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UID:224896
DTSTAMP:20251003T113317Z
DTSTART;TZID=America/New_York:20251006T100000
DTEND;TZID=America/New_York:20251006T110000
URL;TYPE=URI:https://wpiedudev.wpi.edu/news/calendar/events/department-math
 ematical-sciences-financial-math-seminar-nils-detering-heinrich-heine-univ
 ersitat
SUMMARY:Department of Mathematical Sciences Financial Math Seminar: Nils De
 tering, Heinrich-Heine-Universität Düsseldorf
DESCRIPTION:\n\n\n      \n\n\n\nDepartment of Mathematical Sciences\nFinanc
 ial Math Seminar\nMonday, October 6th, 2025\n10:00AM-11:00AM\nSalisbury La
 bs 104\nSpeaker: Nils Detering, Heinrich-Heine-Universität Düsseldorf\nTit
 le: Learning from one graph: transductive learning guarantees viageometry 
 of random small worlds\nAbstract: One of the primary use-cases of graph co
 nvolution neural networks (GCNs) is for transductive learning (TL), such a
 s node-label prediction where missing node labels are inferred using only 
 one realization of a (random) graph and one realization of a (random) node
  features matrix. However, TL for GCNs remains poorly understood since it 
 lies outside of the standard statistical toolbox which requires multiple s
 amples to perform inference. This paper fills these gaps in TL with new co
 ncentration of measure-based tools that exploit the emergent geometry of l
 arge dense random graphs using new, low-dimensional, metric embedding argu
 ments.Our TL guarantees remain meaningful with few labelled nodes N and at
 tain the optimalnon-parametric rate O(N-1/2 ) when N is large. We present 
 two results: one for arbitrarydeterministic k-vertex graphs, and another f
 or random graphs sharing key geometric traits with an Erdős-Rényi graph G=
 G(k, p) in the regime P € (log(k)1/2 /k1/2. We apply our results to the co
 nvolutional neural network (GCN) setting where additional challenges mater
 ialize.\n
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