STAT 593:
Concentration Inequalities
and Empirical Process Methods
for High-Dimensional Statistics
Spring Quarter 2014
Syllabus (last updated: 1/30/14)
Course personnel:
- Professor: Jon A. Wellner
- B320 Padelford Hall
- Phone: 543-6207
- Office hours: 1:30 - 3:30 MWF; or by appointment
Time and Place:
- Time(s): T Th 10:30 - 12:00 or T Th 11:30 - 1:00
- Place: Lowe 105 or Padelford C301
Prerequisites:
- Stat 581-2-3 or Stat 521-2-3 or
- Concurrent registration in Stat 583 or 523.
- An interest in high-dimensional statistics.
Textbooks (not required):
- Concentration Inequalities: a nonasymptotic theory of independence
Stephane Boucheron, Gabor Lugosi, Pascal Massart. Oxford University Press. (2013).
- Weak convergence and empirical measures.
Aad van der Vaart and Jon W. Wellner. Springer, New York. (1996)
- The Concentration of Measure Phenomenon
Michel Ledoux. American Mathematical Society. (2001)
- Statistics for High-Dimensional Data
Peter Buhlmann and Sara van de Geer. Springer, New York (2011).
- The Generic Chaining
Michel Talagrand. Springer, Heidelberg (2005).
-
Oracle inequalities in empirical risk minimization and sparse recovery problems.
Lectures from the 38th Probability Summer School held in Saint-Flour,
Lecture Notes in Mathematics 2033,
Ecole d'Ete de Probabilites de Saint-Flour. Springer.
Course Description:
This special topics course will treat the concentration
inequalities of Talagrand, Bousquet, and Rio.
Methods introduced by Ledoux and Massart will also be covered,
including the Efron-Stein inequality,
Nemirovski's inequality,
and applications of these to problems in
high-dimensional statistics and
machine learning. Further topics treated will be tailored to
the interests of the participants.
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