Abstract:  

We study the multilayer random dot product graph (MRDPG) model, an extension of the random dot product graph to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework. At every time point, we observe a realization from an MRDPG. Across layers, we assume fixed shared common node sets and latent positions but allow for different connectivity matrices. We propose efficient tensor algorithms under both fixed and random latent position cases to minimize the detection delay while controlling false alarms. Notably, in the random latent position case, we devise a novel nonparametric change point detection algorithm based on density kernel estimation that is applicable to a wide range of scenarios, including stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online.



Short Bio of the speaker:

Oscar Hernan Madrid Padilla is an Assistant Professor in the Department of Statistics at University of California, Los Angeles. Previously, from July, 2017 to June, 2019, he was a Neyman Visiting Assistant Professor in the Department of Statistics at University of California, Berkeley. Before that, I earned a Ph.D. in statistics at The University of Texas at Austin in  2017 under the supervision of Prof. James Scott. He also completed a B.S in Mathematics at CIMAT (in Mexico) in 2013.