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SUMMARY:Concentration Inequalities - Professor Stéphane Boucheron\, Unive
 rsité Paris Diderot
DTSTART:20160510T090000Z
DTEND:20160510T110000Z
UID:TALK65618@talks.cam.ac.uk
CONTACT:CCA
DESCRIPTION:Concentration inequalities for functions of independent random
  variables is an area of probability theory that has witnessed a great rev
 olution in the last few decades\, and has applications in a wide variety o
 f areas such as machine learning\, statistics\, discrete mathematics\, and
  high-dimensional geometry.  Roughly speaking\, if a function of many inde
 pendent random variables does not depend too much on any of the variables 
 then it is concentrated in the sense that with high probability\, it is cl
 ose to its expected value.\nThis course offers a host of inequalities to i
 llustrate this rich theory. \n\nIt describes the interplay between the pro
 babilistic structure (independence) and a variety of tools ranging from fu
 nctional inequalities to transportation arguments to information theory.  
 Applications to the study of  empirical  processes\,  random  projections\
 ,  random  matrix  theory\,  and  threshold  phenomena  are  also presente
 d.\n\n*Pre-requisites*\n\nWe shall assume notions of probability theory.\n
 \n*Literature*\n<ol>\n<li>Boucheron\,  S.\,  Lugosi\,  G.\,  &  Massart\, 
  P.  (2013). Concentration  inequalities:   A  nonasymptotic theory of ind
 ependence. OUP Oxford. </li>\n<li>Chatterjee\, S. (2014). Superconcentrati
 on and related topics. Springer. </li>\n<li>Garling\, D. J. (2007). Inequa
 lities:  a journey into linear analysis. Cambridge University Press. </li>
 \n<li>Ledoux\, M. (2005).The concentration of measure phenomenon (No.  89)
 . American Mathematical Soc. </li>\n<li>Raginsky\,  M.\,    Sason\,  I.  (
 2014). Concentration  of  Measure  Inequalities  in  Information  Theory\,
  Communications\, and Coding.\nNow Publishers Inc. </li>\n<li>Tropp\, Joel
  A. An introduction to matrix concentration inequalities. arXiv preprint a
 rXiv:1501.01571 (2015). </li>\n</ol>\n\n*Lecture notes*\nhttp://stephane-v
 -boucheron.fr/part-iii-concentration/
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