GENN: Predicting Correlated Drug-drug Interactions with Graph Energy Neural Networks
Authors: Tengfei Ma
Junyuan Shang
Cao Xiao
Jimeng Sun
Venue:  (2020)
Keywords: graph neural networks
energy model
structure prediction
drug-drug-interaction

Abstract: Gaining more comprehensive knowledge about drug-drug interactions (DDIs) is one of the most important tasks in drug development and medical practice. Recently graph neural networks have achieved great success in this task by modeling drugs as nodes and drug-drug interactions as links and casting DDI predictions as link prediction problems. However, correlations between link labels (e.g., DDI types) were rarely considered in existing works.
 We propose the graph energy neural network (\mname) to explicitly model link type correlations.  We formulate the DDI prediction task as a structure prediction problem and introduce a new energy-based model where the energy function is defined by graph neural networks. Experiments on two real-world DDI datasets demonstrated that \mname is superior to many baselines without consideration of link type correlations and achieved $13.77\%$ and $5.01\%$ PR-AUC improvement on the two datasets, respectively. We also present a case study in which \mname can better capture meaningful DDI correlations compared with baseline models.

Under review as a conference paper at ICLR 2020
GENN: PREDICTING CORRELATED DRUG-DRUG IN- TERACTIONS WITH GRAPH ENERGY NEURAL NET- WORKS
Anonymous authors Paper under double-blind review
ABSTRACT
Gaining more comprehensive knowledge about drug-drug interactions (DDIs) one of the most important tasks in drug development and medical practice. Re- cently graph neural networks have achieved great success this task by modeling drugs nodes and drug-drug interactions as links and casting DDI predictions as link prediction problems. However, correlations between link labels (e.g.. DDI types) were rarely considered in existing works. We propose the graph energy neural network (GENN) to explicitly model link type correlations. We formulate the DDI prediction task structure prediction problem, and introduce new energy-based model where the energy function is defined by graph neural net- works. Experiments on Iwo real world DDI datasets demonstrated that GENN is superior to many baselines without consideration of link type correlations and achieved 13.77% and 5.01% PR-AUC improvement on the two datasets, respec- tively. We also present case study in which GENN can better capture meaningful DDI correlations compared with baseline models.
INTRODUCTION
The use drug combinations is common and often necessary for treating patients with complex dis- eases. However, it also increases the risk of drug-drug interactions (DDI). DDIs are pharmacological interactions between drugs that can alter the action either or both drugs and cause adverse effects. Overall DDIs result in large number of fatalities per year and incur $177 billion DDI associated cost annually (Giacomini et al. 2007). To mitigate these risks and costs, accurate prediction of DDI becomes clinically important task.
While DDI knowledge expensive to gather, several deep learning approaches have been proposed search the large biomedical data for predicting potential DDIs (Zitnik al. 2018 Ma et al., 2018 Ryu et al. 2018). Among them, graph neural networks (GNN) that consider DDI prediction the graph setting have obtained great performance. In DDI graphs, drugs represented nodes and embedded into a low- www-dimesional space. Further prediction can be made based on casting DDI prediction as a link prediction problem where DDI types are represented link types (Kipf & Welling 2016: Zitnik et al. 2018).
However, existing works rarely exploit the correlations between these link types (e.g.. DDI types) despite of their importance. For example, in Fig. [ Warfarin is drug for treating blood clots. Its combined use with antibiotic or nonsteroidal anti-inflammatory drugs can cause multiple DDI types including nhibition of clotting, gastrointestinal bleeding, and hemorrhage. These DDI types are correlated since they are all bleeding related DDIs caused by the increase of Warfarin's effect. Explicit modeling such correlations help infer unseen DDI types.
To fill the gap, we propose GENN, a new deep architecture that predicts correlated DDIs based on graph neural networks and energy based models. Specifically, leverage the dependency structures among DDI types and formulate multi-type DDI detection as a structure prediction problem (Laf- ferty al. 2001a: LeCun et al., (2006) Belanger & McCallum 2016b). Here use energy based approach to incorporate such dependency structures.
To summarize, GENN is enabled by the following technical contributions.

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Anticongulant
Inhibit
hamorrhage
Celecaxdb
Gastrolntestiral bleeding
Gestronttssinal bleeding
Inhibit clotting
hamorfage
Fluconazole
Naproxen
Bleeding related DDI types
Figure 1: Warfarin as an anticoagulant, if taken together with antibiotic drugs such as Cefixime or Fluconazole, will have high risk to cause DDIs inhibition of clotting and gastrointestinal bleeding. Likewise, if Warfarin if concomitant with nonsteroidal anti-inflammatory drugs (NSAIDs) such as Celecoxib and Naproxen, will likely to cause DDI hemorrhage (i.e., loss of blood from broken blood vessel). These DDIs correlated since they are all bleeding related DDIs caused by the increase of Warfarin's ' effect.
1. Modeling link type correlations. GENN bridges graph neural networks and structure prediction to directly capture link type correlations for more accurate link prediction in graphs through minimizing energy function.
2. A new graph neural network based energy function. Inspired by a family of structure pre- diction model called structured prediction energy networks (SPENs) (Belanger & McCallum, 2016a), we design a new graph energy function based on graph neural networks to capture the global dependencies among link types in DDI graphs. This is more flexible and expressive than previous approaches which used CRF-type energy definitions Qu et al. (2019).
Efficient semi-supervised training. We designed one cost-augmented inference network to ap- proximate the output in training and one test inference network to approximate the output in test- ing. Different from the previous inference method for SPENs, we propose a new semi-supervised joint optimization procedure adapt to our problem graphs. The new inference method op- timizes the training-set structured hinge loss together with the test-set energy with respect to the parameters for both inference networks and the energy function.
We evaluated GENN on two real world DDI datasets with both quantitative and qualitative study. Results demonstrated GENN outperformed basic graph neural networks with 13. 77% and 5.01% PR-AUC improvement on the two datasets, respectively.
RELATED WORK
2.1 DDI PREDICTION
To predict unseen DDIs based known ones, drug similarity has been learned via nearest neigh- bor approaches (Zhang et al. 2017). and using random walk methods including label propaga- tion (Zhang al. 2015 Wang al. 2010), and unsupervised methods (Wang al. 2014 An- gione et al. 2016). Recently, deep graph neural networks have been demonstrated to provide much improved performance DDI prediction. Among them, (Ma et al. 2018) integrates different sources of drug-related information with heterogeneous formats into an coherent and information- preserving representation using attentive multi-view graph auto-encoders (Kipf & Welling 2016). Decagon (Zitnik et al. 2018) develops a new graph auto-encoder approach, which allows to de- velop an end-to-end trainable model for link prediction on a multi-modal graph. As the experimental results in Zitnik et al. (2018) show graph neural networks achieved significantly improved perfor- mance than shallow models such as tensor decomposition (Nickel et al.] 2011 Papalexakis et al. 2017), random walk based methods (Perozzi al. 2014 Zong al. (017), and non-graph neural fingerprinting (Duvenaud et al.) 2015 Jaeger et al. 2018), DeepDDI (Ryu et al. (018). None the existing DDI prediction works consider the correlation among multiple DDI types.
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2.2 STRUCTURE PREDICTION AND ENERGY BASED MODELS
Structure prediction is an important problem in various application domains where we want to pre- dict structured outputs instead of independent labels, e.g., structured labels prediction for object detection (Zheng et al.] 2b015b) semantic structure prediction (Belanger et al. (017) or part-of- speeches tagging (Ma & Hovy| 20166). For structure prediction problems, feed-forward networks insufficient since they cannot directly model the interaction or constraints of the outputs. Instead, energy based models (LeCun al., (006) provide one way to address the challenge by defining a much more flexible and expressive energy score, and the prediction is conducted by minimizing the energy function.
One of the well-known structure prediction approaches is the conditional random fields (CRF) Laf- ferty et al. 2001b) which show success application areas such as named entity recognition Sato et al. 2017 2017 and image segmentation (Zheng et al. 2015a). But structured linear model, CRF has limited representation ability. To enhance the flexibility of structure prediction models, Belanger & McCallum (016bb proposed Structured Prediction Energy Networks (SPENs) which uses arbitrary neural networks to define the energy function and optimizes the energy over a continuous relaxation of labels. Thus it can capture high-arity interaction among output labels and approximate the opti- mization of energy function via gradient descent and repeated "loss-augmented inference", [Belanger al. (2017) further developed an "end-to-end" method that unroll the approximate energy optimiza- tion to a different computation graph. However, after learning the energy function, they still have to use gradient descent for test-time inference. Later, Tu & Gimpel (2018) replaced the gradient descent with neural network trained to do inference directly. However, it separates the training of cost-augmented inference network and the fine-tuning of another inference network for testing, which makes it inefficient. In addition, how to optimize the SPENs on graphs for semi-supervised learning remains challenging. this paper our method improves the algorithm of Tu & Gimpel 2018 to solve this problem.
Very recently, GMNN et al. 2019) combines the statistical relational learning (SRL) and graph neural networks. It includes a CRF to model the joint distribution of object labels conditioned on object attributes, and then it is trained with a variational EM algorithm. The model has been used for node classification and link classification. However, it cannot be easily extended for prediction of missing links, since they have to use links as nodes in a "dual graph" for link classification, but the missing links generally cannot be modeled as nodes.
PRELIMINARY
In this section, first summarize our task in Section 3.1 then basic message passing graph neural network (MPNN) is described for embedding the DDI graph in Section 3.2
3.1 TASK FORMULATION
Definition (DDI Graph) Given a DDI graph G {V,E}, V the node set which contains N drug nodes with node features X E TRNN and E is the edge set which contains all DDIs between drug pairs. For a specific drug pair x; R. X2 E RR,, the DDIs of this pair erjj can have multiple types, i.e. ei, E {0, 13 where D is the feature dimension and L is the total number of DDI types. And these DDI vectors e form the edge features (or labels) Y E {0, 11
Problem 1 (DDI Prediction) We cast the DDI prediction into a multi-type link prediction problem. We assume there are some missing edges Yo in the graph, i.e. Y x= YY,,, Yu). Given the node features X and some known DDI links YT, to the goul to predict the unknown DDIs Yu-
3.2 MESSAGE PASSING NEURAL NETWORKS FOR DDI PREDICTION
Recently graph neural networks (GNNs) have been successfully applied to DDI prediction (Zimik jet al., 2018.) Ma et al, 2018). To predict the unknown DDIs in a graph, a GNN first learns the node embeddings of all the drug nodes and then make prediction based on these embedding. In this
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Graph Edge Representation
predicted labels neighbor edges neighbor
Graph Node Representation
E,(X,
Figure 2: Graphical structure of GENN. Message passing procedure is conducted using Eq. | to update i-th node hidden state by aggregating neighbor edges and nodes information. Prediction made for edge ei based on Eq. 2 Furthermore, interaction among all labels globally as introduced in Eq.
an energy function via GNN build
section, we describe a basic message passing based graph neural network (Gilmer et al. 2017) for drug node embedding. Considering that our graph contains different types of edges, we select schema including edge information in the message passing. Given the graph G with node features X, for each node with hidden state hy and neighborhood Mii, we define the message passing layer to update the node hidden state as follows:
h W.h
E JEN()
(5.S(e,))) Vi V, = Wox;
where es, E R is the edge (DDI type vector) between nodes x,, X, E RD, W. E MXM Wo E M are both learnable weight, and f(.) MRM is a neural network, i.. MLP.
The message passing layer can then be stacked get the final state h; for each node, iee the node embedding. Then we can use these final states to predict the probability of DDI types for each edge:
Vi. Sigmoid W (ha/[hh)++1
+
where || indicates concatenation, W I and b e RRM are parameters and Sigmoid is the activation function commonly used for multi-label prediction.
The model is trained on the partially known DDI edges Yz by optimizing cross entropy loss LeE (YL, Yz) Ee,,ey,, (Vi,( ct,)) between the predictions and the true edges. After training, it can directly used for prediction of unknown DDIs Ye.
THE GENN METHOD
We present our GENN framework in this section (Fig. 2}. framework for DDI prediction and the design of our graph energy functions based MPNN. Then we propose a joint learning strategy with semi-supervised learning setting in Section 4.3
We first discuss the design of energy based
Obviously the aforementioned message passing neural network does not explicitly consider the DDI correlation the prediction. However, in practice, the labels are often correlated as we stated the introduction section. So re-formulate labels by optimizing an energy function. In order to get extremely powerful representation for the energy model, follow the ideas of SPENs to formulate the energy function neural network.
problem as structure prediction problem and infer the
4.1 ENERGY FUNCTION DESIGN
The SPENs define the energy E(X,Y) as a neural network that takes both the input features X and labels Y as inputs and returns the energy. Although the SPENs can almost obtain arbitrarily high expressiveness, in practice it requires trade-off between using increasingly expressive energy networks and being more vulnerable overfitting (Belanger & McCallum 2016b), so the energy function need to be properly designed.
Energy function via GNN Recall the message passing neural network we used before, the edge information is also included in the neural networks. If aggregate all the nodes' and edges'
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information to get the whole graph's representation. it is natural to derive an "energy" over the graph. Motivated by this intuition, we formulate a new and simple energy function from a graph neural network:
1 N h.))
E(X, Y) (ea,out(Gu(X, Y)) ReLP
Eb))
(3)
Where Go is an arbitrary graph neural network (GNN) which accepts node features X and edge features Y which can be initialized by multi-hot encoding storing labels, h, is the node embedding of final output of GNN which contains information of neighbor nodes and edges, MLP is a multi- layer perceptron network. Obviously, Eq. (3 contains both the interaction between each X and Y and the interaction among all labels Y. When we have an energy function, the inference of the predicted label then simply becomes minimize the energy function:
= arg min E(X, Y,, Yu) Yo
(4)
4.2 TRAINING COST-AUGMENTED INFERENCE NETWORK
The training of SPENs usually takes the structured hinge loss (Tsochantaridis et al. 20004] Belanger & McCallum 2016b) and relaxes the edge labels to be continuous for easier optimization. Assume the parameters for the energy function Eq. (3) is O our problem becomes:
min max ma (Y, Y2)) (X, Y,) Ex(X, Y Y
(5)
where Yz are the ground -round-truth DDI edges for training, and Y are the predictions on these edges. A the structured error function which returns non-negative value to indicate the difference between the ground truth and prediction; and [+]+ means max(0,) -). In this paper, we use L1 loss as A.
This above training loss is expensive to directly optimize due the cost-augmented inference step. Following the idea of & (201), we use a augmented inference network (i.e. a graph neural network) Go (X, Y.)) to approximate the output Ý, L in the training phase.
min max maxima (G+ Y)), YL) - Ee X, G& (X, YL)) + (x Y +
(6)
The problem can be seen as minimax game and optimized by alternatively optimizing e and 4.
(1) Fix O, we can optimize the parameters for the cost-augmented inference networks max (X, YL), Y.) Ee(X, G XX Y.)) + Ex Yt))+
(2) Fix T optimize O:
min min[A(G4(XX, YL), Y2) (e)))Ee((( Ee(X, (X, Y1)) (X( Yz)
(8)
4.3 SEMI-SUPERVISED JOINT TRAINING AND INFERENCE
The trained cost-augmented inference network cannot be directly used for test inference because of the cost augmentation. Notice that objective function to infer the unknown labels in the testing phase is Eq. Due to the additional term in the loss function Eq. K during training, the derived training inference network cannot lead to minimized energy. Thus we need another test inference network to optimize Eq. in the testing phase.
We propose the test inference network Yú = (X, YL) to directly approximate the test output. Since the test edge features not given(instead, we only know the indices of edges to test), so this test inference network also use and Y,. as its inputs. In the DDI prediction problem, the training set and test set share the same set of nodes X in single graph. In this graph, the energy optimization in the test phase should not be regarding only Yo but the all graph including both Y, and the predicted Yv, as we showed in Eq. (4). Since this energy function is a graph neural network, that is to say, we use both Y and the prediction Yū as edge attributes for the computation of Eq. (4). When the parameter θ for the energy function given, the objective for this inference network is as below:
min Es (X, YL, G (X.Y YL))
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The previous methods (e.g. Tu & Gimpel 2018 first fine-tune the trained inference network on training data again with respect to the original inference objective without cost augmentation arg ming ( Go (X, (X,Yr))) Y)).. But the real effect of this fine-tuning is actually doubted (Tu & Gim-
pel (2088). Also considering that the definition of training-set energy and the test-set energy are in the same graph, and the test inference network should not deviate too much from the training cost-augmented inference network, we are proposing a new joint training strategy as follows.
We design the test inference network to share some bottom layers with the training cost-augmented inference networks. Then we do the optimization with the two following steps:
(1) Fix 6 optimize the parameters for both the cost-augmented inference networks and the test inference network.
max V.V
( X, YL), Ee(X, X Gb (X, YL)) (X, Yx)] Ee Y,, G YL))
(10)
To better discriminate the two inference networks, we use G to indicates the predictions on training edges, and G are the predictions on and missing edges. À is a hyperparameter which often set as 1 in practice. Notice that & and v are not independent but share some parameters.
To better understand the benefit of the joint training, let us rewrite the parameter and v into (oo, L1) } and (oo, 1 where Do is the shared parameter set between & and v for the shared layers of the two inference networks. Then the above optimization problem becomes:
max [A(Gt (X, YL), YL) (X, G 01 (X, YL)) Ex(X, Y2)I+ 4o.91.99 11
(11)
Eo, YL, G. v, (z)
From this equation we can see the optimization of the second term, i.c. the test-set energy, can also impact the training of the cost-augmented inference network. If we fix all other parameters, the 1 still gives the test inference network enough flexibility to only optimize the test energy term; meanwhile the shared layers and the shared parameter 2g kept the two inference networks not deviate too much
(2) Fix & and V, we do not want the test inference network to impact the energy function (so that objective for optimizing θ is still from Eq. (6), so the min function is unchanged, i.c. still Eq. (8)
5 EXPERIMENT
We evaluate GENN model to answer the following questions:
1. Q1: Does GENN provide more accurate DDI prediction than foed-forward GNNs? If so, we can demonstrate the usefulness of the energy function.
2. Q2: Does GENN improves the supervised inference method (Section 4.2 ? If sf, we can demon-
strate the effectiveness of new optimization algorithm.
3. Q3: How does GENN respond to various fraction of edge missingness?
4. Q4: Does the model really capture meaningful label correlation?
5.1 EXPERIMENTAL SETUP
Data We implemented our experiments on two public datasets (with some modification of the set- ting): DeepDDI and Decagon. For both datasets, we randomly select 80% of the drug-drug pairs as training data, 10% as validation data and the remaining 10% test data. For a given drug-drug pair, we predict its DDI types. Note that one drug-drug pair can have zero, one or multiple DDI types, so it is multi-label prediction problem.
DeepDDI Dataset Ryu et al. 2018) consists of 1861 drugs (nodes) and 222,127 drug-drug pairs (edges) from DrugBank which results in 113 different DDI types as labels. 99.87% drug-drug pairs only have one type of DDI. The edge exists when two drugs has at least one DDI type. The input feature for each drug is generated based on structural similarity profile (SSP), then its dimension
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is reduced to 50 using principal components analysis (PCA) as suggested by DeepDDI. Moreover, Chemical- basee similarity measure is used to reduce the the effect of redundant drugs on prediction accuracy where redundant similar drugs in training and test dataset will overestimate the predictive performanc as noted in Gottlieh et al. al.] (2012). In particular, we use Tanimoto score (Tanimoto 1957) and find 90% drug pairs has less than 0.4721 similarity score which show that there need to tackle the effect of redundant drugs.
BIOSNAP-sub Dataset (Marinka Zitnik& & Leskoved 2018 consists of 645 drugs (nodes) and 46,221 drug-drug pairs (edges) from TWOSIDES dataset which results in 200 different DDI types as labels. We extract data from Zimik et al. 2018) and only keep 200 medium DDI types ranging from Top-600 to Top-800 800 that every ddi type has at least 90 drug combinations which contains proper number of edges for fast evaluation. 73.2 23.27% drug-drug pairs have more than one type of DDI. The input feature is 32-dimension vector by transforming one-hot encoding by Gaussian random projection using Pedregosa al. (201T).
coammonl--occurriig
Baselines We compared GENN with the following baselines.
1. Label Propragation (LP) (hu et al. 2003 is a similarity-basee semi-supervised method which makes use of unlabeled data to better generalize to new samples.
2. MLP is the model used in original DeepDDI dataset which accepts pairwise features (e.g. struc- tural similarity profile (SSP) between two drugs to predict DDI.
3. Walk learns d-dimensional neural features for nodes based on biased random walk proce- dure exploring network neighborhoods of nodes. For each drug pair, we concatenate the learned DeepWalk feature vectors and its original drug feature representation and use the MLP same as the above method to do classification.
4. GNN is basic graph neural network based on MPNN framework introduced in
5. GLENN is designed to be an energy model with a CRF-style local energy function and the same inference algorithm GENN. Notice that each node and all its connected edges form clique (because these edges are mutual neighbors and they are also connected to each other due to the correlation),
E- = E, fx EjeN()) f2(e),)). The difference between Eq. (3) and Eq. ① is that it does not include the neighbor node features the equation. It is linear and has only one layer. We call it graph local energy neural network (GLENN) and use the same optimization strategy as our final model.
6. GENN is an ablation model without semi-supervee supervised joint training and inference. GENN is our final model that incorporates the power of GNNs and energy models.
The Implementation Details can be found in Appendix B
Metries. To measure the prediction accuracy, we used the following metrics
1. ROC-AUC: Area under the receiver operating characteristic curve: the area under the plot of the true positive rate against the false positive rate at various thresholds.
2. PR-AUC: Area under the precision-recal curve: the area under the plot of precision versus recall
curve various thresholds.
3. P@ K: short for Precision at K which is the mean percentage of correct predicted labels among
TOP-K over all samples. Here, specially choose P@1 1 and P@5 to validate performence as usually done in multi-label learning setting.
Following Decagon ZZinik et al. 2018), we calculated the ROC-AUC and PR-AUC for each single label, and then use the average scores the final values.
5.2 RESULTS
Performance Comparison For each dataset, use 3 different random splits and run all the models on that split. The results are then averaged over runs and we report the mean and std values in test dataset see Table I] Note that the results on DeepDDI dataset in Table i is based on the 60% randomly sampled data, because it will take more than 2 days for models to converge with limited performance gain total dataset.
From Table. π we can see Welk and the methods based on MPNN framework outperform MLP and I.P in both datasets with large margin. It indicates the neighbor edges and nodes information
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Table I: Performance on DeepDDI and BIOSNAP-sub Dataset (I.P caused memory emror in Deep-
DDI dataset).
Method
P@0 1
P655
PR-AUC
ROC-AUC
LP
MLP
0.7311 (.0026)
0.1926 (.0005)
0.5888 (.0362)
0.9736 (.0032)
DeepWalk
0.7773 (.0029)
0.1962 (.0019)
0.6276 (.0139)
0.9786 (.0046)
DeepDDI
GNN
0,9002 (:0119)
0.1986 (.0002)
0.7606 (.0187)
0.9861 (.0066)
GLENN
0.8928 (.0067)
0.1986 (.0002)
0.7590 (.0095)
0.9891 (.0058)
GENN
0,9020 (.0220)
0.1987 (.0004)
0.8389 (.0512)
0.9871 (.0071)
GENN
0,9077 (.0293)
0.1990 (.0003)
0.8635 (.0286)
0.9928 (.0052)
LP
0.1089 (.0049)
0.0850 (.0040)
0.0607 (.0013)
0.6414 (.0010)
MLP
0.2120 (:0019)
0.1508 (.0009)
0.1675 (.0022)
0.8041 (.0009)
DeepWalk
0.2463 (.0012)
0.17119 (.0011)
0.1908 (.0029)
0.8311 (.0019)
BIOSNAP-sub
GNN
0.3275 (00231)
0.2215 (.0184)
0.2494 (.0208)
0.8757 (.0172)
GLENN
0.3255 (.0192)
0.2213 (.0181)
0.2476 (.0209)
0.8756 (.0172)
GENN
0.3290 (.0102)
0.2216 (.0137)
0.2503 (.0175)
0.8788 (.0159)
GENN
0.3396 (.0072)
0.2326 (.0016)
0.2602 (.0034)
0.8855 (.0026)
actually help the representation learning which improve the performance. Compared with GNN, GLENN achieves nearly the same performance and gets little better score with respect to ROC- AUC. As for GENN, it outperforms others with respect all metrics in both datasets which give the positive answer to Q1 that GENN does provide more accurate DDI prediction. Especially, compared to GNN and GLENN, it demonstrates the power of new designed graph neural network based global energy function. It more expressive and flexible to capture the label correlation. In addition, for variants of GENN, the supervised learning model GENN" setting performs worse compared with GENN which give the answer of Q2
Analysis of Robustness
DDI
TYPE
17
36
102
0.5
Performance (w.r:t PR. with Dufferent Edge Ratio
0.0
1.0
recthed
11.4
1P
0.88
Doup Walk
0.5
CNN
PR-Ato Score
GLEN
0.0
8.8
GENN
0.5
Truth
0.4
75
MLP
DeepWalk
0.5
GNN
0.0
GLENN
0.2
GENN
0.1
102
0.5
Edge OF Perrsmt
0.0
Figure 3: Analysis of Robustness. Methods are trained on 5%. 10% and 30% of edges on Deep- DDI dataset. Mean PR-AUC with standard devia- tion values are reported on the rest of edges. (Note that the performance of LP is missing at the ratio of 30% because of memory error.
Figure 4: Correlation Analysis. Pearson corre- lation coefficients between four randomly chosen DDI types. Each diagnoal subplot shows the cor- relations between ground truth and different meth- ods, while upper diagonal subplot shows the pair- wise correlations between DDI types.
We design experiments to show that compared with baseline models, GENN achieved empirically more robust performance in the setting high edge missingness. We let each method be trained on 5%, 10%, and 30% of edges DeepDDI dataset, and predict on the rest of them. From Figure. we can see that GENN is better than all the baselines in every percentage point (Q3).
Correlation Analysis
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In correlation analysis experiment, chose the models trained 60% DeepDDI dataset same as the models reported in Table. [ and made DDI type predictions on the rest of the edges (40% left test dataset). To illustrate that GENN is able to capture correlation between labels, i.c., different DDI types by incorperating energy function, we further calculate the pearson correlation coefficent between distribution of DDII types. For each of the 113 DDI types define its distribution by counting the number of occurrences in the prediction on each drug node over all edges in test dataset.
The PairGrid figure shows the pairwise relation between these randomly chosed four DDI types, numbered as 17, 36, 75. 102. For instance, DDI type 17 means "Drug may increase the cardiotoxic activities of Drug b" and DDI type 36 means "Drug a may decrease the bronchodilatory activities of Drug b". For the ground truth, DDI type 17 has medium correlation with DDI type 36 but MLP and DeepWalk overestimate the coefficient. Especially for DDI type 102, only GLENN and GENN capture the true distribution same with the ground truth. On the one hand, it is consistent with the high performance achieved by GENN. On the other hand, the consistency between Truth and GENN demonstrates that GENN really capture some label correlation which answers Q4.
CONCLUSION
In this paper, we proposed GENN to cast DDI detection structure prediction problem with new GNN based energy function. Experiments on two real DDI datasets demonstrated that GENN superior to the models without consideration of link type correlations and achieved up 0.8635 (13.53% relative improvement) with respect to PR-AUC. Future works includes extending the corre- lated GNNs heterogeneous networks and incorporating medical domain knowledge with structure information such as drug classification ontology in the learning.
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Under review as a conference paper at ICLR 2020
A NOTATIONS
Table 2: Notations used in GENN.
Notation
Definition
the whole graph data with nodes, edges set 3 node feature matrix with nodes and features dimension D
XERAXD
ei E 10,
DDI type vector between nodes i, with different types
YE 1llxL Y E [0, 1
ground truth labels and prediction labels of all graph
h h E RR
i-th node's feature at t-th update and final out of MPNN graph neural networks (GNN)
G())
B,U.W.
learnable weight matrices and bias energy function parameterized by θ training and testing inference network
E)(X.Y) Y)
Go Go,Go
B IMPLEMENTATION DETAILS
Most methods are implemented in PyTorch-vI.In 1.0 (Paszke et al. 2017) based on Fey Lenssen 2019) and trained Ubuntu 18.04 with 56 CPUs and 64GB memory.
We use the implementation from Pedregosa et al. (20II) for Label Propagation method with the setting of 0.25 gamma value for rbf kernel and 200 maximum number of iteration. As for Deep Walk method, the official implementatior 33 is used with the setting of embedding dimension as 50 and the length of random walk as 20.
We implement training inference network (G&), test inference network (G₂) and energy network Ee with the same 2-layer message passing neural network (MPNN) encoder and 1-hidden-layer MLP decoder structure. Hidden dimension are all set as 100, and to reduce the number of parameters and ensure the two inference networks (G4 and G do not deviate too much, we share the message passing layer for them, while make the MLP layer different. For energy network Ee, we also use message passing for node encoding, but the layer has different set of parameters from the inference networks in order to make the minimax training schema more effective. For MLP decoder, we use natch-normalization technology (Toffe Szegedy 2015) with Relu non-linear activation function.
For training efficiency, we first train the basic MPNN (i.e. GNN baseline) on the training data, and then initialize all MPNN layers used in inference networks and energy networks with the these pre-trained parameters. We use the learning rate 0.01 for methods to train and 0.001 to fine tuning on two datasets with carly-stop mechanism (i.c., training is stopped when there is no performance improvement on validation dataset with 35 consecutive epochs). Threshold for prediction is simply set as 0.4.
C
CROSS ENTROPY REGULARIZATION
From the experience of Tu & Gimpel (2018). adding local cross entropy loss to the energy func- tion could improve the performance a lot. It can be seen as multi-task training with two objectives: energy optimization and reconstruction error minimization. We add the reconstruction cross-entropy loss of both the training and test inference networks in Eq. (1O) to train better inference network ap- proximations.
max (A(G) Y.), Y,) - Es X, (X, Yr)) + Eg (X, Yr.))+ 4.
(12)
- Ee G (X, YD)) - X2L CF - X3 CE
where LE Lo (x, Yz), Yt), LE = Loe XX Y Yz) and X2, A3 are hyperpa- rameters which can all be set as the same as A practice. Note that these additional regularization terms are independent of θ, so we do not need to add it when minimizing over θ (Eq. ( is still unchanged).
12

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Under review as a conference paper at ICLR 2020
Table 3: Correlation Analysis Between Pair of DDI Type. (1 means increase while J means de- crease).
Pair of DDI Types
Truth
GENN
GNN
Metabolism
Bradycardic Activitics
0.6423
0.5375
0.3176
Risk Hypotension f
Neuromuscular Blocking Activities
0.3347
0.2954
-0.0027
Risk of Hyperkalemia
Neuromuscular Blocking Activities
0.2854
0.2822
0.3913
D CORRELATION ANALYSIS
As shown in table there are three pairs DDI type which shows large (0.6423), medium (0.3347) and small postive correlation (0.2854) indicated by Truth column. For the first pair of DDI type, decreasing metabolism has large correlation with increasing the bradycardic activities in ground truth but GNN only got medium correlation coefficient much lower than GENN'. As for the last two pairs of DDI type, GNN performed bad and gave nearly zero coefficient for the second and overestimated the coefficient for the last. In the meantime, GENN corresponds with the ground truth which in some extent gives the evidence that GENN has the power to capture correlation between labels.
13


Reviews:
[{"review_id": "ryx_dOHk9r", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper proposes a framework to learn correlated drug-drug interaction based on structured prediction energy networks (SPEN). The core idea is to model the dependency structure of the labels (multi-label) by minimizing a designed energy function. The graph energy is designed as MLP over the mean of all nodes embeddings, where the nodes embeddings are obtained through a graph convolutional network. The edge information is included in the node embedding when aggregating neighborhood information. The proposed method also introduces an additional test inference network to jointly train with the cost-augmented training network under the semi-supervised setting. The authors tested on two DDI datasets and the result shows improvement compared to several baseline methods.\n\nStrengths\n- motivation: the authors consider the correlations between DDI labels (multi-label) which could potentially improve prediction of DDI. The proposed method uses structure prediction energy networks to model such dependency.\n\n- method: the proposed method introduce an additional test inference network to fit the energy minimization framework into a semi-supervised setting.\n\nWeakness\n- The core part of the proposed method which differs from previous works needs to be elaborated more.\n- The performance improvement seems to be marginal, especially on the second dataset.\n\nDetailed comments\n- The work is based on structured prediction energy networks (SPEN, Belanger, et al. 2016) and its follow-up works (eg., Belanger et al. 2016, Lifu Tu et al. 2018), the overall framework is very similar with previous work, where the feature extraction part is replaced by a graph convolutional network module. The core difference lies in the additional testing inference network which is jointly trained for adapting supervised SPEN into a semi-supervised setting. This part actually differs from all previous works and needs to be elaborated more. Why does such design make sense and what benefit can be brought through such design? The formulation for semi-supervised SPEN could be defined more clearly and worth elaboration.\n\n- The experiments are run on 3 different random splits, based on the mean(std) of the evaluation metric, the performance of the proposed method does not vary much compared to baselines, especially on the second dataset, eg., GNN 0.25 +/- 0.02 compared with GENN 0.26. Also, GLENN < GNN seems to imply including energy is not the most important part for helping the task, but rather the semi-supervised joint training truly improves the performance. ", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A"}, "extra_text": {}}, {"review_id": "r1gnZ-O-qr", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper presents a graph neural network for drug-to-drug interaction (DDI) prediction, which explicitly models link type correlation. Basically, the drug-to-drug interaction prediction problem is a specific type of link prediction task, with drugs as vertices and interaction as edges, and the authors propose a graph neural network with an energy-based formulation where the link types are encoded as the graph edges. The authors validate their method against feedforward GNNs on two DDI prediction datasets, and achieve significantly improved performances.\n \nPros\n- The drug-to-drug interaction prediction is a relatively less explored application of deep learning with growing interests.\n- The proposed energy-based formulation that considers link type correlation intuitively makes sense and performs significantly better than some of the existing GNN approaches. \n \nCons\n- Using energy-based formulation for graph neural network is not novel, and thus the paper lacks novelty in methodology point of view. Thus this paper seems to fit better for a pharmaceutical journal or a journal rather than a top-tier deep learning conference such as ICLR. I do not think the paper will be of interest to a large audience.\n \n- The experimental validation is limited. The authors only compare against GNN and GLENN, without even mentioning other relevant baselines such as GCN and GAT. Thus I suggest the authors to perform a more extensive comparative study.\n \n- The qualitative analysis is insufficient, even as a domain-specific empirical study paper. It would be better if the authors included actual examples of drug-drug interaction predicted by the proposed model and an existing model, for further analysis and interpretation.\n \nIn sum, while I believe that DDI prediction is an interesting application of deep learning with growing interests, I do not believe the paper has sufficient novelty or experimental validation / qualitative examples to be a meaningful contribution to ICLR. I suggest the authors to work on the experimental validation and qualitative analysis part and submit it to a workshop or a pharmaceutical journal instead.  \n", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory."}, "extra_text": {}}, {"review_id": "S1lFnblnKS", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Abstract:\nUnderstanding drug-drug interactions (DDI) is an important task in drug development and prescription management. The authors proposed a new graph energy neural network (GENN) for DDI prediction. Comparing to the existing Decagon model (Zitnik et al. 2018), the proposed new model considered correlations between DDI types and used a new energy function to capture this information. By comparing to the previous baselines, the authors demonstrated their approach was able to achieve the SOAT performance in terms of prediction accuracy, be more robust to missing DDI data, and better capture the correlations between DDI types.\n\nMajor comments:\nThe authors succeed in combining graph neural networks and structure prediction to capture correlations of DDI types between drug-drug pairs.   They used an energy function based on graph neural networks to capture the dependencies among edge types in DDI graphs.  \n\nHowever, the description of training cost-augmented inference network and test inference network is convoluted. The authors didn't elaborate on why trained cost-augmented inference network cannot be directly used for test inference, and why the prediction for unknown DDI type is different in test inference.  In addition, the notations used in the last sentence of the second paragraph of section 4.3 seem to be inconsistent with Eq. (4)\n\nThe authors compared their model (GENN) with multiple baselines and demonstrated superior performance only in PR-AUC. In the description for Table 1, the authors claimed: \"GENN largely outperforms others with respect to all metrics in both datasets.\"  However, this conclusion can not be supported by Table 1, in which GENN only shows trivial improvement comparing to GNN for the most reported metrics.\n\nLast but not least, the authors did not provide any limitations of their work. \n\nMinor comments:\nIn general, the paper is well written and easy to follow, except for sections 4.2 and 4.3.  As mentioned above, the notations used in the last sentence of the second paragraph of section 4.3 seem to be inconsistent with Eq. (4)", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I did not assess the derivations or theory.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I made a quick assessment of this paper."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper studies the use of a graph neural network for drug-to-drug interaction (DDI) prediction task (an instance of a link prediction task with drugs as vertices and interaction as edges). In particular, the authors apply structured prediction energy networks (SPEN) and model the dependency structure of the labels by minimising an energy function. The authors empirically validate the proposed approach against feedforward GNNs on two DDI prediction tasks. The reviewers feel that understanding drug-drug interactions is an important task and that the work is well motivated. However, the reviewers argued that the proposed methodology is not novel enough to merit publication at ICLR and that some conclusions are not supported by the empirical analysis. For the former, the benefits of the semi-supervised design need to be clearly and concisely presented. For the latter, providing a more convincing practical benefit would greatly improve the manuscript. As such, I will recommend the rejection of this paper at the current state.
Decision: Reject