A1734
Title: Latent space models for grouped multiplex networks
Authors: Alexander Kagan - University of Michigan (United States) [presenting]
Ji Zhu - University of Michigan (United States)
Liza Levina - University of Michigan (United States)
Abstract: Latent space models such as the stochastic block model and the random dot product graph are popular ways of modeling single-layer networks. However, their application to more complex network structures has not received a lot of attention so far. MacDonald et al. [2021] made a substantial step in this direction by introducing the MultiNeSS model allowing to extract a latent space component shared by a sample of multiplex networks: multiple, heterogeneous networks observed on a shared node set together. This work, however, has an apparent limitation arising from the fact that groups of networks within this sample may have individual group structures besides the one that is common for the whole sample. Such group stratification may arise when for each network in a sample we additionally observe a categorical attribute, e.g.together with the patients' brain region connectivity networks we can have access to their gender, ethnicity, age group, or control/treatment label. For this more general model that we call GroupMultiNeSS, we establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions. We compare the model with the original MultiNeSS model in various synthetic and real-world scenarios and observe an apparent improvement in the modeling accuracy when the group component is accounted for.
