Latent space models for grouped multiplex networks

Oregon Convention Center 

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. Mac Donald et al. [2021] made a substantial step in this direction by introducing the MultiNeSS model allowing extraction of a latent space component shared by a sample of multiplex networks: multiple, heterogeneous networks observed on a shared node set together. However, this work has an apparent limitation arising from the fact that groups of networks within this sample may have individual group structures besides the one 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 patient's protein-protein-interaction (PPI) network we can have access to their gender, ethnicity, or age group.
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 as long as there is sufficient separation between the shared, group-specific, and individual latent subspaces. We compare the model with the original MultiNeSS model in various synthetic scenarios and observe the apparent improvement in the modeling accuracy when the signal strength of the group components is comparable to the one of the shared component.

SIR model

COVID-19

Networks 

Section on Statistics in Epidemiology