Tensorial and bipartite block models for link prediction in layered networks and temporal networks

Many real-world complex systems are well represented as multilayer networks; predicting interactions in those systems is one of the most pressing problems in predictive network science. To address this challenge, we introduce two stochastic block models for multilayer and temporal networks; one of them uses nodes as its fundamental unit, whereas the other focuses on links. We also develop scalable algorithms for inferring the parameters of these models. Because our models describe all layers simultaneously, our approach takes full advantage of the information contained in the whole network when making predictions about any particular layer. We illustrate the potential of our approach by analyzing two empirical data sets: a temporal network of e-mail communications, and a network of drug interactions for treating different cancer types. We find that multilayer models consistently outperform their single-layer counterparts, but that the most predictive model depends on the data set under consideration; whereas the node-based model is more appropriate for predicting drug interactions, the link-based model is more appropriate for predicting e-mail communication.

[1]  Kathryn B. Laskey,et al.  Stochastic blockmodels: First steps , 1983 .

[2]  Dane Taylor,et al.  Clustering Network Layers with the Strata Multilayer Stochastic Block Model , 2015, IEEE Transactions on Network Science and Engineering.

[3]  Marta Sales-Pardo,et al.  Long-Term Evolution of Email Networks: Statistical Regularities, Predictability and Stability of Social Behaviors , 2015, PloS one.

[4]  A. Raftery,et al.  Probabilistic forecasts, calibration and sharpness , 2007 .

[5]  Tamara G. Kolda,et al.  Temporal Link Prediction Using Matrix and Tensor Factorizations , 2010, TKDD.

[6]  O. Sporns,et al.  Network neuroscience , 2017, Nature Neuroscience.

[7]  Roger Guimerà,et al.  Consistencies and inconsistencies between model selection and link prediction in networks. , 2017, Physical review. E.

[8]  Vito Latora,et al.  Structural reducibility of multilayer networks , 2015, Nature Communications.

[9]  Toni Vallès-Català,et al.  Consistencies and inconsistencies between model selection and link prediction in networks. , 2017, Physical review. E.

[10]  A. Arenas,et al.  Mathematical Formulation of Multilayer Networks , 2013, 1307.4977.

[11]  Sonia Kéfi,et al.  How Structured Is the Entangled Bank? The Surprisingly Simple Organization of Multiplex Ecological Networks Leads to Increased Persistence and Resilience , 2016, PLoS biology.

[12]  Roger Guimerà,et al.  Accurate and scalable social recommendation using mixed-membership stochastic block models , 2016, Proceedings of the National Academy of Sciences.

[13]  Santo Fortunato,et al.  Network structure, metadata and the prediction of missing nodes , 2016, ArXiv.

[14]  Tin Chi Nguyen,et al.  Community assessment of cancer drug combination screens identifies strategies for synergy prediction , 2017, bioRxiv.

[15]  A. Barrat,et al.  Estimating the outcome of spreading processes on networks with incomplete information: A dimensionality reduction approach. , 2017, Physical review. E.

[16]  Jukka-Pekka Onnela,et al.  Community Structure in Time-Dependent, Multiscale, and Multiplex Networks , 2009, Science.

[17]  Ciro Cattuto,et al.  Detecting the Community Structure and Activity Patterns of Temporal Networks: A Non-Negative Tensor Factorization Approach , 2013, PloS one.

[18]  Edoardo M. Airoldi,et al.  Mixed Membership Stochastic Blockmodels , 2007, NIPS.

[19]  Tiago P. Peixoto.  Hierarchical block structures and high-resolution model selection in large networks , 2013, ArXiv.

[20]  Tiago P. Peixoto.  Inferring the mesoscale structure of layered, edge-valued, and time-varying networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Marta Sales-Pardo,et al.  Optimal prediction of decisions and model selection in social dilemmas using block models , 2018, EPJ Data Science.

[22]  Cristopher Moore,et al.  Detectability thresholds and optimal algorithms for community structure in dynamic networks , 2015, ArXiv.

[23]  Peter Kulchyski.  and , 2015 .

[24]  Cristopher Moore,et al.  Community detection, link prediction, and layer interdependence in multilayer networks , 2017, Physical review. E.

[25]  Roger Guimerà,et al.  Missing and spurious interactions and the reconstruction of complex networks , 2009, Proceedings of the National Academy of Sciences.

[26]  Roger Guimerà,et al.  A Network Inference Method for Large-Scale Unsupervised Identification of Novel Drug-Drug Interactions , 2013, PLoS Comput. Biol..

[27]  Esteban Moro,et al.  Impact of human activity patterns on the dynamics of information diffusion. , 2009, Physical review letters.

[28]  Roger Guimerà,et al.  Predicting future conflict between team-members with parameter-free models of social networks , 2013, Scientific Reports.

[29]  Mercedes Pascual,et al.  The multilayer nature of ecological networks , 2015, Nature Ecology &Evolution.

[30]  Mark E. J. Newman,et al.  Structure and inference in annotated networks , 2015, Nature Communications.

[31]  Martin Rosvall,et al.  Modelling sequences and temporal networks with dynamic community structures , 2015, Nature Communications.

[32]  Y.-Y. Liu,et al.  The fundamental advantages of temporal networks , 2016, Science.