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Here are lecture notes for Sparse Linear Model in High Dimension in 2024 winter stat DRP.

Mainly refers to the book: High-Dimensional Statistics: A Non-Asymptotic Viewpoint, Wainwright, M. (2019).

Last update: 2/29/2024

Content

• Week 1: Introduction of the linear model
• Lecture note: Introduction of the linear model.
• Handwritten note: Squared loss and linear model.
• Reference section: sec. 7.1.
• Week 2: Recovery in the noiseless setting
• Lecture note: Recovery in the noiseless setting.
• Handwritten note: Two equivalent optimization problems.
• Reference section: sec. 7.2.
• Week 3: Estimation in noisy settings
• Lecture note: Estimation in noisy settings.
• Handwritten note: Equivalent programs due to Lagrangian duarity.
• Reference section: sec. 7.3.
• Week 4: Consistency of Lagrangian Lasso
• Lecture note: Consistency of Lagrangian Lasso.
• Handwritten note: consistency of Lagrangian Lasso.
• Reference section: sec. 7.3.
• Week 5: Concentration and the Gaussian example
• Lecture note: Concentration and the Gaussian example.
• Handwritten note: Concentration and the Gaussian example.
• Reference section: sec. 7.3.
• Week 6: Review session
• Lecture note: Recap on main theorems.
• Week 7: Exercise of the Lasso experiment
• Exercise: Tutorial on the Lasso simulation experiment.
• Code: Tutorial on the Lasso simulation experiment.
• Week 8: Exercise of the Lasso experiment Part II
• Exercise: Tutorial on the Lasso simulation experiment Part II.
• Code: Tutorial on the Lasso simulation experiment Part II.