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SUMMARY:Distilled Sensing: Adaptive Sequential Experimental Designs for La
 rge-Scale Multiple Hypothesis Testing - Rob Nowak (University of Wisconsin
 -Madison)
DTSTART:20100430T150000Z
DTEND:20100430T160000Z
UID:TALK24452@talks.cam.ac.uk
CONTACT:8047
DESCRIPTION:The engineering and scientific study of large-scale systems is
  now a\nmajor focus in technology\, biology\, sociology\, and cognitive\ns
 cience. Deciding where\, when\, what and how to sense or measure is a\ncru
 cial question in the scientific study of such systems.  The most\ncommon a
 pproaches to experimental design are non-adaptive in the sense\nthat all d
 ata are collected prior to analysis and processing. One can\nenvision\, ho
 wever\, adaptive strategies in which information gleaned\nfrom previously 
 collected data is used to guide the selection of new\ndata.\n...\nIn this 
 talk I will discuss the role of adaptive experimental designs\nin the cont
 ext large-scale multiple hypothesis testing problems\, which\nare of centr
 al importance in the biological sciences today.  Formally\,\nconsider p in
 dependent tests of the form H0: X ~ N(0\,1) vs. H1: X ~\nN(m\,1)\, for m>0
 .  It is well known reliable decisions are possible\nonly if m\, the signa
 l amplitude\, exceeds sqrt(2 log p)\, when p is very\nlarge.  This is simp
 ly because the magnitude of the largest of p\nindependent N(0\,1) noises i
 s on the order of sqrt(2 log p).  All\nstandard techniques in multiple tes
 ting (e.g.\, Bonferroni\, FDR) are\nlimited by this fact.  However\, I'll 
 show that this limitation only\nexists because all the data are collected 
 prior to testing.  What if\nwe could collect and test a bit of data first\
 , then refine our data\ncollection by focusing only on the most promising 
 cases?\n...\nDistilled Sensing (DS) is an adaptive multi-stage experimenta
 l design\nand testing procedure that implements this refinement idea.  Giv
 en the\nsame experimental budget\, DS is capable of reliably detecting far
 \nweaker signals than possible from non-adaptive measurements.  I'll\nshow
  that reliable detection is possible so long as the signal\namplitudes exc
 eed any arbitrarily slowly growing function of p. For\npractical purposes\
 , this means that DS is capable of reliable\ndetection at signal-to-noise 
 ratios that are roughly log(p) weaker\nthan that required by non-adaptive 
 methods.  If one were interesting\nin testing p=10000 genes\, for example\
 , then DS can handle noise levels\n10 times greater than the limits of non
 -adaptive methods.\nThis is joint work with J. Haupt and R. Castro.  A rel
 ated manuscript\nis online at http://arxiv.org/abs/1001.5311.\n\n\nhttp://
 www.ece.wisc.edu/~nowak/
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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