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SUMMARY:Least squares regression on sparse grids - Bastian Bohn (Universit
 ät Bonn)
DTSTART:20190222T094000Z
DTEND:20190222T101500Z
UID:TALK120259@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk\, we first recapitulate the framework of least sq
 uares regression on certain sparse grid and hyperbolic cross spaces. The u
 nderlying numerical problem can be solved quite efficiently with state-of-
 the-art algorithms. Analyzing its stability and convergence properties\, w
 e can derive the optimal coupling between the number of necessary data sam
 ples and the degrees of freedom in the ansatz space.<span>Our analysis is 
 based on the assumption that the least-squares solution employs some kind 
 of Sobolev regularity of dominating mixed smoothness\, which is seldomly e
 ncountered for real-world applications. Therefore\, we present possible ex
 tensions of the basic sparse grid least squares algorithm by introducing s
 uitable a-priori data transformations in the second part of the talk. Thes
 e are tailored such that the resulting transformed problem suits the spars
 e grid structure.<br><br></span>Co-authors: Michael Griebel (University of
  Bonn)\, Jens Oettershagen (University of Bonn)\, Christian Rieger (Univer
 sity of Bonn)<br>
LOCATION:Seminar Room 1\, Newton Institute
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