DRP (IAP 2021)

This is the webpage for a directed reading program (DRP) I am leading during MIT's Independent Activities Period (IAP 2021). The subject is high-dimensional statistics.

References

  • [W] Wainwright, High-Dimensional Statistics: A Non-Asymptotic Viewpoint (2019).
  • [vdV] van der Vaart, Asymptotic Statistics (1998).

Readings

  • (pre-reading) Sub-Gaussian and subexponential random variables; Hoeffding's lemma; Bernstein's inequality; bounded differences inequality. [W] 2.1.1-2.1.3, 2.2, 2.4-2.5.
  • (pre-reading) Glivenko-Cantelli classes; symmetrization. [W] 4.1-4.2.
  • (pre-reading) VC dimension, Sauer-Shelah lemma. [W] 4.3.
  • (pre-reading) Covering, packing, and metric entropy; volumetric argument; chaining and Dudley's entropy integral. [W] 5.1, 5.3.1, 5.3.3.
  • (pre-reading) Non-parametric least squares; localization. [W] 13.1-13.2.
  • (1/4) Stochastic order symbols; convergence of stochastic processes; limiting distributions of M-estimators. [vdV] 2.2, 18.2-18.3, 5.1-5.2, 5.8-5.9.
  • (1/6) Sparse estimation via LASSO; restricted eigenvalue condition and restricted isometry property. [W] 7.1-7.3.2.
  • (1/8) Oracle inequalities. [W] 7.3.3, 13.3.
  • (1/11) Low-rank matrix recovery. [W] 10.1-10.3.
  • (1/13) Sudakov-Fernique Gaussian comparison inequality; Sudakov minoration. [W] 5.4-5.5.
  • (1/13) Minimax lower bounds. [W] 15.1-15.2.
  • (1/15) Minimax lower bounds via Fano's inequality and the Yang-Barron method. [W] 15.3.1-15.3.3, 15.3.5-15.4.
  • (1/18) Contiguity, differentiability in quadratic mean, local asymptotic normality. [vdV] 6.1-6.2, 5.5, 7.1-7.2.
  • (1/20) Convergence to Gaussian experiments; local asymptotic minimax theorem. [vdV] 7.3-8.1, 8.3-8.4, 8.7.
  • (1/22) Bernstein-von Mises theorem. [vdV] 10.1-10.4.
  • (1/25) Entropy and the Herbst argument; concentration of Lipschitz functions and blow-up of sets. [W] 3.1-3.2.
  • (1/27) Optimal transport distances; transportation-cost inequalities and concentration. [W] 3.3.

Exercises