36-709 Advanced Statistical Theory I

This course covers a variety of advanced topics in non-asymptotic theoretical statistics.

Syllabus

The syllabus provides information on grading, class policies etc.

Lecture Notes

• Lecture 1: (1/14) Introduction to High-Dimensional Analyses
• Lecture 2: (1/16) Metric Entropy and Its Uses
• Lecture 3: (1/21) More Metric Entropy Calculations
• Lecture 4: (1/23) Relating Metric Entropy and sub-Gaussian Stochastic Processes
• Lecture 5: (1/28) Dudley’s Chaining
• Lecture 6: (1/30) Matrix Estimation via Singular Value Thresholding
• Lecture 7: (2/11) Operator Norm for Wigner Matrices + Estimating SST Matrices
• Lecture 8: (2/13) Gaussian and Sub-Gaussian Covariance Matrix Estimation
• Lecture 9: (2/18) Matrix Chernoff, Hoeffding and Bernstein
• Lecture 10: (2/20) Estimating Sparse Covariance Matrices + Basis Pursuit
• Lecture 11: (2/25) More on Basis Pursuit, RIP and Pairwise Incoherence
• Lecture 12: (2/27) Estimation Error Bounds for the LASSO
• Lecture 13: (3/3) Prediction Error Bounds and Support Recovery using the LASSO
• Lecture 14: (3/5) Debiasing the LASSO + Minimax Lower Bounds
• Lecture 15: (3/19) Le Cam’s Two-point Method Examples
• Lecture 16: (3/24) Fano’s Method Examples
• Lecture 17: (3/26) Yang-Barron and more Fano Examples
• Lecture 18: (3/31) Applying Yang-Barron, Non-parametric MLE
• Lecture 19: (4/2) Non-parametric MLE, Yatracos and Sieves
• Lecture 20: (4/7) Non-parametric Least Squares I
• Lecture 21: (4/9) Non-parametric Least Squares II
• Lecture 22: (4/14) Non-parametric Least Squares III
• Lecture 23: (4/16) Minimax Hypothesis Testing I
• Lecture 24: (4/21) Minimax Hypothesis Testing II
• Lecture 25: (4/23) Estimating Smooth Integral Functionals