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SUMMARY:Analysis of p-Laplacian Regularization in Semi-Supervised Learning
  - Matthew Thorpe (University of Cambridge)
DTSTART:20171026T140000Z
DTEND:20171026T150000Z
UID:TALK93364@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:This talk concerns a family of regression problems in a semi-s
 upervised setting. The task is to assign real-valued labels to a set of n 
 sample points\, provided a small training subset of N labelled points. A g
 oal of semi-supervised learning is to take advantage of the (geometric) st
 ructure provided by the large number of unlabelled data when assigning lab
 els. In this talk the geometry is represented by the random geometric grap
 h model with connection radius r(n). The framework is to consider objectiv
 e functions which reward the regularity of the estimator function and impo
 se or reward the agreement with the training data\, more specifically we w
 ill consider discrete p-Laplacian regularization.\n\nThe talk concerns the
  asymptotic behaviour in the limit where the number of unlabelled points i
 ncreases while the number of training points remains fixed. The results ar
 e to uncover a delicate interplay between the regularizing nature of the f
 unctionals considered and the nonlocality inherent to the graph constructi
 ons. I will give almost optimal ranges on the scaling of r(n) for the asym
 ptotic consistency to hold. For standard approaches used thus far there is
  a restrictive upper bound on how quickly r(n) must converge to zero as n 
 goes to infinity. I will present a new model which overcomes this restrict
 ion. It is as simple as the standard models\, but converges as soon as r(n
 ) -> 0.\n\nThis is joint work with Dejan Slepcev (CMU).
LOCATION:MR 14\, CMS
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