Abstract:

\nMuc
h of our world is organized around categories or communities. These may be
defined by nature\, e.g.\, species\, genes\, galaxies\, or by humans\, e.
g.\, society\, products\, knowledge. In many important cases these communi
ties are not given to us and need to be learned based on local interaction
s or comparisons of the relevant entities. In mathematical terms: one has
access to a graph and one wants to extract clusters of similar nodes. As w
ith most unsupervised learning tasks\, much of the challenge in community
detection is to understand when and how such structures can be learned. Th
is talk focuses on random graph models\, showing how techniques ranging fr
om statistics\, information theory\, discrete mathematics and computer sci
ence factor in to characterize the fundamental limits.

\nBiography

\nEmmanuel Abbé received his Diploma from EPFL in 2003 and his Ph.D. deg
ree from MIT in 2008. He joined Princeton University as an Assistant Profe
ssor in 2012 and became Associate Professor in 2016. He was a visiting pro
fessor at the Simons Institute\, Berkeley\, in 2015 and a von Neumann Fell
ow at the Institute for Advanced Study\, Princeton\, in 2017. Since 2018\,
he is a Professor at EPFL in the Department of Mathematics and in the S
chool of Computer and Communication Sciences\, where he holds the Chair of
Mathematical Data Science.

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