Reading material for the class will be assigned from:

[W] High-dimensional statistics: A non-asymptotic viewpoint, by M. Wainwright. This is a book draft and the material given out in class is not to be disseminated.

Date	Lecture Topic	Readings	Scribe Notes	Notes
36-755, Fall 2016 Class Schedule
Aug 29, M	Introduction: high-dimensional statistical models	[W], Chapter 1
Aug 31, M	Sub-Gaussian variables and Hoeffding Inequality	[W], Chapter 2, 2.1.1, 2.1.2.	pdf
Sep 7, W	Sub-Exponential variables and Bernstein Inequality	[W], Chapter 2.1.3, 2.1.4	pdf
Sep 12, M	Maxima, Quadratic Forms, Martingales	[W], Chapter 2.2.1 and 2.2.2	pdf
Sep 14, W	The bounded difference inequality with applications. Concentration of Lipschitz functions of Gaussians.	[W], Chapter 2.3	pdf	HW1 is due. Here are the Solutions
Sep 19, M	Covering and packing numbers, metric entropy volumetric ratios, concentration of maxima over infinite sets.	[W], 5.1	pdf
Sep 21, W	Matrix algebra review. covariance estimation in the operator norm.	[W], 6.1 and 6.3	pdf
Sep 26, M	Upper bound on the prediction consistency of least squares and penalized least squares.	[W], 7.1	pdf	HW2 is due. Here are the Solutions
Sep 28, W	Slow rates for the lasso. Restricted eigenvalue condition for fast rates.	[W] 7.4 and 7.3.1.	pdf
Oct 3, M	Class canceled.
Oct 5, W	Fast rates for the lasso. Oracle inequality for least squares.	[W] 7.3	pdf	HW3 is due. Here are the Solutions
Oct 10, M	Persistence and Introduction to PCA	[W] 8.1 and Greenshtein and Ritov (2007)	pdf
Oct 12, W	Davis-Kahan theorem and application to eigenspace estimation.	See references page.	pdf
Oct 17, M	Eigenvector recovery for sparse PCA under the spiked covariance model. Introduction to the uniform law of large numbers.	[W] Theorem 8.1 and section 4.1.	pdf
Oct 19, W	Uniform law of large numbers via Rademchaer complexities.	[W]: Section 4.2	pdf	HW4 is due. Here are the Solutions
Oct 24, M	Polynomial discrimination, shattering coefficients, VC dimension, Sauer Lemma and VC inequality. Examples of VC classes of sets.	[W]: Section 4.3	pdf
Oct 26, W	Classic derivation of the VC inequality, relative deviations, extension to functions, Talagrand inequality for empirical processes and separability.	[W]: Section 4.3	pdf
Oct 31, M	Sub-Gaussian processes and one-step discretization technique with applications.	[W]: Sections 5.1, 5.2 and 5.3.	pdf	HW5 is due. Here are the Solutions
Nov 2, W	Chaining and Dudley entropy integral bound.	[W]: Sections 5.4.	pdf
Nov 7, M	Orlicz processes and their concentration properties.	[W]: Section 5.7.	pdf
Nov 9, W	Nonparametric least squares. Critical radius from local Gaussian complexity.	[W]: Sections 13.1 and 13.2.		HW6 is due. Here are the Solutions
Nov 14, M	Nonparametric least squares. Critical radius from local Gaussian complexity.	[W]: Sections 13.1 and 13.2.	pdf
Nov 16, W	Oracle Inequality for Nonparametric least squares.	[W]: Sections 13.3.	pdf
Nov 21, M	Uses of Oracle Inequality for Nonparametric least squares. Introduction to U-statistics.	[W]: Sections 13.3.1.	pdf
Nov 28, M	Examples of U-statistics. Variance of a U-statistics.	See references webpage.	pdf
Nov 30, W	Hajek projection and asymptotic normality of U-statistics.	See references webpage.		HW7 is due. Here are the Solutions
Dec 5, M	Concentration of U-statistics and review.		pdf
Dec 7, W	Final exam.			Here are the Solutions

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