High-Dimensional Statistics
Estimation when the dimension grows with the sample size: covariance estimation, sparsity, the lasso and minimax rates.
Level 3 — Graduate
Level 4 — Research
Problems (10)
Open in the browser| Solved | Problem | Type | Difficulty | Time |
|---|---|---|---|---|
| Derive the soft-thresholding operator | Proof | 30 min | ||
| Measure the covariance estimation rate run | Coding | 1 hour | ||
| Sample complexity of covariance estimation | Numerical | 30 min | ||
| The geometry of l1 versus l2 constraints | Proof | 30 min | ||
| Implement ISTA and verify the lasso rate run | Coding | 3 hours | ||
| Optimal linear shrinkage | Proof | 1 hour | ||
| Union bound over supports for the restricted isometry property | Proof | 1 hour | ||
| Weyl's inequality and eigenvalue perturbation | Proof | 30 min | ||
| The lasso error vector lies in a cone abyss | Proof | 1 hour | ||
| Open: explicit RIP matrices beyond the square-root barrier abyss | Proof | Research |