Deep Inductive Matrix Completion for Biomedical Interaction Prediction In many real tasks, side information in addition to the observed entries is available in the matrix completion problem. To make good use of this information, an inductive approach to matrix completion was proposed where the matrix entries are modeled as a bilinear function of realvalued vectors associated with the rows and the columns. However, it is not effective in handling data of nonlinear structures. In this paper, we propose a novel model called Deep Inductive Matrix Completion (DIMC) for nonlinear inductive matrix completion, which consists of two deepstructure neural networks to extract latent features from highdimensional known side vectors, and then to predict their relationships using the latent features. In DIMC, the parameters of the neural networks are alternatively optimized to minimize the reconstruction error. Then the missing entries can be readily recovered with the side vectors of rows and columns. We compare DIMC with stateoftheart methods of linear and nonlinear matrix completion in the tasks of drug repositioning, genedisease and miRNAdisease association prediction. The experimental results verified that DIMC is capable to provide higher accuracy than existing methods and is applicable to predict inductively on new rowcolumn interactions with auxiliary side information. In addition, we discuss the effects of alternating training frequency on the performance of DIMC and how we can utilize such property to implement a GPUbased parallel computing algorithm that significantly shortens the training time.

Learning a LowRank Tensor of Pharmacogenomic Multirelations from Biomedical Networks Learning pharmacogenomic multirelations among diseases, genes and chemicals from contentrich biomedical and biological networks can provide important guidance for drug discovery, drug repositioning and disease treatment. Most of the existing methods focus on imputing missing values in the diseasegene, disease chemical and genechemical pairwise relations from the observed relations instead of being designed for learning highorder diseasegenechemical multirelations. To achieve the goal, we propose a general tensorbased optimization framework and a scalable GraphRegularized Tensor Completion from Observed Pairwise Relations (GTCOPR) algorithm to infer the multirelations among the entities across multiple networks in a lowrank tensor, based on manifold regularization with the graph Laplacian of a Cartesian, tensor or strong product of the networks, and consistencies between the collapsed tensors and the observed bipartite relations. Our theoretical analyses also prove the convergence and efficiency of GTCOPR. In the experiments, the tensor fiberwise and slicewise evaluations demonstrate the accuracy of GTCOPR for predicting the diseasegenechemical associations across the largescale proteinprotein interactions network, chemical structural similarity network and phenotypebased human disease network; and the validation on Genomics of Drug Sensitivity in Cancer cell line dataset shows a potential clinical application of GTCOPR for learning diseasespecific chemicalgene interactions. Statistical enrichment analysis demonstrates that GTCOPR is also capable of producing both topologically and biologically relevant disease, gene and chemical components with high significance.