GENN: Predicting Correlated Drug-drug Interactions with Graph Energy Neural Networks

1 INTRODUCTION . The use of drug combinations is common and often necessary for treating patients with complex diseases . However , it also increases the risk of drug-drug interactions ( DDI ) . DDIs are pharmacological interactions between drugs that can alter the action of either or both drugs and cause adverse effects . Overall DDIs result in a 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 a clinically important task . While DDI knowledge is expensive to gather , several deep learning approaches have been proposed to search the large biomedical data for predicting potential DDIs ( Zitnik et al. , 2018 ; Ma et al. , 2018 ; Ryu et al. , 2018 ) . Among them , graph neural networks ( GNN ) that consider DDI prediction in the graph setting have obtained great performance . In DDI graphs , drugs are represented as nodes and embedded into a low-dimensional space . Further prediction can be made based on casting DDI prediction as a link prediction problem where DDI types are represented as 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 . 1 Warfarin is a 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 can 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 , we leverage the dependency structures among DDI types and formulate multi-type DDI detection as a structure prediction problem ( Lafferty et al. , 2001a ; LeCun et al. , 2006 ; Belanger & McCallum , 2016b ) . Here we use an energy based approach to incorporate such dependency structures . To summarize , GENN is enabled by the following technical contributions . 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 an energy function . 2 . A new graph neural network based energy function . Inspired by a family of structure prediction 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 ) . 3 . Efficient semi-supervised training . We designed one cost-augmented inference network to approximate the output in training and one test inference network to approximate the output in testing . Different from the previous inference method for SPENs , we propose a new semi-supervised joint optimization procedure to adapt to our problem on graphs . The new inference method optimizes 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 . 2 RELATED WORK . 2.1 DDI PREDICTION . To predict unseen DDIs based on known ones , drug similarity has been learned via nearest neighbor approaches ( Zhang et al. , 2017 ) , and using random walk methods including label propagation ( Zhang et al. , 2015 ; Wang et al. , 2010 ) , and unsupervised methods ( Wang et al. , 2014 ; Angione et al. , 2016 ) . Recently , deep graph neural networks have been demonstrated to provide much improved performance in DDI prediction . Among them , ( Ma et al. , 2018 ) integrates different sources of drug-related information with heterogeneous formats into an coherent and informationpreserving 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 us to develop 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 performance than shallow models such as tensor decomposition ( Nickel et al. , 2011 ; Papalexakis et al. , 2017 ) , random walk based methods ( Perozzi et al. , 2014 ; Zong et al. , 2017 ) , and non-graph neural fingerprinting ( Duvenaud et al. , 2015 ; Jaeger et al. , 2018 ) , DeepDDI ( Ryu et al. , 2018 ) . None of the existing DDI prediction works consider the correlation among multiple DDI types . 2.2 STRUCTURE PREDICTION AND ENERGY BASED MODELS . Structure prediction is an important problem in various application domains where we want to predict structured outputs instead of independent labels , e.g. , structured labels prediction for object detection ( Zheng et al. , 2015b ) , semantic structure prediction ( Belanger et al. , 2017 ) or part-ofspeeches tagging ( Ma & Hovy , 2016 ) . For structure prediction problems , feed-forward networks is insufficient since they can not directly model the interaction or constraints of the outputs . Instead , energy based models ( LeCun et al. , 2006 ) 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 ) ( Lafferty et al. , 2001b ) which show success in application areas such as named entity recognition ( Sato et al. , 2017 ) and image segmentation ( Zheng et al. , 2015a ) . But as a structured linear model , CRF has limited representation ability . To enhance the flexibility of structure prediction models , Belanger & McCallum ( 2016b ) 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 optimization of energy function via gradient descent and repeated “ loss-augmented inference ” . Belanger et al . ( 2017 ) further developed an “ end-to-end ” method that unroll the approximate energy optimization 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 a 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 . In this paper our method improves the algorithm of Tu & Gimpel ( 2018 ) to solve this problem . Very recently , GMNN ( Qu 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 can not 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 can not be modeled as nodes . 3 PRELIMINARY . In this section , we first summarize our task in Section 3.1 , then a basic message passing graph neural network ( MPNN ) is described for embedding the DDI graph in Section 3.2 . 3.1 TASK FORMULATION . Definition 1 ( DDI Graph ) Given a DDI graph G = { V , E } , V is the node set which contains N drug nodes with node features X ∈ RN×D , and E is the edge set which contains all DDIs between drug pairs . For a specific drug pair xi ∈ RD , xj ∈ RD , the DDIs of this pair ei , j can have multiple types , i.e . ei , j ∈ { 0 , 1 } L , 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 ∈ { 0 , 1 } |E|×L . Problem 1 ( DDI Prediction ) We cast the DDI prediction into a multi-type link prediction problem . We assume there are some missing edges YU in the graph , i.e . Y = { YL , YU } . Given the node features X and some known DDI links YL , the goal is 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 ( Zitnik et 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 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 a schema including edge information in the message passing . Given the graph G with node features X , for each node with hidden state hti and its neighborhood N ( i ) , we define the message passing layer to update the node hidden state as follows : ht+1i = Wsh t i + ∑ j∈N ( i ) htj · f ( ei , j ) ; ∀i ∈ V , h0i = W0xi ( 1 ) where ei , j ∈ RL is the edge ( DDI type vector ) between nodes xi , xj ∈ RD , Ws ∈ RM×M , W0 ∈ RM×D are both learnable weight , and f ( · ) ∈ RM×M is a neural network , i.e . MLP . The message passing layer can then be stacked to get the final state hi for each node , i.e . the node embedding . Then we can use these final states to predict the probability of DDI types for each edge : ŷi , j = Sigmoid ( W [ hi||hj ] + b ) ( 2 ) where || indicates concatenation , W ∈ RL×2M and b ∈ R2M are parameters and Sigmoid is the activation function commonly used for multi-label prediction . The model is trained on the partially known DDI edges YL by optimizing cross entropy loss LCE ( ŶL , YL ) = ∑ ei , j∈YL LCE ( ŷi , j , ei , j ) between the predictions and the true edges . After training , it can be directly used for prediction of unknown DDIs YU . 4 THE GENN METHOD We present our GENN framework in this section ( Fig . 2 ) . We first discuss the design of energy based framework for DDI prediction and the design of our graph energy functions based on MPNN . Then we propose a joint learning strategy with a semi-supervised learning setting in Section 4.3 . Obviously the aforementioned message passing neural network does not explicitly consider the DDI correlation in the prediction . However , in practice , the labels are often correlated as we stated in the introduction section . So we re-formulate our problem as a structure prediction problem and infer the labels by optimizing an energy function . In order to get extremely powerful representation for the energy model , we follow the ideas of SPENs to formulate the energy function as a neural network .

Summary: 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.