高维统计

High-Dimensional Statistics · Interactive

A rigorous, visualization-driven course through modern high-dimensional statistics: concentration inequalities, random matrix theory, sparse estimation, and minimax theory.

Course Roadmap

Part A: 高维概率基础

  • Ch 0: The Strangeness of High Dimensions
  • Ch 1: Concentration I — Sub-Gaussian Theory
  • Ch 2: Concentration II — Sub-Exponential
  • Ch 3: Random Vectors in High Dimensions
  • Ch 4: Covering Numbers & Metric Entropy

Part B: 随机矩阵基础

  • Ch 5: Wigner Matrices & Semicircle Law
  • Ch 6: Marchenko-Pastur Law
  • Ch 7: Spiked Models & Tracy-Widom

Part C: 稀疏估计

  • Ch 8: Lasso — Basic Theory
  • Ch 9: Lasso Variants & Extensions
  • Ch 10: Computational Methods

Part D: 高维检验与推断

  • Ch 11: Multiple Testing & FDR
  • Ch 12: Debiased Lasso
  • Ch 13: Selective Inference & Knockoffs

Part E: 矩阵估计

  • Ch 14: Matrix Completion
  • Ch 15: High-Dimensional PCA
  • Ch 16: Covariance & Graphical Models
  • Ch 17: Low-Rank Recovery

Part F: 极小极大理论

  • Ch 18: Minimax Lower Bounds
  • Ch 19: Optimal Rates & Adaptation

Select a chapter from the sidebar to begin.