IDS.160 / 18.S998 / 9.521 Spring 20

Mathematical Statistics: A non-asymptotic approach.

 

Notes

Instructions

Schedule

Relvant reading material, if available, is indicated ahead of time but is not mandatory. We use the following nomenclature:
  • W: Martin Wainwright, High-Dimensional Statistics: A Non-Asymptotic Viewpoint.
  • RH: Philippe Rigollet and Jan-Christian Huetter, High Dimensional Statistics. Lecture Notes.
  • V: Roman Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science.
  • vH: Ramon van Handel, Probability in High Dimension.
Lecture Topic(s) Reading Date Link
1IntroductionW (Ch. 1), RH (intro)Feb. 4
2Sub-Gaussian random variables.
Chernoff bounds.
Hoeffding’s inequality.
RH (1.1, 1.2), V (2.1-2.5), W (2.1.1, 2.1.2)Feb. 6
3Sub-Exponential random variables.
Bernstein’s inequality.
RH (1.3), V (2.7-2.8), W (2.1.3)Feb. 11
4Bernstein’s inequality and applications. RH (1.3), V (2.7-2.8), W (2.1.3)Feb. 13
5Maximal inequalities. RH (1.4)Feb. 20
6Linear regression.
Least squares
RH (2.1-2.2)Feb. 25
7Sparsity. Thresholing.RH (2.2-2.3)Feb. 27
8Misspecified linear models.
Matrix estimation.
RH (3.1, 5.1)Mar. 3
9Singular value thresholding.
Perturbation analysis
RH (5.2, 5.4), V (4.4, 4.5.3)Mar. 5
10Community detection.RH (5.3), V (4.5, 4.7), W (6.3, 6.4.5, 8.1, 8.2)Mar. 10
11Covariance matrix estimation. PCARH (5.3, 5.4), V (4.7), W (8.1, 8.2)Mar. 12
12CANCELLEDMar. 17
13CANCELLEDMar. 19
14-15Uniform Laws of Large NumbersW (4.1-4.2)Mar. 31- Apr. 2
16-17Suprema of subGaussian Processes. Chaining.W (5.1-5.3), V (7.1, 8.1-8.2)Apr. 7-9
18-19 Covering, packing. Combinatorial dimensions.V (8.3), vH (7.1-7.3)Apr. 14-16
20-21Nonparametric Least Squares.W (13.1-13.2)Apr. 21-23
22-23Oracle Inequalities. Regularization.RH (Ch. 3), W (13.3-13.4)Apr. 28-30
24-25Random design regression. W (14.2)May 5-7
26Sequential complexities and online learning.May 12