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CATEGORIES:Statistics
SUMMARY:Low rank as a model for quantum and classical esti
mation problems - David Gross\, University of Frei
burg
DTSTART;TZID=Europe/London:20141031T160000
DTEND;TZID=Europe/London:20141031T170000
UID:TALK55708AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/55708
DESCRIPTION:The theory of compressed sensing provides rigorous
methods for analyzing the performance of estimato
rs that include a sparsity-enhancing 1-norm regula
rization term. Since around 2009\, a "non-commutat
ive" version of compressed sensing has been develo
ped. Here\, the aim is to efficiently\nrecover mat
rices under a low-rank assumption\, most commonly
using nuclear-norm regularization. The program was
initially motivated by purely classical estimatio
n problems - e.g. the influential "Netflix\nproble
m" of predicting user preferences in online shops.
However\, early on\, a fruitful interaction betwe
en classical and quantum theory ensued:\nIn one di
rection\, it has been realized that low-rank metho
ds lead to rigorous and very tight performance gua
rantees for quantum state estimation procedures. I
n the other direction\, mathematical methods\norig
inally developed in the context of quantum informa
tion theory allowed for a significant generalizati
on and simplification of the\nrigorous results on
low-rank recovery. I will give an introduction to
the theory\, as well as classical and quantum appl
ications.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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