Sparse matrix-variate Gaussian process blockmodels for network modeling

摘要

We face network data from various sources, such as protein interactions and online social networks. A critical problem is to model net work interactions and identify latent groups of network nodes. This problem is chal lenging due to many reasons. For exam ple, the network nodes are interdependent in stead of independent of each other, and the data are known to be very noisy (e.g., miss ing edges). To address these challenges, we propose a new relational model for network data, Sparse Matrix-variate Gaussian pro cess Blockmodel (SMGB). Our model gener alizes popular bilinear generative models and captures nonlinear network interactions us ing a matrix-variate Gaussian process with latent membership variables. We also assign sparse prior distributions on the latent mem bership variables to learn sparse group as signments for individual network nodes. To estimate the latent variables efficiently from data, we develop an efficient variational ex pectation maximization method. We com pared our approaches with several state-of-the-art network models on both synthetic and real-world network datasets. Experimen tal results demonstrate SMGBs outperform the alternative approaches in terms of dis covering latent classes or predicting unknown interactions.