36755, Fall 2016 Class Schedule  
Date  Lecture Topic  Readings  Scribe Notes  Notes 

Aug 28, M  Introduction: highdimensional statistical models 


Aug 30, M  SubGaussian variables 


Sep 6, W  SubGaussian variables. Hoeffding bounds and sharpening. Subexponential variables. 

HW1 is out. Solutions  
Sep 11, M  Subexponential variables, Bernstein inequality, expected value of maxima. 


Sep 13, W  The bounded difference inequality and applications. 


Sep 18, M  Concentration of Lipschitz functions of Gaussian vectors. Covering and Packing numbers. 


Sep 20, W  Discretization argument. Review of matrix alegbra. Estimation of the covriance matrix in operator norm. 

HW2 is out. Solutions  
Sep 25, M  Matrix Calculus and Matrix Bernetsin Inequality 


Sep 27, W  Matrix Bernstein Inequality and application to covariance matrix estimation. 


Oct 2, M  Matrix Bernstein Inequality and its use in network community recovery. Linear regression. 


Oct 4, W  Finite sample performance for Linear regression. Penalized regression. 

HW3 is out. Solutions  
Oct 9, M  Slow rate for the LASSO. The RE condition. 


Oct 11, W  More on ridge regression and thresholding estimation. Fast rates for the lasso. 


Oct 16, M  Oracle inequalities for least squares and the lasso. 


Oct 18, W  Persistence. Intro to PCA. 

HW4 is out. Solutions  
Oct 23, M  Distance between linear subspaces and Davis Kahan theorem. 


Oct 25, W  PCA in highdimensions. Spiked covariance model. Sparse PCA. 


Oct 30, M  Sparse PCA. Spectral clustering for SBMs.  
Nov 1, W  Uniform law of larger numbers. Symmetrization Lemma. 

HW5 is out. Solutions  
Nov 6, M  No Class.  
Nov 8, W  Uniform law of larger numbers. Symmetrization Lemma. 


Nov 13, M  VC theory. 


Nov 15, W  VC theory for functions. 


Nov 20, M  Maximal Inequalities for SubGaussian Processes. 


Nov 27, M  Chaining and Dudley's entropy integral. 
