Kidney transplantation is the preferred treatment for people suffering from end-stage renal disease. Successful kidney transplants still fail over time, known as graft failure; however, the time to graft failure, or graft survival time, can vary significantly between different recipients. A significant biological factor affecting graft survival times is the compatibility between the human leukocyte antigens (HLAs) of the donor and recipient. We propose to model HLA compatibility using a network, where the nodes denote different HLAs of the donor and recipient, and edge weights denote compatibilities of the HLAs, which can be positive or negative. The network is indirectly observed, as the edge weights are estimated from transplant outcomes rather than directly observed. We propose a latent space model for such indirectly-observed weighted and signed networks. We demonstrate that our latent space model can not only result in more accurate estimates of HLA compatibilities, but can also be incorporated into survival analysis models to improve accuracy for the downstream task of predicting graft survival times.

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks.

Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time networks of relational events, using a latent space representation for nodes. We model relational events between nodes using mutually exciting Hawkes processes with baseline intensities dependent upon the distances between the nodes in the latent space and sender and receiver specific effects. We demonstrate that our proposed LSH model can replicate many features observed in real temporal networks including reciprocity and transitivity, while also achieving superior prediction accuracy and providing more interpretable fits than existing models.