Books, Lecture Notes, Expository Articles

Lecture 1, Tue Sep 1
Some applications of concentration inequalities in high-dimensional statistics: Parameter consistency and central limit theorems for models with increasing dimension d (but still d < n): Some central limit theorem results in increasing dimension (in the second mini we will see more specialized and stronger results).

Lecture 2, Thu Sep 3
For those interested in the mathematical theory of the conecntration of measure, these are good references:

Lecture 3, Tue Sep 8
Most of the material on sub-gaussianity was taken from here: More comprehensive treatment of sub-gaussian variables and processes (and more) are: References for Chernoff bounds for Bernoulli (and their multiplicative forms): Improvement of Hoeffding's ineqaulity by Berend and Kantorivich: Example of how the relative or multiplicative version of Chernoff bounds will lead to substantial improvements:

Lecture 4, Thu Sep 10
For more information on sub-exponential variables, consult:

Lecture 5, Tue Sep 15
Empirical Bernstein Inequality: Concentration of chi-squared variables: For classic proofs of Hoeffding, Bennet and Bernstein, see, e.g., For an example of how Bernstein's inequality is preferable to Hoeffding, see Lemma 13 in

Lecture 6, Thu Sep 17
Some references on JL Lemma and random projections: On embedding of of finite metric spaces (of which the JL Lemma is an example): A nice, dense monograoh devoted to uses of random projections: A sherpening of the JL Lemma, based on empirical process theory: JL Lemma and the RIP condition in compressed sensing: The JL Lemma and manifolds: And finally, a nice reading course:

Lecture 7, Thu Sep 22
The DKW inequality with the best constant:

Lecture 8, Thu Sep 24
Ale out of town.

Lecture 9, Tue Sep 29
References for martingale methods to get concentration inequalities: Interesting improvements:

Lecture 10, Thu Oct 1
References the entropy method

Lecture 11, Tue Oct 6
References for Max's lectture:

Lecture 12, Thu Oct 8
For today's lecture, the main references are:

Lecture 13, Tue Oct 13
Same references as the previous lecture.

Lecture 13, Thu Oct 15
The basic references for matrix concentration inequalities are: and references therein.

Lecture 14, Tue Oct 20
Same references as the last time.

Lecture 15, Tue Oct 22