Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Himanshu Tyagi
NPTEL Co-ordinating Institute : IISc Bangalore
NPTEL Lecture Count : 26
NPTEL Course Size : 2.7 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Why study concentration inequalities?
Lecture 2 - Chernoff bound
Lecture 3 - Examples of Chernoff bound for common distributions
Lecture 4 - Hoeffding and Bernstein inequalities
Lecture 5 - Azuma and McDiarmid inequalities
Lecture 6 - Bounding variance using the Efron-Stein inequality
Lecture 7 - The Gaussian-Poincare inequality
Lecture 8 - Tail bounds using the Efron-Stein inequality
Lecture 9 - Herbst's argument and the entropy method
Lecture 10 - Log-Sobolev inequalities
Lecture 11 - Binary and Gaussian Log-Sobolev inequalities and concentration
Lecture 12 - Variational formulae forKullback-Leibler and Bregman Divergence
Lecture 13 - A modified log-Sobolev inequality and concentration
Lecture 14 - Introduction to the transportation method for showing concentration bounds
Lecture 15 - Transportation lemma and a proof of McDiarmid's inequality using the transportation method
Lecture 16 - Concentration bounds for functions beyond bounded difference using transportation method
Lecture 17 - Marton's conditional transportation cost inequality
Lecture 18 - Isoperimetry and concentration of measure
Lecture 19 - Isoperimetry and bounded difference
Lecture 20 - Equivalence of Stam's inequality and log Sobolev inequality
Lecture 21 - An information theoretic proof of log Sobolev inequality
Lecture 22 - Hypercontractivity and strong data processing inequality for Rényi divergence
Lecture 23 - An information theoretic characterization of hypercontractivity
Lecture 24 - Equivalence of Gaussian hypercontractivity and Gaussian log Sobolev inequality
Lecture 25 - Uniform deviation bounds for random walks and the law of the iterated logarithm
Lecture 26 - Self normalized concentration inequalities and application to online regression