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Summary Latent space models are frequently used for modelling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well developed for more complex network structures, which are becoming increasingly common in practice. In this article we propose a new latent space model for multiplex networks, i.e., multiple heterogeneous networks observed on a shared node set. Multiplex networks can represent a network sample with shared node labels, a network evolving over time, or a network with multiple types of edges. The key feature of the proposed model is that it learns from data how much of the network structure is shared between layers and pools information across layers as appropriate. 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 provided there is sufficient separation between the shared and the individual latent subspaces. We compare the model with competing methods in the literature on simulated networks and on a multiplex network describing the worldwide trade of agricultural products.
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This content will become publicly available on March 27, 2027
Efficient Analysis of Latent Spaces in Heterogeneous Networks
This work proposes a unified framework for efficient estimation under latent space modeling of heterogeneous networks. We consider a class of latent space models that decompose latent vectors into shared and network-specific components across networks. We develop a novel procedure that first identifies the shared latent vectors and further refines estimates through efficient score equations to achieve statistical efficiency. Oracle error rates for estimating the shared and heterogeneous latent vectors are established simultaneously. The analysis framework offers remarkable flexibility, accommodating various types of edge weights under general distributions.
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- Award ID(s):
- 2515523
- PAR ID:
- 10680731
- Publisher / Repository:
- Taylor & Francis on behalf of American Statistical Association
- Date Published:
- Journal Name:
- Journal of the American Statistical Association
- ISSN:
- 0162-1459
- Page Range / eLocation ID:
- 1 to 13
- Subject(s) / Keyword(s):
- Data integration, Heterogeneity, Latent space model, Low rank, Network
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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