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DTSTAMP:20121204T112411Z
UID:4F28D426-8F55-1030-AD29-0050568D3657
DTSTART;TZID=Asia/Calcutta:20120730T170000
DTEND;TZID=Asia/Calcutta:20120730T180000
DESCRIPTION:Title: Pointwise Relations between Information and Estimation i
 n Gaussian Noise Abstract: Many of the classical and recent relations betw
 een information and estimation in the presence of Gaussian noise can be vi
 ewed as identities between expectations of random quantities. These includ
 e the I-MMSE relationship of Guo et al.\; the relative entropy and mismatc
 hed estimation relationship of Verdu ?\; the relationship between causal e
 stimation and mutual information of Duncan\, and its extension to the pres
 ence of feedback by Kadota et al.\; the relationship between causal and no
 n-casual estimation of Guo et al.\, and its mismatched version of Weissman
 . We dispense with the expectations and explore the nature of the pointwis
 e relations between the respective random quantities. The pointwise relati
 ons that we find are as succinctly stated as - and give considerable insig
 ht into - the original expectation identities. As an illustration of our r
 esults\, consider Duncan?s 1970 discovery that the mutual information is e
 qual to the causal MMSE in the AWGN channel\, which can equivalently be ex
 pressed saying that the difference between the input-output information de
 nsity and half the causal estimation error is a zero mean random variable 
 (regardless of the distribution of the channel input). We characterize thi
 s random variable explicitly\, rather than merely its expectation. Classic
 al estimation and information theoretic quantities emerge with new and sur
 prising roles. For example\, the variance of this random variable turns ou
 t to be given by the causal MMSE (which\, in turn\, is equal to the mutual
  information by Duncan?s result). Speaker Bio: Kartik Venkat is currently 
 a PhD candidate in the Department of Electrical Engineering at Stanford Un
 iversity\, under the supervision of Prof. Tsachy Weissman. His research in
 terests include the interaction between information and estimation theory\
 , probability theory\, and applications of information theory in wireless 
 networks. Kartik received a Bachelors degree in Electrical Engineering fro
 m the Indian Institute of Technology\, Kanpur in 2010\, and a Masters degr
 ee in Electrical Engineering from Stanford University in 2012. He was awar
 ded the Stanford Graduate Fellowship for Engineering and Sciences\, and th
 e Numerical Technologies Founders Prize in 2011 at Stanford. He received a
  Student Best Paper Award at the International Symposium on Information Th
 eory (ISIT) 2012.\n\nCo-sponsored by: Dr. Kumar Vaibhav Srivastava\n\nSpea
 ker(s): \, \, \, \, \, \n\nRoom: DA 229\, Bldg: ACES\, Department of Elect
 rical Engineering\, Indian Institute of Technology Kanpur\, Kanpur\, Uttar
  Pradesh\, India\, 208016
LOCATION:Room: DA 229\, Bldg: ACES\, Department of Electrical Engineering\,
  Indian Institute of Technology Kanpur\, Kanpur\, Uttar Pradesh\, India\, 
 208016
ORGANIZER:kvs@iitk.ac.in
SEQUENCE:0
SUMMARY:Pointwise Relations between Information and Estimation in Gaussian 
 Noise
URL;VALUE=URI:https://events.vtools.ieee.org/m/15625
X-ALT-DESC:Description: <br />Title:\n\nPointwise Relations between Informa
 tion and Estimation in Gaussian Noise\n\nAbstract:\n\nMany of the classica
 l and recent relations between information and estimation in the\npresence
  of Gaussian noise can be viewed as identities between expectations of\nra
 ndom quantities. These include the I-MMSE relationship of Guo et al.\; the
  relative\nentropy and mismatched estimation relationship of Verdu ?\; the
  relationship between\ncausal estimation and mutual information of Duncan\
 , and its extension to the\npresence of feedback by Kadota et al.\; the re
 lationship between causal and\nnon-casual estimation of Guo et al.\, and i
 ts mismatched version of Weissman. We\ndispense with the expectations and 
 explore the nature of the pointwise relations\nbetween the respective rand
 om quantities. The pointwise relations that we find are\nas succinctly sta
 ted as - and give considerable insight into - the original\nexpectation id
 entities.\n\nAs an illustration of our results\, consider Duncan?s 1970 di
 scovery that the mutual\ninformation is equal to the causal MMSE in the AW
 GN channel\, which can equivalently\nbe expressed saying that the differen
 ce between the input-output information density\nand half the causal estim
 ation error is a zero mean random variable (regardless of\nthe distributio
 n of the channel input). We characterize this random variable\nexplicitly\
 , rather than merely its expectation. Classical estimation and information
 \ntheoretic quantities emerge with new and surprising roles. For example\,
  the variance\nof this random variable turns out to be given by the causal
  MMSE (which\, in turn\, is\nequal to the mutual information by Duncan?s r
 esult).\n\nSpeaker Bio:\n\nKartik Venkat is currently a PhD candidate in t
 he Department of Electrical\nEngineering at Stanford University\, under th
 e supervision of Prof. Tsachy Weissman.\nHis research interests include th
 e interaction between information and estimation\ntheory\, probability the
 ory\, and applications of information theory in wireless\nnetworks.\nKarti
 k received a Bachelors degree in Electrical Engineering from the Indian\nI
 nstitute of Technology\, Kanpur in 2010\, and a Masters degree in Electric
 al\nEngineering from Stanford University in 2012. He was awarded the Stanf
 ord Graduate\nFellowship for Engineering and Sciences\, and the Numerical 
 Technologies Founders\nPrize in 2011 at Stanford. He received a Student Be
 st Paper Award at the\nInternational Symposium on Information Theory (ISIT
 ) 2012.
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