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SUMMARY:Principal component analysis for learning tree tensor networks - A
 nthony Nouy (Université de Nantes)
DTSTART:20180309T114500Z
DTEND:20180309T123000Z
UID:TALK102259@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We present an extension of principal component analysis for fu
 nctions of multiple random variables and an associated algorithm   for the
  approximation of such functions using tree-based low-rank formats (tree t
 ensor networks). A multivariate function is here considered as an element 
 of a Hilbert tensor space of functions defined on a product set equipped w
 ith a  probability measure. The algorithm only requires evaluations of fun
 ctions on a structured set of points  which is constructed adaptively. The
  algorithm constructs a hierarchy of subspaces associated with the differe
 nt nodes of a dimension partition tree and a corresponding hierarchy of pr
 ojection operators\, based on interpolation or least-squares projection. O
 ptimal subspaces are estimated using empirical principal component analysi
 s of interpolations of partial random evaluations of the function.  The al
 gorithm is able to provide 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 f
 ormat.
LOCATION:Seminar Room 1\, Newton Institute
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