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SUMMARY:The Dantzig Selector - Matthew Parry\, University of Cambridge
DTSTART:20090605T150000Z
DTEND:20090605T163000Z
UID:TALK18656@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:In a series of papers from 2004-7\, Candes and Tao\, in conjun
 ction with\nothers\, obtained some remarkable results for signal recovery 
 and\, more\ngenerally\, for large p small n problems. The work culminated 
 with the paper\nthat introduced the Dantzig selector.\n\nI will discuss ju
 st a few of the results from these papers. In the\nnoise-free case\, they 
 show that *exact* signal reconstruction is possible\nfrom highly incomplet
 e data [1]. I will illustrate this with an example and\noutline when one c
 an achieve exact reconstruction. It turns out the results\nare robust to n
 oise and the Dantzig selector is the approach suggested in\nsuch a scenari
 o [2]. I will run through the proofs for the accuracy of the\nresulting es
 timators in the sparse case.\n\n[1] Candes\, E. J.\, Romberg\, J. and Tao\
 , T. Robust uncertainty principles:\nexact sig-\nnal reconstruction from h
 ighly incomplete frequency information. IEEE Trans.\nInform.\nTheory (2006
 ) 52 489-509\n\nhttp://www.acm.caltech.edu/~emmanuel/papers/ExactRecovery.
 pdf\n\n[2] Candes\, E. J. and Tao\, T. The Dantzig selector: statistical e
 stimation\nwhen p is much larger than n. Annals of Statistics (2007) vol. 
 35 (6) pp.\n2313-2351\n\nhttp://projecteuclid.org/DPubS?service=UI&version
 =1.0&verb=Display&handle=euclid.aos/1201012958\n
LOCATION:MR5\, CMS
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