless, our proposed subgraph selection space poses two technical challenges: First, we cannot directly apply relaxation strategies, which is prerequisite for differentiable NAS methods, make the discrete selection space continuous. This limitation arises because different subgraphs in the selection space contain diverse nodes and edges, making it challenging to design relaxation function that unifies subgraphs of varying sizes. Second, to enable searching within the subgraph selection space, we would need to first generate all subgraphs in the space. However, sampling such large number of subgraphs is computationally intractable.
To address these challenges, we design a subgraph selection space relaxation mechanism in Sec- tion 3.3.2. Additionally, we introduce an intuitive subgraph representation approximation strategy in Section 3.3.3 to reduce the high costs associated with explicit sampling.
3.3.2 Relaxation of Subgraph Selection Space
Technically, as in existing NAS works [45, 47], one typically needs to relax the search space into continuous form to enable effective backpropagation training. However, for the subgraph selection space, the traditional continuous relaxation strategy is not directly applicable due to the structural mismatch between graphs and vectors.
To address this, we first utilize encoding function f(-) to encode subgraphs with different scopes. This approach provides all subgraphs with representations of the same dimension, making it feasible to implement relaxation strategy. Additionally, inspired by the reparameterization trick [48], we adopt the Humbel-Softmnn function to facilitate differentiable learning over a discrete space:
exp(log(s(S(O3))) + G..)/T)
Σ 1SA ex exp(log((([(()))) + GR.))/T) f(G
(6)
where g(.) scores the subgraph representations using multiple linear layers, G.y Hog(-loge U.,)) is the Gumbel random variable, U2, is uniform random variable, and r is the temperature parameter controlling sharpness. 2). is the mixed selection operation of subgraph Giu used to optimize searching process.
3.3.3 Subgraph Representation Approximation Strategy
To solving the optimization problem as Eq. (4) and (5), we need to explicitly sample all the candidate subgraphs within the subgraph selection space S,, for each query. However, one of the most challenging aspects of subgraph- approaches their inefficient subgraph sampling process [49, 50, 51].
5

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Upon examining our subgraph selection space, we observe that all subgraphs are generated by combining multi-hop ego-networks of the target nodes, encompassing multiple neighborhood hops. Inspired by the k-subtree extractor [52], we apply an encoding function to the entire graph and use the resulting node representations of and v as the ego-network representations for these nodes. The representation of the drug pair can then be obtained by concatenating the ego-network representations of u and v. Formally, if we denote by f(GDDI, u, i) the i-layer hidden representation of node u produced by encoding function applied to GDDI, then
f(ght) CONCAT(f u, ((DDI, U,j)),
The k-subtree extractor represents the k-subtree structure rooted given node, which mirrors the structure as the h-hop ego-network. This approximation strategy only requires executing the encoding function the entire drug interaction network, thereby efficiently yielding subgraph representations of varying scopes, which significantly improves the efficiency in solving the bi-level optimization problem.
3.3.4 Robust Search Algorithm
Using the proposed subgraph selection relaxation mechanism, we can transform the overall discrete search space in Definition. 1 into continuous form, allowing the search problem to be solved by the one-shot NAS paradigm. Additionally, our subgraph representation approximation strategy efficiently obtains subgraph representations and reduces search costs
Following [53], we adopt the single path one-shot training strategy (SPOS) [54] to reduce the
computational cost of supernet training. However, the one-shot approach [55, 56, 45], i.e., using the same supernet parameters W for all architectures, can decrease the consistency between the supernet's performance estimation and the ground-truth performance [57]. Inspired by few-shot NAS [36], we propose a message-awand partitioned supernet training strategy to mitigate the coupling effect of different
operators [58]. By partitioning the superent to form sub-supemnets based on the type of message- message-computing function, this strategy improves the consistency and accuracy of supernet, enabling the search algorithm more stable and robust. Algorithm delineates the full procedure, with further details provided in Appendix A.2.
Algorithm 1: The search algorithm of CSSE-DDI.
Input:
Supernet number partitions based on message computing function categories M (M = 4), subsupernet S; (i ,1....,.......
// supernet training phase
Train S continuously sampling single path until convergence;
// supernet partition phase
2 Partition S into M sub-supernets S,,... ,SM:
// sub-supernet training phase i, .M do
Initialize S, with weights transferred from S;
Train S by contimuously sampling a single path until convergence;
end
// searching phase
Search the optimal encoding function from sub-supernets Si, ... Sar on validation data by natural
gradient descent;
Select the optimal subgraphs from sub-supernets St.... Su validation data by preserving the subgraphs with the largest probabilities;
3.4 Comparison with Existing Works
While many works [12, 13, 14] have explored DDI prediction using subgraph-based methods, approach introduces two significant advancements. First, to the best of our knowledge, our method (CSSE-DDI) is the first to customize the subgraph selection and encoding processes specifically for subgraph-based DDI prediction. In contrast, previous methods rely on fixed subgraph selection strategy to sample subgraphs and employ hand-designed functions for encoding, as summarized in Table 1. Consequently, our method can adapt data-specific components within subgraph- pipelines, outperforming existing methods in both performance and efficiency (Section 4.2). Moreover, our approach not only selects fine- fine-graine grained drug-pair subgraphs that enhance interpretability through potential pharmacokinetic and metabolic concepts (Section 4.6. but also searches for data-specific encoding functions that accurately capture the semantic features of drug interactions (Section 4.6.2).

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Experiments
4.1 Experimental Setup
Datasets Experiments are conducted on two public benchmark DDI datasets: DrugBank [42] and TWOSIDES [43]. Detailed descriptions of these datasets are presented in Appendix B.I.
Experimental Settings Following [13], we examine two DDI prediction task settings: SO and S1. Let the drug pairs for DDI prediction be denoted as (u,v). In the SO setting, both drug nodes and are present in the known DDI graph. Existing DDI prediction methods are typically evaluated in this setting, In contrast, the SI setting involves pair (u, v) where one drug known and the other is a novel drug not represented in the known DDI graph. This scenario highlights the critical need for DDI predictions involving new drugs in real-world applications.
Evaluation Metric We follow [12] to evaluate our method. For the DrugBank dataset, where each drug pair contains only one interaction, we use the following metrics: Fl Score, Accuracy and Cohen's K. For the TWOSIDES dataset, where multiple interactions may exist between a pair of drugs, we consider the following metrics: ROC-AUC, PR-AUC and AP@50. Additional details are provided in Appendix B.2.
Baselines We compare CSSE-DDI with the following representative DDI prediction method: (i)
GNN-based methods include Decagon [8], GAT [59], SkipGNN [9], CompGCN [60], ACDGNN [61], and TransFOL [62]. (ii) Subgraph- based methods include SEAL [18], GralL [19]. SumGNN [12],
SNRI [20], KnowDDI [37] and LaGAT [63]. (iii) NAS-based method include MR-GNAS [21], and AutoGELI
We also compare our method with two variants, including CSSE-DDI-FS and CSSE-DDI-FF, The configurations of these variants are as follows: (i) CSSE-DDI-FS: This variant omits fine-grained subgraph selection for each query, using fixed k-layer drug node representations to generate the subgraph representation. (ii) CSSE-DDI-FF: This variant does not search for the encoding function, instead using a fixed encoding function backbone to capture semantic and topological features in the drug interaction network. In this case, we employ a 3-layer CompGCN model as the backbone. For all baselines, we obtain the results by rerunning the released codes.
Implementation We implement our method based on PyTorch framework [64]. Following existing GNN-based methods [37], we select a 3-layer encoding function backbone for both datasets. The maximum threshold 17 for the subgraph selection space is set to 3. More experimental details are given the Appendix B.3.
4.2 Performance Comparison in SO settings
Table 2 shows the overall results across all benchmarks in SO setting. As can be seen, CSSE-DDI consistently outperforms all baselines on each dataset, demonstrating its effectiveness in searching for data-specific subgraph-based pipelines for DDI prediction task. Among the baselines, subgraph-based methods significantly outperform hell-graph-basee methods due to their enhanced ability to reason over local subgraph contexts. Within the subgraph-based methods, SEAL, GralL, SumGNN, and SNRI use a fixed sample strategy to select subgraphs, which may not be optimal for different drug-pat queries.
When it comes to NAS-based method, MR-GNAS and AutoGEL contain well-established search spaces that embrace multi-relational cassage-passing schema, focusing primarily on automated encoding function design using the one-shot NAS paradigm. While CSSE-DDI adopts a single path supernet training strategy and message-aware partitioning approach search for data-adaptive subgraph-based pipelines with stability and robustness, enabling the model to achieve excellent performance across various datasets. Moreover, the consistent performance gains of CSSE-DDI over its two variants validate the importance of jointly customizing subgraph-basee pipeline components, i... fine- -naiindd subgraphs and data -ate-spec encoding functions, to fit datasets rather than relying on fixed approach.
Figure 2 shows the learning curves of several competitive methods both datasets, including CompGCN, KnowDDI and the proposed CSSE-DDL. As can be seen, the searched models not only outperform the baselines but also demonstrate clear advantage in efficiency, highlighting that enhancing model flexibility and adaptability is essential for improving performance and efficiency.
Our code is available at https://gghhbbcomm/LLABrereeeeee
7

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Table CSSE-DDI achieves the best predictive performance compared state-of thetherrrt baselines in DDI prediction. Average and standard deviation of five runs are reported. For these metrics, higher values always indicate better performance.
Dataset
Dataset 1: DrugBank
Dataset 2: TWOSIDES
Model
Type
Task Type
Multi-class
Multi-label
Methods
F1 Score
Accuracy
Cohen's K
ROC-AUC
PR-AUC
AP@50
Decagon
57.35
87.191028
86.07
91.72
90.60
82.06:t0.45
GAT
33.4911036
77.18
91.18 7..20
89.8610.5
82.80
GNN- based
SkipGNN
59.66.10.26
85.83-10.18
1..20
92.04
90.90
84.25.:0.25
CompGCN
71.20.10:00 88.30
86.15
93.00
91.2610007
86.1810.10
ACDGNN
86.24 90,53++038
87.81 =0.33
93.69
92.12+0.11
87.45++024
TransFOL
19.97
91.92++089
90.92=0.72
94.16=0.62
93.52+0.53
88. 13.40.9
SEAL
48.82::0.98
16.61
71.91
90.74
10.17
84. 13:10.13
GralL
73.20
85,40+0039
82.70
92.93+0.10
91.69+0.14
87.43=00.9
Subgraph-
SumGNN
78.35+0051
89.05-1036
87.28
92.6210004
90.80
85.75++0.10
based
SNRI
85.57 90.15+001
88.94
93.12
92.64
87.53+00111
KnowDDI
90,06:+0.27
93.15-+0.19
91.87=0211
95.05
93.75
09.244+0.06
LaGAT
81.63+00.6
86.21
85.38
89.78
86.33+0.15
83. 03.75
MR-GNAS
74.24
88.17=0.24
87.31
93.85+0007
91,80+0005
87. 17.16
AutoGEL
76.87#0.63
89.35=0059
86.14
94.11
92.35++.29
88. 13
NAS- based
CSSE-DDI-F'
86.3 91.08++021
89.17=0.27
94.35
93.01+0006
89.08=0000
CSSE-DDI-FF
80.96
90.27-1023
88.69=0.31
94.26:20.08
92.74
88.91 +0.09
CSSE-DDI
92.08
95.56:10155
94.72=0.26
95.47=0002
94.21
89.76=:0.05
4.3 Choices of Search Strategy
To demonstrate the effectiveness of our search strategy, we introduce two variants with different search strate- gies: (i) CSSE-DDI w/o MAP: This variant uses only one trained supernet to serve performance evaluator for candidate architectures, instcad of generating multiple sub-supernets by Message-Aware Partition (MAP) strat- egy. (ii) CSSE-DDI w/o SPOS: This variant utilizes the message-awan par- tition strategy jointly optimize the supernet weights and architectural pa- rameters, without using the Single Path One-Shot (SPOS) strategy [54].
Testing F1 Scores (96)
Testing ROC-AUC AUC (96
90-
995
80
70
CSSE-DDI
85
CSSF DDI
60
KnowDDI
KnowDDI
CompECN
CompGCN
50
80
3
6
7
10
20 30 40 50
Training time (in hour)
Training time (in minute)
(a) DrugBank
(b) TWOSIDES
Figure 2: Comparison on convergence between the searched
architectures by CSSE-DDI and human-designed methods.
In Table 3, compare CSSE-DDI with other variants. As can be seen, the absence of either message-aware partition strategy or caapling-based NAS strategy negatively impacts per- formance. The performance gains achieved through the message-aware partition strategy arise from using multiple sub-supernets. which provide more accurate performance estima-
Table 3: Performance of CSSE-DDI using different variants of search algorithm.
Variant
DrugBank TWOSIDES
CSSE-DDI w/o MAP
90.1711.0
95.12
CSSE-DDI w/o SPOS
90.97
94.89
CSSE-DDI
92.08
95.47:10.2
tions to guide the search process. Regarding the SPOS strategy, decouples supernet training from architecture search, making it more efficient and robust in practice.

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4.4 Sensitivity Analysis of the Threshold
Here, we analyze the effect of the threshold used in subgraph selection space. Figure 3 shows the impact of varying v)- As can be observed, model performance continues to get better as the threshold grows. When the threshold = 3, the model performance nears saturation, as larger thresholds do not lead to fur- ther improvements. This is likely be- cause most of the essential informa-
95
E 95
tion for DDI prediction is contained within the 3-hop ego-subgraphs of target drugs. Intuitively, larger sub- graphs may provide additional use- ful information. However, in prac- tice, due to the inherent biases of the search algorithm, achieving an opti- mal model may be challenging. When 7 is too large, it may introduce noise and dilute the critical information. A similar phenomenon has been found in the existing work SumGNN [12]. Besides, excessively large
94
94
93
93
92
PR-AUC
91-
FI Score
92
90
Accuracy
Test
89
Cohen's Kappa
Test
90
3
(a) DrugBank
(b) TWOSIDES
Figure 3: Performance given different hyperparameter ?).
thresholds will only lead to unnecessary expansion of the search space and higher computational costs.
4.5 Performance Comparison in S1 settings
To further validate the effectiveness of method, we the S1 setting in the EmerGNN [13] method, to predict drug-drug interactions between emerging drugs and existing drugs. The experimental results are shown in Table 4. A significant performance drop from the transductive setting (S0) the inductive setting (SI) demonstrates that DDI prediction for new drugs is more challenging. Although Emergnn, which specifically designed for new drug prediction, achieves optimal performance, CSSE-DDI still demonstrates impressive results, outperforming existing GNN-based and subgraph- based methods. This strong performance is largely due to the robust learning capability of NAS technology in handling unknown data.
Table Experimental results in S1 setting.
Dataset
Dataset 1: DrugBank
Dataset 2: TWOSIDES
Task Type
Multi-class
Multi-label
Methods
Fl Score
Accuracy
Cohen's K
ROC-AUC
PR-AUC
Accuracy
CompGCN
30.98
52.7610.46
3..87
84.83+1.02
+3.68
74.64+
Decagon
11.39
32.56:0.92
20.2941.33
57.49
59.38+1.09
52.27
SumGNN
26.57=1159
44.30+1.04
40.24
80.02+2.17
78.42+1.2
69,81
KnowDDI
31.14+1.24
53,4441.73
43.93
84.23+2.6
82.58+1194
1..72+1.51
EmerGNN
58.13
69.53
62.19
87.42
86.20
79.23 10.54
CSSE-DDI
37.24+1.13
58.57
49.97+1001
88.33
86.47
80.01
4.6
Case Study
4.6.1
Fine-grained Subgraph Selection
We visualize exemplar query-specific subgraphs from the DrugBank dataset in Figure 4, highlighting domain concepts such as pharmacokinetics, metabolism, and receptor interactions. As shown, CSSE-DDI can identify dis- tinctive subgraphs containing seman- tic information to support inference for different queries, revealing pharma- cokinetic and metabolic relationships.
[DBAEHS, wwt.oooptaar acthittrrr DUBBON2) Selgrrghh seaper (l.))
(DDHISSE, Jhnngyortc officeyy (ID93562) Subgroph scapei (1.3
DHMMMMAN soticegghent
Becopeate
excrefis rare
DBM8250
Iherapentic efficeyl
zefroncclani Artithel
Aheraanuto
incettion ratel
DHB8334
DB40662
Figure 4: Visualization the searched subgraphs corre- sponding to the specific drug pairs.

---

For example, to predict the interaction between DB00945 (Aspirin) and DB00682 (Warfarin), CSSE- DDI searches out the subgraph scope (1. 1). as depicted on the left part of Figure Firstly, can be seen from the figure that the therapeutic efficacy of DB00233 (Aminosalicylic acid) can decrease when combined with DB00945 (Aspirin), suggesting similarity between the two drugs [65, 66] Given that DB00233 (Aminosalicylic acid) may increase the anticoagulant activity of DB00682 (Warfarin) and that DB00233 resembles DB00945 (Aspirin), it can be inferred that DB00945 (Aspirin) may similarly increase the anticoagulant activity of DB00682 (Warfarin). This example demonstrates that the identified subgraph contains sufficient semantic information to reason about the interaction between DB00945 (Aspirin) and DB00682 (Warfarin).
4.6.2 Data-specific Encoding Function
Furthermore, we visualize the searched structure of encoding functions across all datasets in Figure 5. It is clearly illustrated that different combinations of the designed operations, i.e., data-specific encoding functions, are obtained.
CORR
IDNIITY
MULT
MLP
RELU
MEAR
CORR
CONCAT
RELU
SUM
DONCAT
IDENIITY
MEAN
MEAR
MULT
CONCAT
IDENIITY
MULT
DONCAT
TANH
In particular, the searched message- computing functions contain more CORR operations in the DrugBank dataset, while more MULT functions searched in the TWOSIDES dataset. The CORR function non- commutative [67], making it suitable for modeling asymmetric interactions (e.g., metabolic-based interactions) present in DrugBank. While MULT is suitable for modeling
MRANN
SUX
DrugBank
TWOSIDES
Figure 5: The searched encoding functions on all benchmark datasets.
symmetric relations (phenotype-basee interactions) due to its exchangeability [68].
Conclusion
We propose a searchable framework, CSSE-DDI, for DDI prediction. Specifically, we design refined search spaces to enable fine-grained subgraph selection and data-specific encoding function optimization. To facilitate efficient search, we introduce relaxation mechanism convert the discrete subgraph selection space into a continuous one. Additionally, we employ a subgraph representation approximation strategy to accelerate the search process, addressing the inefficiencies of explicit subgraph sampling. Extensive experiments demonstrate that CSSE-DDI significantly outperforms state-of-thee of-thh--rttttttt methods. Moreover, the search results generated by CSSE-DDI offer interpretability in the context of drug interactions, revealing domain-specift concepts such pharmacokineties and metabolism.
Acknowledgements
We thank the anonymous reviewers for their valuable comments. This work was supported in part by the National Key Research and Development Program of China (Grant No. 00222D0160300),
in part by the National Science Fund for Distinguished Young Scholars (Grant No. 62025602), in part by the National Natural Science Foundation of China (Grant Nos. U22B2036, 1 11931015, 62203363, and 92270106), in part by the Technology Innovation Leading Program of Shaanxi (Grant No. 2023GXLH-086), in part by the Beijing Natural Science Foundation (Grant No. 4242039). in part by the Fok Ying-Tore Tong Education Foundation, China (Grant No. 171105), part by the Fundamental Research Funds for the Central Universities (Grant Nos. G2024WD015I and D5000240309), and in part by the Tencent Foundation and XPLORER PRIZE.
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Appendix
More Method Details
17
A.1
Subgraph Encoding Space
17
A.2
Robust Search Algorithm
17
More Experiment Setting
18
B.1
Datasets
18
B.2 Evaluation Metric
18
B.3
Implementation and Hyperparameters
19
C More Experimental Results
19
C.I Subgraph Scope Distribution Analysis
19
D Some Discussions about Checklist
20
D.I Limitations
20
16

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A More Method Details
A.1 Subgraph Encoding Space
An expressive subgraph encoding space can be naturally designed by including human- designd operations, the details of which given in Table 5.
Table 5: The operations used in our search space.
Function name
Operations
SUB, MULT,
Message Computing Function
CORR, ROTATE
Aggregation Function
SUM, MAX, MEAN
Combination Function
MLP, CONCAT
RELU, TANH, IDENTITY
Activation Function
In particular, given the embedding h. of node u and the embedding h, of interaction r, the message
computing function takes the following form: MESguB h, h, MESHuLT h, * h,, MEScoma ha h,, MESROTATE h o hy, where stands for the circular correlation operation [67], o represents the rotation operation [69].
A.2 Robust Search Algorithm
adopt the single path one-shot (SPOS) training strategy to solve the customized search problem, which decouple supernet training and architecture searching. In particular, definition can be transformed into a two-step optimaztion [54]:
arg m
i c.)
(8)
W arg --arggmngg min EaEA (u,re)e L(W; Gu,ei ox),
(9)
where W denotes the shared learnable weights in the supernet with its optimal value W for all the architectures in the overall search space.
Eq. (8) represent the supernet training and architecture searching phase, respectively. In the following, we will describe the detailed process of the two phases.
A.2.1 Supernet Training
In supernet training phase, sub-model is sampled according to the discrete distribution r(A). Thus, Eq. (9) can be formulated as
W
arg minw Ea)a((A) E ( L(W; (u,iua
(10)
where the discrete distribution (AA) is set uniform distribution.
First, we need to perform single path sampling to train the supernet until it converges. In the next step, need to partition the supernet into sub-supernets. which is key step aiming to isolate operations that are coupled with each other. This allows the supernet to be trained and converge more stably.
message-awan partitions strategy duc to the fact that the degree of dissimilarity between the operations in the message computing function MES is much higher compared with others. These operations focus capture different semantic types of interactions, which has been discussed in existing works [70, 69, 58]. Therefore, we partition four operations of the message computing function of the first layer of the supernet, to improve the accuracy of the performance estimation.
In supernet,
After partitioning operation, we initialize four sub-supernets with weights transferred from the original supernet. Next, we train these sub-supernets to convergence by sampling single path. Here, the supernet training phase is all done.
17

---

A.2.2 Architecture Searching
After completing sub-supernet training phase, we have obtained well-trained superner weights. In the searching phase, Eq. (8) can be transformed as
arg max G
E D(unno)D...
M(W"; (u,eia))
(11)
arg max Σ (u.r.))ED
M(W" Gu,0i "uW"i Ox)
(12)
For suugraph encoding function searching in Eq. (12), following [71], we adopt stochastic relaxation on and natural policy gradient strategy [72] to obtain the optimal subgraph encoding function a². For subgraph selection in Eq. (11), we obtain the optimal subgraph Gü.e by preserving the subgraph with the largest probability pu. i.c.,
z ((9h)))
(13)
0.v
B = g(zu,e))
(14)
exp(log(B1)) + G..)/T)
Pa.
(15)
E Ei exp(log(Ei,) Geg))T""
Gú arg max Pu (9 E Sup). s
(16)
B
More Experiment Setting
B.1 Datasets
Experiments are performed on two public benchmark DDI datasets: DrugBank and TWOSIDES.
DrugBank dataset contains 1,710 drugs and drug pairs, which related to 86 types of pharmacological interactions between drugs, such as increase of anticoagulant activity, decrease of excretion rate and etc.
DrugBank
TWOSIDES TWOSIDES dataset contains 604 drugs and drug pairs with 200 drug side effects as interaction labels. For each edge, it may be associated with multiple interactions.
The detailed descriptions for datasets are presented in Table 6 and Table 7.
Table 6: The statistics of the datasets.
Dataset
#nodes
#edges
#interaction types
DrugBank TWOSIDES
1,710
134641 57778
86
604
200
Table 7: Diverse semantic properties in drug-drug interactions.
Dataset
Interaction Type
Examples
Semantic Property
#Drugl may decrease the excretion rate of #Drug2 Combination #Drug and #Drug may cause headaches
asymmetry
DrugBank
Metabolic levels-based
(r(z, v) # r(y, 2))
symmetry (r(2, v) = r r(y,
TWOSIDES
Phenotype-based
B.2
Evaluation Metric
We follow [12] to evaluate our method. Specifically, in terms of the multi-class prediction on DrugBank, we followc[12] and evaluate the performance by three metrics: (i) Macro Fl score (Macro F1) is computed by taking the arithmetic mean (aka unweighted mean) of all the per-class scores. (ii Accuracy (ACC) is calculated by dividing the number of correct predictions by the total prediction
18

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number. (iii) Coken's Kappa (Cohen'ss 's к) measures inter-rater reliability. As to the multi-label prediction on TWOSIDES, we consider the following measure and use the average performance over all interaction types: (i) ROC-AUC (AUROC) stands for "Area Under the Curve (AUC)" of the "Receiver Operating Characteristic (ROC)" curve. (ii) PR-AUC (AUPRC) the average area under precision-recall curve. (iii) AP@ 50 is the average precision at 50.
B.3 Implementation and Hyperparameters
All the experiments are implemented in Python with the PyTTrrc framework [64] and run on server machine with single NVIDIA RTX 3090 GPU with 24GB memory and 64GB of RAM. Our code is added in the supplementary material.
For CSSE-DDI, we set the epoch to 400 for training supernet and set the epoch to 400 for training sub-supernets. We the the temperature parameter as 0.05, Repeat 5 times with different seeds, we can get 5 candidates. The searched candidates are finetuned individually with the hyper-parameters In the stage of fine-tuning, we use the ReduceL_ROnPlateau scheduler adjust the learning rate dynamically. Each candidate has 10 hyper steps. In each hyper step. set of hyperparameter will be sampled from Table 8.
Table 8: Hyperparameters used during the fine-tuning stage.
Hyperparameter
Value range
Learning rate
[10-3.1 3.1, 10 10-
Weight decay
[10-9,10 3]
C More Experimental Results
C.1 Subgraph Scope Distribution Analysis
We visualize the learned distributions of subgraph scope on all datasets by using CSSE-DDI in Figure 6. By comparing the distributions across different benchmarks, we have the following observation: CSSE-DDI can effectively learn different subgraph scope distributions for various datasets. By identifing specific subgraph scopes for different queries, CSSE-DDI is able to precisely control the extent of information propagation required for reasoning about the interactions of different drug pairs. In addition, our method can skip some subgraph scopes if they are not optimal for any queries. For example, queries assigned to the propagation scope (3, 3) TWOSIDES dataset. is worth mentioning that our searched subgraph scopes are consistent with the sensitivity analysis results for the hop of subgraph in SumGNN [12), which further validates the effectiveness of approach.
0.7-
DrugBank
0.6
Resqunccy
0.3-
0.4
0.3
(2.1) (1.2) (1.3) (2.1) (2,2) (2.3) (5.1) (B,2) (3(3)
Subgraph Scope Selection
Figure 6: Distribution of the searched subgraph scopes by CSSE-DDI on all benchmark datasets.
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D Some Discussions about Checklist
D.1 Limitations
There are three limitations for CSSE-DDI. (1) CSSE-DDI is focused on method design rather than system design. In the future, we will co-design the algorithm and the system further improve the efficiency. (2) At present, CSSE-DDI only search for data-specific components of subgraph- based pipeline, while explore how to efficiently search network architectures and hyper- parameters simultaneously.
are also important for DDI prediction. A promising direction is to
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Reviews:
[{"review_id": "dVktYwA2qR", "reviewer": "Reviewer_Qw7Z", "summary": "This paper addresses the challenge of predicting drug-drug interactions (DDIs), crucial for medical practice and drug development, using subgraph-based methods. It highlights the importance of customizing subgraph selection and encoding but notes the high cost of manual adjustments. Inspired by neural architecture search (NAS), the authors propose a method to search for data-specific components in the subgraph-based pipeline. They introduce extensive subgraph selection and encoding spaces and design a relaxation mechanism to efficiently explore optimal configurations. Extensive experiments demonstrate the method's effectiveness and adaptability.", "questions": "1. Why is the performance of GAT in DrugBank so poor? In [1], it seems to work well.\n2. Why does the NAS method proposed by the authors appear to perform much better than other NAS methods in the DrugBank dataset? What is the core reason for this?\n\n[1] Hong Y, Luo P, Jin S, et al. LaGAT: link-aware graph attention network for drug–drug interaction prediction[J]. Bioinformatics, 2022, 38(24): 5406-5412.", "limitations": "See weakness.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Extensive experiments demonstrate the method's effectiveness. Compared to existing hand-designed methods, the CSSE-DDI framework shows superior performance, enhancing the proposed method's validity.\n2. The writing quality is good.\n3. Using NAS for precise prediction of drug-drug interactions is novel.", "weaknesses": "1. The motivation for using NAS to search components is not clear.\n2. Despite the designed efficiency mechanisms, the inherent overhead of neural architecture search remains significant, especially for large-scale DDI prediction tasks.\n3. While the paper compares the proposed method with existing ones, a more detailed comparative analysis, including discussions on computational costs and efficiency metrics, would provide a clearer picture of the trade-offs involved.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your time and efforts in reviewing our paper. Please find our responses below to your concerns.\n\n> W1. The motivation for using NAS to search components is not clear.\n\n**R1**. The use of NAS technology to customize components stems from our analysis and understanding of the DDI prediction problem and datasets in the following two ways:\n\n1.\tDifferent DDI datasets have different semantic natures of interactions. (asymmetric patterns in DrugBank and symmetric in TWOSIDES)\n2.\tReasoning that different drug-pair queries should require different ranges of subgraph information, rather than a fixed range. (Our empirical analysis in the supplementary PDF(Figure A1))\n\nBased on the above analysis, we believe that in the face of diverse data properties, the use of customized search techniques, i.e., NAS, can help improve the performance of DDI prediction task and the interpretability of the results, as evidenced by our extensive experiments.\n\n> W2. Despite the designed efficiency mechanisms, the inherent overhead of neural architecture search remains significant, especially for large-scale DDI prediction tasks.\n\n**R2**. We would like to kindly argue that our design for the search algorithm with the implicit subgraph sampling strategy is precisely to cope with the large-scale graph data. Tab. I shows the running overhead of our method and other subgraph methods on the drugbank dataset, for the subgraph methods, before the \"+\" sign represents the explicit subgraph sampling overhead, and for our method, before the \"+\" sign represents the searching overhead, and after the \"+\" sign represents the model's single running time. \n\nAs can be seen, CSSE-DDI and the subgraph approach are comparable or even superior in terms of time overhead, which stems from the fact that our implicit subgraph sampling strategy saves a lot of time in the subgraph sampling and representation phases. It is conceivable that if the size of the dataset is further increased, the number of subgraph sampling will be further increased and the advantage of our implicit sampling strategy will be even more significant.\n\n|Table 1|Running time(minutes)|\n|-------|-------|\n|SumGNN|342+361|\n|KnowDDI|379+393|\n|**CSSE-DDI**|444+32|\n\n> W3. While the paper compares the proposed method with existing ones, a more detailed comparative analysis, including discussions on computational costs and efficiency metrics, would provide a clearer picture of the trade-offs involved.\n\n**R3**.  For the discussion of the time overhead, please refer to **R2**.\nOverall, compared with subgraph methods, CSSE-DDI has lower time overheads, which is the advantage brought by our proposed implicit subgraph sampling strategy. Compared with GNN-based methods, CSSE-DDI, by analyzing the DDI prediction problem and datasets, designs a search space that can be adapted to different data by analyzing the DDI prediction problem. By efficiently searching for the components, it substantially improves the prediction performance under tolerable time overhead compared with the traditional GNN-based methods. In addition, CSSE-DDI can design robust and customized model structures to cope with unknown datasets, which is exactly the advantage of utilizing NAS technology to solve the DDI prediction problem.\n\n> Q1.1. Why is the performance of GAT in DrugBank so poor?\n\n**R4.1**. A large number of literature[1-3] points to the fact that although GAT[4] considers the attention on different edges, it fails to consider more generalized and more complex multi-relational graph data, which contains diverse semantic information, as its performance is also not good. Therefore, the direct application of GAT on DDI graphs results in suboptimal solutions.\n\n> Q1.2. In [3], it seems to work well.\n\n**R4.2**. Compared with GAT, LaGAT extends the graph encoding module of SumGNN, and utilizes multi-relational GAT to take into account the diverse types of relations and the attention weights of different edges in the DDI data. We re-run its code in the DrugBank and  TWOSIDES data, and the comparison results are shown in Table 2. As shown below, our approach still achieves the best performance by customizing subgraph selection and encoding process. For the performance reported by LaGAT, we were unable to reproduce it. The official repository does not release the corresponding dataset, although it claims it uses the same DrugBank dataset as SumGNN.\n\n|Table 2|Drugbank||TWOSIDES||\n|-------|-------|-------|-------|-------|\n| |F1|ACC|ROC-AUC|PR-AUC|\n|LaGAT|81.63±0.56|86.21±0.18|89.78±0.21|86.33±0.15|\n|**CSSE-DDI**|92.08±0.22|95.56±0.15|95.47±0.02|94.21±0.05|\n\n> Q2. Why does the NAS method proposed by the authors appear to perform much better than other NAS methods in the DrugBank dataset? What is the core reason for this?\n\n**R5**. Compared with other NAS methods, our method has advantages in both search space and search algorithm.\n\n- **Search space**: we design subgraph selection spaces and subgraph encoding spaces adapted to the DDI dataset (Sec 3.2), whereas other methods are only limited to generalized multi-relational graphs and do not have task-specific customization for the DDI prediction task.\n\n- **Search algorithm**: we design a message-aware partition supernet training strategy for the operation coupling problem(Sec 3.3.4), which improves the consistency and accuracy of supernet, enabling the search algorithm more stable and robust, whereas the other methods only use the traditional one-shot search algorithm, which leads to sub-optimal performance.\n\n**References**\n\n[1] SumGNN: Multi-typed Drug Interaction Prediction via Efficient Knowledge Graph Summarization, Bioinformatics' 21.\n\n[2] r-GAT: Relational Graph Attention Network for Multi-Relational Graphs. Arxiv' 21.\n\n[3] LaGAT: link-aware graph attention network for drug–drug interaction prediction, Bioinformatics' 22.\n\n[4] Graph Attention Networks, ICLR' 18.", "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": "Act7L6i2Bz", "reviewer": "Reviewer_2Vrd", "summary": "This work introduces CSSE-DDI, a searchable framework for DDI prediction, which refines search spaces for fine-grained subgraph selection and data-specific encoding. To improve search efficiency, CSSE-DDI employs a relaxation mechanism to continuousize the discrete subgraph selection space and use subgraph representation approximation to accelerate the search process. Extensive experiments demonstrate that CSSE-DDI significantly outperforms state-of-the-art methods, and the results are interpretable, revealing domain concepts like pharmacokinetics and metabolism.", "questions": "CSSE-DDI-FF and KnowDDI both are fine-grained Subgraph Selection. What is the reason for the performance difference？\nWhether CSSE-DDI can be used to predict ddi for new drugs?", "limitations": "NA", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "it introduces comprehensive subgraph selection and encoding spaces to cover the diverse contexts of drug interactions for DDI prediction. Faced with overwhelming sampling overhead, this work designs an effective relaxation mechanism to efficiently explore optimal subgraph configurations using an approximation strategy, enabling a robust search algorithm to explore the search space efficiently.", "weaknesses": "Examples of symmetric semantic patterns(headache, pain in throat) are not very convincing.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your time and efforts in reviewing our paper. Please find our responses below to your concerns.\n\n> W1. Examples of symmetric semantic patterns(headache, pain in throat) are not very convincing.(sematic property)\n\n**R1**. In the field of multi-relational graphs, the modeling of different semantic types of interaction relationships has been a research hotspot. Many works[1-4] have tried to propose diverse hand-designed interaction functions to model different properties of semantic attributes. In the DDI dataset, the semantic nature of drug interactions is diverse, and our example for asymmetric type and symmetric type is to validate the semantic diversity in different datasets. Such diversity is what motivates us to use NAS to search for adaptive models.\n\n> Q1.1 CSSE-DDI-FF and KnowDDI both are fine-grained Subgraph Selection. What is the reason for the performance difference？\n\n**R2.1**. It should be noted here that the query subgraph of KnowDDI, which is extracted by combining external biological knowledge graphs (HetioNet), contains richer external information, such as genes, diseases, proteins, etc. We label KnowDDI as a fine-grained subgraph selection method, which means that it utilizes a graph structure learning module to realize a fine-grained information supplementation and pruning of the extracted subgraphs. Whereas, although our variant (CSSE-DDI-FF) carries out fine-grained subgraph selection, the variant only employs a basic GNN backbone (CompGCN) to encode subgraphs without external knowledge, which makes it difficult to effectively capture the semantic information in the subgraphs, and thus lead to some performance differences. \n\nAnd CSSE-DDI still outperforms KnowDDI without relying on external knowledge by fine-grained subgraph selection and data-specific encoding function, which directly demonstrates the effectiveness of our method in capturing complex interactions in DDI datasets.\n\n> Q1.2 Whether CSSE-DDI can be used to predict DDI for new drugs?\n\n**R2.2**. As the reviewer pointed out, there is a strong need to predict DDI related to new drugs in real-world scenarios. Therefore, to further validate the effectiveness of our method, we use the inductive setting and datasets in the EmerGNN[5] method, to predict drug-drug interactions between emerging drugs and existing drugs. The experimental results are shown in Table 3. It can be seen that there is a significant performance drop from the transductive setting to the inductive setting, which shows that the DDI prediction for new drugs is more difficult. Emergnn, which is specifically designed for new drug prediction, achieves optimal performance. However, CSSE-DDI still achieves impressive performance, which is mainly due to the robust learning ability of NAS technology for unknown data.\n\n|Table 3|Drugbank||TWOSIDES||\n|-------|-------|-------|-------|-------|\n| |F1|ACC|ROC-AUC|PR-AUC|\n|CompGCN|30.98±3.26|52.76±0.46|84.83±1.02|83.68±1.86|\n|Decagon|11.39±0.79|32.56±0.92|57.49±1.75|59.38±1.09|\n|SumGNN|26.57±1.59|44.30±1.04|80.02±2.17|78.42±1.62|\n|KnowDDI|31.14±1.24|53.44±1.73|84.23±2.63|82.58±1.94|\n|EmerGNN|58.13±1.36|69.53±1.97|87.42±0.39|86.20±0.71|\n|**CSSE-DDI**|37.24±1.13|58.57±0.85|88.33±0.52|86.47±0.27|\n\n**References**\n\n[1] Translating Embeddings for Modeling Multi-relational Data, NeurIPS' 13.\n\n[2] Embedding Entities and Relations for Learning and Inference in Knowledge Bases, ICLR' 15.\n\n[3] Holographic Embeddings of Knowledge Graphs, AAAI' 16.\n\n[4] RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space, ICLR' 19.\n\n[5] Emerging Drug Interaction Prediction Enabled by Flow-based Graph Neural Network with Biomedical Network. Nature Computational Science' 23.", "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": "Kc98CPkoDZ", "reviewer": "Reviewer_zvSg", "summary": "The article presents a novel method for predicting drug-drug interactions (DDIs) by using a customized subgraph selection and encoding process. The authors propose a framework called Customized Subgraph Selection and Encoding for Drug-Drug Interaction prediction (CSSE-DDI), which leverages neural architecture search (NAS) to tailor the subgraph selection and encoding components for different datasets.Extensive experiments demonstrating superior performance of the CSSE-DDI framework compared to hand-designed methods.", "questions": "If the author solves the above weaknesses, I am willing to change my score.\n\nIn addition, the author's method solves the subgraph sampling problem. Whether the model can perform visual analysis on the sampled subgraphs is critical for the interpretability of the model.\n\nIf possible, I hope the author can provide more baseline comparisons and include a greater variety of experimental settings (such as inductive settings, which are common in many DDI tasks), as well as experiments on more datasets.", "limitations": "N/A", "rating": 3, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.The use of NAS to customize subgraph selection and encoding for DDI prediction is a novel approach that addresses the limitations of fixed, hand-designed methods.\n\n2. The creation of extensive subgraph selection and encoding spaces allows for more accurate and context-specific predictions.\n\n3. The framework's ability to adapt to different datasets and customize subgraph components based on data-specific characteristics is a significant strength.", "weaknesses": "1.The author applies NAS to the DDI task, but it does not exhibit the task-specific customization expected for DDI. For instance, the primary focus of the DDI task should be the interactions between drugs. However, the author raises the following issues: \"The relaxation strategy is a prerequisite for differentiable NAS methods. This is because the subgraphs in the selection space comprise different nodes and edges, making it challenging to design a relaxation function that unifies subgraphs of varying sizes. Additionally, to search within the subgraph selection space, we must first obtain all subgraphs within this space, but the task of sampling such a large number of subgraphs is computationally infeasible.\" These issues are also present in subgraph extraction tasks on a single graph.\n\n2.To address the problem of subgraph sampling, the author employs an implicit encoding sampling method. However, its effectiveness in terms of time efficiency and accuracy lacks sufficient evidence.\n\n3.In the DDI task, the subgraph sampling space grows exponentially. The author's method for addressing the excessively large sampling space does not offer any advantages over the methods used to address the large sampling space in a single graph.\n\n4.The author does not provide a comparison of the time overhead between their NAS method and the baseline methods. Given that NAS is likely to have significantly high time overhead, this comparison is crucial for evaluating model performance.\n\n5.The author lacks comparisons with the latest baselines to highlight the performance advantages of their model. For instance, only one of the baselines chosen by the author is from 2023.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your time and efforts in reviewing our paper. Please find our responses below to your concerns.\n\n> W1. About task-specific customization expected for DDI.\n\n**R1**. Please refer to the general response **GR1**.\n\n> W2. Time efficiency and accuracy about implicit encoding sampling method.\n\n**R2**. The time overhead of using explicit subgraphs is huge. When we use explicit subgraphs, we need to sample all candidate subgraphs of a query. For $\\eta=3$ on Drugbank, the sampling time is 15 hours. In the process of searching, the memory overhead will be multiple times that of the subgraph-based method. \n\nHowever we can prove the effectiveness of our method in the following way: We collect the corresponding subgraph sizes of different queries obtained from the search process, explicitly sample the subgraphs of the corresponding sizes and use the searched message functions to encode the subgraphs and predict the interactions between drug pairs， called CSSE-DDI(explicit). Table 4 shows the experimental results. It can be seen that the prediction performance of explicit sampling and implicit sampling is similar. However, in terms of single running time, the explicit sampling method needs to perform a separate message passing on each subgraph, whereas the implicit sampling method is more efficient as it can quickly obtain subgraph representations using the subgraph representation approximation strategy.\n\n|Table 4|Drugbank|||\n|-------|-------|-------|-------|\n| |F1|ACC|Running time(minutes)|\n|CSSE-DDI(explicit)|91.63±0.29|94.23±0.54|201|\n|**CSSE-DDI**|92.08±0.22|95.56±0.15|32|\n\n> W3. About the advantage of the proposed subgraph sampling space.\n\n**R3**. Please refer to the general response **GR1**.\n\n> W4. About time overhead between their NAS method and the baseline methods. \n\n**R4**. Please refer to the general response **GR2**.\n\n> W5. Lack comparisons with the latest baselines.\n\n**R5**. Thanks for the suggestion. We add the results of comparisons with multiple latest baselines, as shown in Table 6, including LaGAT[1] published in 2022, ACDGNN[2] published in 2023, and TransFOL[3] published in 2024. All codes are publicly available.\n\n|Table 6|Drugbank||TWOSIDES||\n|-------|-------|-------|-------|-------|\n| |F1|ACC|ROC-AUC|PR-AUC|\n|LaGAT (2022)|81.63±0.56|86.21±0.18|89.78±0.21|86.33±0.15|\n|ACDGNN (2023)|86.24±0.93|90.53±0.38|93.69±0.47|92.12±0.21|\n|TransFOL (2024)|89.97±1.64|91.92±0.89|94.16±0.62|93.52±0.53|\n|**CSSE-DDI**|92.08±0.22|95.56±0.15|95.47±0.02|94.21±0.05|\n\nAs can be seen, CSSE-DDI is still competitive against the latest baselines. For LaGAT[1], it still extracts the same range of subgraphs for different queries, and in addition R-GAT is still a suboptimal solution for handling diverse DDI interaction data. For ACDGNN, its overall framework is still based on a complete bio-heterogeneous network for reasoning, and its expressive power is still limited compared with the subgraph-based approach.For TransFOL, which utilizes cross-transformers and graph convolutional networks to deal with interactions in DDI datasets, it mainly focuses on complex logical query tasks in DDI data, and does not have any advantage in single drug-drug interaction prediction tasks.\n\n> Q1. About visual analysis.\n\n**R6**. We visualize some of the sampled subgraphs in Section 4.5.1 and make some case studies to demonstrate the effectiveness and interpretability of our method. In the revised version, we will add more visual analysis.\n\n> Q2. Provide more baseline comparisons, inductive setings, as well as experiments on more datasets. \n\n**R7**. For the experimental results of the latest baselines, please refer to **R5**.\n\nIn terms of inductive settings. we use the inductive setting and datasets in EmerGNN[4] method, to predict drug-drug interactions between emerging drugs and existing drugs. The experimental results are shown in Table 7. Emergnn, which is specifically designed for new drug prediction, achieves optimal performance. However, CSSE-DDI still achieves impressive performance, which is mainly due to the robust learning ability of NAS technology for unknown data.\n\n|Table 7|Drugbank||TWOSIDES||\n|-------|-------|-------|-------|-------|\n| |F1|ACC|ROC-AUC|PR-AUC|\n|CompGCN|30.98±3.26|52.76±0.46|84.83±1.02|83.68±1.86|\n|SumGNN|26.57±1.59|44.30±1.04|80.02±2.17|78.42±1.62|\n|KnowDDI|31.14±1.24|53.44±1.73|84.23±2.63|82.58±1.94|\n|EmerGNN|58.13±1.36|69.53±1.97|87.42±0.39|86.20±0.71|\n|**CSSE-DDI**|37.24±1.13|58.57±0.85|88.33±0.52|86.47±0.27|\n\nFor more datasets, most of the research work on DDI prediction only uses the DrugBank and TWOSIDES datasets, but we have been continually looking to see if there are other available datasets to validate the effectiveness of our approach.\n\n[1] LaGAT: link-aware graph attention network for drug–drug interaction prediction, Bioinformatics' 22.\n\n[2] Attention-based cross domain graph neural network for prediction of drug–drug interactions, Briefings in Bioinformatics' 23.\n\n[3] TransFOL: A Logical Query Model for Complex Relational Reasoning in Drug-Drug Interaction, IEEE Journal of Biomedical and Health Informatics' 24.\n\n[4] Emerging Drug Interaction Prediction Enabled by Flow-based Graph Neural Network with Biomedical Network. Nature Computational Science' 23.", "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": "6IM9QfbUwN", "reviewer": "Reviewer_KE8i", "summary": "The paper proposes a novel subgraph-based approach for predicting drug-drug interactions (DDIs) that harnesses neural architecture search (NAS) to customize subgraph selection and encoding process. The authors first introduce refined search spaces to realize fine-grained subgraph selection and expressive encoding function searching. Then, based on the well-defined bi-level search problem, the subgraph space relaxation mechanism and the representation approximation strategy are proposed, enabling differentiable searching efficiently. Extensive experiments show that CSSE-DDI extensively outperforms the state-of-the-art approaches.", "questions": "Given the method itself is general, is there any reason why the authors would like to specifically focus on DDI prediction?", "limitations": "The authors have adequately addressed the limitations.", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1.The problem and the method are well-motivated and formulated, with extensive experimental support. The results are solid.\n2.The idea of customizing subgraph selection and encoding is a conceptually strong and justified innovation, which can distinguish this paper from other approaches, as shown in Table 1. \n3.The manuscript is well-structured and clearly written, facilitating comprehension.\n4.CSSE-DDI demonstrates superior performance on two recognized benchmarks, indicating its practical effectiveness. The case study shows interpretability in the context of drug interactions, which is a very important aspect in such an application paper.", "weaknesses": "1. For the supernet training phase, in addition to the algorithm process, the authors are encouraged to provide an illustration to help the reader understand the corresponding steps more clearly.\n2. A typo error in line 220: “Subgraph Repersentation“", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your time and efforts in reviewing our paper. Please find our responses below to your concerns.\n\n> W1.\tFor the supernet training phase, in addition to the algorithm process, the authors are encouraged to provide an illustration to help the reader understand the corresponding steps more clearly.\n\n**R1**. Thanks to your suggestion, we will add a graphical illustration of the search process in the revised version to show the supernet training process more clearly.\n\n> W2.\tA typo error in line 220: “Subgraph Repersentation“\n\n**R2**. Thank you for your careful review! We have thoroughly checked the entire text and corrected all spelling and formatting issues.\n\n> Q1.\tGiven the method itself is general, is there any reason why the authors would like to specifically focus on DDI prediction?\n\n**R3**. DDI is a critical task in pharmacology and healthcare. Compared with the generalized multi-relational graph link prediction, DDI prediction has more explicit application scenarios and practical needs. Therefore, we design CSSE-DDI based on the DDI prediction task and dataset. However, our method can also be used for generalized multi-relational graph link prediction, i.e., knowledge graph relation prediction, after the modification of search space, And we will include some discussions about knowledge graph relation prediction in the revised version.", "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:
Dear reviewers,

Thank you for your time and comments in reviewing our paper. To summarize, all reviewers agree that **the use of NAS to customize subgraph selection and encoding for DDI prediction is a novel approach** (Qw7Z, zvSg, KE8i, 2Vrd). **The manuscript is well-structured and clearly written, facilitating comprehension** (Qw7Z, KE8i). **The problem and the method are well-motivated and formulated, with extensive experimental support** (zvSg, KE8i). The proposed method, CSSE-DDI, **addresses the DDI prediction problem effectively** (Qw7Z, zvSg, KE8i). The case study **shows interpretability in the context of drug interactions, which is a very important aspect in such an application paper** (KE8i).

We believe all of the reviewers’ concerns can be addressed. In the following, we respond to the main concerns and suggestions raised in the review:

### GR1. Task-specific customization for DDI (zvSg, Qw7Z)

Our customization for the DDI prediction task is the search space adapted to the DDI datasets:

- **Search Space**: We design subgraph selection spaces **(the dense property of DDI dataset)** and subgraph encoding spaces **(the diverse semantic nature of DDI dataset, i.e., asymmetric patterns in DrugBank and symmetric in TWOSIDES)** adapted to the DDI dataset (Sec 3.2).

### GR2. The inherent overhead of neural architecture search (Qw7Z, zvSg)

We would like to kindly argue that **our design for the search algorithm with the implicit subgraph sampling strategy is efficient**. Table G1 shows the running overhead of our method and other subgraph methods on the DrugBank dataset, for the subgraph methods, before the "+" sign represents the explicit subgraph sampling overhead, and for our method, before the "+" sign represents the searching overhead, and after the "+" sign represents the model's single running time. 

|Table G1|Running time(minutes)|
|-------|-------|
|SumGNN|342+361|
|KnowDDI|379+393|
|**CSSE-DDI**|444+32|


In general, **CSSE-DDI and the subgraph approach are comparable or even superior in terms of time overhead**, which stems from the fact that our implicit subgraph sampling strategy saves a lot of time in the subgraph sampling and representation phases.

### GR3. Inductive setting (Qw7Z,2Vrd)

There is a strong need to predict DDI related to new drugs in real-world scenarios. Therefore, to further validate the effectiveness of our method, we use the inductive setting and datasets in the EmerGNN[1] method, to predict drug-drug interactions between emerging drugs and existing drugs. The experimental results are shown in Table G2. It can be seen that there is a significant performance drop from the transductive setting to the inductive setting, which shows that the DDI prediction for new drugs is more difficult. Emergnn, which is specifically designed for new drug prediction, achieves optimal performance. However, **CSSE-DDI still achieves impressive performance**, which is mainly due to the robust learning ability of NAS technology for unknown data.

|Table G2|Drugbank||TWOSIDES||
|-------|-------|-------|-------|-------|
| |F1|ACC|ROC-AUC|PR-AUC|
|CompGCN|30.98±3.26|52.76±0.46|84.83±1.02|83.68±1.86|
|Decagon|11.39±0.79|32.56±0.92|57.49±1.75|59.38±1.09|
|SumGNN|26.57±1.59|44.30±1.04|80.02±2.17|78.42±1.62|
|KnowDDI|31.14±1.24|53.44±1.73|84.23±2.63|82.58±1.94|
|EmerGNN|58.13±1.36|69.53±1.97|87.42±0.39|86.20±0.71|
|**CSSE-DDI**|37.24±1.13|58.57±0.85|88.33±0.52|86.47±0.27|

Please let us know if there are any outstanding concerns, and we are happy to discuss them. We would appreciate it if you could take our responses into consideration when making the final evaluation of our work.

Sincerely,

Authors


**References**

[1] Emerging Drug Interaction Prediction Enabled by Flow-based Graph Neural Network with Biomedical Network. Nature Computational Science' 23.

Meta-review: The paper presents an approach for drug-drug interactions (DDIs) prediction, based on subgraph selection and encoding. Specifically, they use  neural architecture search (NAS) to customize the subgraph-based pipeline to the data at hand, motivated by the fact that different DDI datasets have different semantic natures of interactions.

The presented approach seems sufficiently novel, the experimental part is convincing, the use case is a nice add-on that showcases the interpretability of the approach. I recommend acceptance.
Decision: Accept (poster)