Seminar| Institute of Mathematical Sciences
Time: Friday, November 21th, 2025,16:10-17:00
Location: RS408, IMS
Speaker: Siliang Zhang, East China Normal University
Abstract: Joint latent space models (JLSMs) offer a powerful framework for analyzing network data alongside node attributes, which is common in fields like psychometrics. A critical and unresolved challenge, however, is selecting the dimension of the latent space. Current methods often rely on ad-hoc pre-specification or computationally expensive post-hoc procedures, limiting their practical use and reliability.
In this talk, we introduce a novel Bayesian JLSM that solves this problem. By incorporating a cumulative ordered spike-and-slab (COSS) prior, our model automatically and simultaneously infers the appropriate latent dimension from the data while estimating all other model parameters. We present an efficient MCMC algorithm for computation and establish strong theoretical guarantees, including posterior concentration on the true dimension and near-optimal estimation rates. Extensive simulations and two real-data applications demonstrate the method's superior performance in both dimension recovery and parameter estimation. Our framework provides a principled, efficient, and theoretically-grounded solution for one of the most persistent challenges in network modeling.