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SUMMARY:Stochastic approximation techniques\, continuum scaling limits of 
 high dimensional networks\, and bias of network sampling algorithms
DTSTART:20230706T151500
DTEND:20230706T170000
DTSTAMP:20260501T053312Z
UID:c56f6fad4010dfa5a76d284c1e4d0c0f089ca93a56d90b8bc2d71401
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Shankar Bhamidi University of North Carolina\, Chapel Hi
 ll\nThe last few years have seen an explosion in the development and use o
 f network models in a host of real world applications. Canonical examples 
 include the understanding of bias of network sampling algorithms in measur
 ing and promoting individuals in a network with multiple types\, and the u
 se of objects such as the single linkage clustering tree (i.e. the Minimal
  spanning tree(MST)) in understanding unsupervised learning problems.\n \
 nDynamic network models arise naturally either in studying the evolution o
 f real world networks or for inherent algorithmic pipelines to analyze dat
 a (e.g. Kruskal's algorithm for constructing the MST). In this talk\, we w
 ill describe the use of stochastic approximation techniques to understand 
 two major themes in dynamic networks\, where stochastic approximation tech
 niques play a key role:\n \na) We will described ideas building up to und
 erstanding the following conjecture from the early 2000s from statistical 
 physics: for network models where edges are given iid random edge weights\
 , the minimal spanning tree with edges properly rescaled should converge i
 n the limit to compact random fractals. Further if the degree exponent of 
 the model \\tau > 4\, then graph distances in the MST scale like n^{1/3} w
 hile for \\tau \\in (3\,4) graph distances scale like n^{(\\tau-3)/(\\tau-
 1)}. \n \nb) We will describe ideas for studying the bias of network cen
 trality algorithms in measuring popularity of individuals in a canonical m
 odel in social networks with vertices of different attribute types (e.g. m
 inorities and majorities)\,  in particular showing that while the degree 
 exponent can depend on the attribute type\, more global measures such as t
 he Page-rank do not depend on the attribute type. A surprising by-product 
 of this analysis is the efficacy of Page-rank driven sampling in settings 
 of rare minorities.\n 
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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