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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Principal component analysis for learning tree ten
 sor networks - Anthony Nouy (Université de Nantes)
DTSTART;TZID=Europe/London:20180309T114500
DTEND;TZID=Europe/London:20180309T123000
UID:TALK102130AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/102130
DESCRIPTION:We present an extension of principal component ana
 lysis for functions of multiple random variables a
 nd an associated algorithm   for the approximation
  of such functions using tree-based low-rank forma
 ts (tree tensor networks). A multivariate function
  is here considered as an element of a Hilbert ten
 sor space of functions defined on a product set eq
 uipped with a  probability measure. The algorithm 
 only requires evaluations of functions on a struct
 ured set of points  which is constructed adaptivel
 y. The algorithm constructs a hierarchy of subspac
 es associated with the different nodes of a dimens
 ion partition tree and a corresponding hierarchy o
 f projection operators\, based on interpolation or
  least-squares projection. Optimal subspaces are e
 stimated using empirical principal component analy
 sis of interpolations of partial random evaluation
 s of the function.  The algorithm is able to provi
 de an approximation in any tree-based format with 
 either a prescribed rank or a prescribed relative 
 error\, with a number of evaluations of the order 
 of the storage complexity of the approximation for
 mat.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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