Theoretical / proof-based
High-dimensional statistics · Graduate · Math
Learning objectives from the High-dimensional statistics syllabus, grouped by unit. Click an objective for study materials.
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)
Learning objectives
Click an objective for study materials.
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)
Definitions and structure
- 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
Proofs and reasoning
- Recovery — Recovery
- Multiple testing in high dimensions — Multiple testing in high dimensions
- Lasso and elastic net — Lasso and elastic net
- Group lasso theory — Group lasso theory
- Restricted eigenvalue — Restricted eigenvalue
Abstraction and generalization
- 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
- High-dimensional PCA — High-dimensional PCA
Modeling and computation
- Apply curse of dimensionality in engineering contexts — Apply curse of dimensionality in engineering contexts
- Apply sparsity assumptions in engineering contexts — Apply sparsity assumptions in engineering contexts
- Apply concentration inequalities: hoeffding, bernstein in engineering... — Apply concentration inequalities: hoeffding, bernstein in engineering contexts
- Apply random matrix theory preview in engineering contexts — Apply random matrix theory preview in engineering contexts
- Apply phase transitions in detection in engineering contexts — Apply phase transitions in detection in engineering contexts
Data and technology
- Use software to explore high-dimensional statistics problems numerically — Use software to explore high-dimensional statistics problems numerically
- Interpret computational results against analytic predictions — Interpret computational results against analytic predictions
- Build spreadsheets or scripts for routine calculations — Build spreadsheets or scripts for routine calculations
- Visualize functions, fields, or datasets tied to course topics — Visualize functions, fields, or datasets tied to course topics
- Connect course methods to lab, industry, or research workflows — Connect course methods to lab, industry, or research workflows
Problem-solving practice
- Recovery — Recovery
- Multiple testing in high dimensions — Multiple testing in high dimensions
- Lasso and elastic net — Lasso and elastic net
- Group lasso theory — Group lasso theory
- Restricted eigenvalue — Restricted eigenvalue
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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$1,162 · High-dimensional statistics · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.