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CATEGORIES:Statistics
SUMMARY:Latent space models for multiplex networks with sh
ared structure - Elizaveta Levina (University of M
ichigan)
DTSTART;TZID=Europe/London:20221028T140000
DTEND;TZID=Europe/London:20221028T150000
UID:TALK182723AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/182723
DESCRIPTION:Statistical tools for analysis of a single network
are now widely available\, but many practical set
tings involve multiple networks. These can arise
as a sample of networks (for example\, brain conne
ctivity networks for a sample of patients)\, a sin
gle network with multiple types of edges (for exam
ple\, trade between countries in many different co
mmodities)\, or a single network evolving over tim
e. The term multiplex networks refers to multiple
and generally heterogeneous networks observed on
the same shared node set\; the two examples above
are both multiplex networks. We propose a new la
tent space model for multiplex networks which answ
ers a key question: what part of the underlying
structure is shared between all the networks\, and
what is unique to each one? Our model learns thi
s from data and pools information adaptively. We
establish identifiability\, develop a fitting proc
edure using convex optimization in combination wit
h a nuclear norm penalty\, and prove a guarantee o
f recovery for the latent positions as long as the
re is sufficient separation between the shared and
the individual latent subspaces. We compare the
model to competing methods in the literature on s
imulated networks and on a multiplex network descr
ibing the worldwide trade of agricultural products
.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Qingyuan Zhao
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