High-Dimensional Statistics

Statistics when p ≫ n: sparsity, regularization, and minimax bounds.

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High-Dimensional Statistics. Statistics when p ≫ n: sparsity, regularization, and minimax bounds.

Foundations and canonical references

The standard treatments of high-dimensional statistics approach the subject from complementary angles. Wainwright, High-Dimensional Statistics: A Non-Asymptotic Viewpoint (2019) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Vershynin, High-Dimensional Probability (2018) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for high-dimensional statistics include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2019
    High-Dimensional Statistics: A Non-Asymptotic Viewpoint
    wainwright-2019
  • textbook · primary · 2018
    High-Dimensional Probability
    vershynin-2018

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Explore

  1. 01

    Sparse Recovery and Compressed Sensing

    L1 minimization, restricted isometry property, and recovery guarantees.
  2. 02

    Lasso and Regularized Regression

    Penalized estimators, oracle inequalities, and elastic net.
  3. 03

    Matrix Completion and Low-Rank Recovery

    Nuclear-norm minimization and noisy matrix completion.
  4. 04

    High-Dimensional Covariance Estimation

    Sparse and structured covariance, graphical lasso, and shrinkage.
  5. 05

    Statistical Learning Theory

    VC dimension, Rademacher complexity, and PAC-Bayes.

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