High-dimensional statistics
Graduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate High-dimensional statistics — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
High-dimensional framework
- Curse of dimensionality — Curse of dimensionality
- Sparsity assumptions — Sparsity assumptions
- Concentration inequalities: Hoeffding, Bernstein — Concentration inequalities: Hoeffding, Bernstein
- Random matrix theory preview — Random matrix theory preview
- Phase transitions in detection — Phase transitions in detection
- Recovery — Recovery
- Multiple testing in high dimensions — Multiple testing in high dimensions
Regularized estimation
- Lasso and elastic net — Lasso and elastic net
- Group lasso theory — Group lasso theory
- Restricted eigenvalue — Restricted eigenvalue
- Compatibility conditions — Compatibility conditions
- Oracle inequalities for Lasso — Oracle inequalities for Lasso
- False discovery rate control methods — False discovery rate control methods
- Covariance estimation in high dimensions — Covariance estimation in high dimensions
Advanced topics
- High-dimensional PCA — High-dimensional PCA
- Factor models — Factor models
- Community detection in networks (intro) — Community detection in networks (intro)
- Nonparametric regression in high dimensions — Nonparametric regression in high dimensions
- Minimax lower bounds (introduction) — Minimax lower bounds (introduction)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- High-dimensional framework
Curse of dimensionality
Coming soon - Regularized estimation
Lasso and elastic net
Coming soon - Advanced topics
High-dimensional PCA
Coming soon
Notes
Graduate High-dimensional statistics — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable). Topic outline: `content/topics/graduate/high_dimensional.json`.