High-dimensional statistics
Graduate · Statistics
Syllabus focus
Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Theoretical / proof-based
High-dimensional framework
- Curse of dimensionality and sparsity assumptions
- Concentration inequalities: Hoeffding, Bernstein
- Random matrix theory preview
- Phase transitions in detection and recovery
- Multiple testing in high dimensions
Regularized estimation
- Lasso, elastic net, and group lasso theory
- Restricted eigenvalue and compatibility conditions
- Oracle inequalities for Lasso
- False discovery rate control methods
- Covariance estimation in high dimensions
Advanced topics
- High-dimensional PCA and factor models
- Community detection in networks (intro)
- Nonparametric regression in high dimensions
- Minimax lower bounds (introduction)
Notes
Graduate course on modern high-dimensional statistics. Covers sparsity, concentration inequalities, and theoretical properties of regularized estimators.