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Course10810818127 lectures

Concentration Inequalities

Prof. Aditya Gopalan Prof. Himanshu tyagi · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

week-01

  1. mod01lec01 Why study concentration inequalities? Video
  2. mod01lec02 Chernoff bound Video
  3. mod01lec03 Examples of Chernoff bound for common distributions Video

week-02

  1. mod02lec04 Hoeffding and Bernstein inequalities Video
  2. mod02lec05 Azuma and McDiarmid inequalities Video

week-03

  1. mod03lec06 Bounding variance using the Efron-Stein inequality Video
  2. mod03lec07 The Gaussian-Poincare inequality Video
  3. mod03lec08 Tail bounds using the Efron-Stein inequality Video

week-04

  1. mod04lec09 Herbst's argument and the entropy method Video
  2. mod04lec10 Log-Sobolev inequalities Video
  3. mod04lec11 Binary and Gaussian Log-Sobolev inequalities and concentration Video

week-05

  1. mod05lec12 Variational formulae forKullback-Leibler and Bregman Divergence Video
  2. mod05lec13 A modified log-Sobolev inequality and concentration Video
  3. mod05lec14 Introduction to the transportation method for showing concentration bounds Video
  4. mod05lec15 Transportationlemma and a proof of McDiarmid's inequality using the transportation method Video

week-06

  1. mod06lec16 Concentration bounds for functions beyond bounded difference using transportation method Video
  2. mod06lec17 Marton's conditional transportation cost inequality Video
  3. mod06lec18 Isoperimetry and concentration of measure Video
  4. mod06lec19 Isoperimetry and bounded difference Video

week-07

  1. mod07lec20 Equivalence of Stam's inequality and log Sobolev inequality Video
  2. mod07lec21 An information theoretic proof of log Sobolev inequality Video
  3. mod07lec22 Hypercontractivity and strong data processing inequality for Rényi divergence Video
  4. mod07lec23 An information theoretic characterization of hypercontractivity Video
  5. mod07lec24 Equivalence of Gaussian hypercontractivity and Gaussian log Sobolev inequality Video

week-08

  1. mod08lec25 Uniform deviation bounds for random walks and the law of the iterated logarithm Video
  2. mod08lec26 Self normalized concentration inequalities and application to online regression Video

Live Session

  1. Live Session 22-09-2021 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Electrical Engineering
Teacher
Prof. Aditya Gopalan Prof. Himanshu tyagi
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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