Advanced & Applied Topics · High-Dimensional Statistics & Sparsity

FDR, linear models, and regularization in high dimensions

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Technical Statistical Reference Treatise

Overview

Topics covered

  • Introduction
  • FDR, Linear Models and High Dimensional Inference
  • The Problem of the High Dimension ( )
  • 1.1 Singularity of the Gram Matrix and Algebraic Indeterminacy
  • 1.2 Curse of Dimensionality and High Dimensional Geometry
  • Asymptotic Theory and Thinning Models (Sparsity)

Related concepts

Main connections

  • Regularization (Lasso / Ridge / Elastic Net)
  • Multiple testing & FWER/FDR
  • Linear algebra & matrices
  • p-value & significance
  • Bayes' theorem & priors
  • Hypothesis testing

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

β^OLS=(XTX)−1XTy
View LaTeX source\hat{\beta}_{\text{OLS}} = (X^T X)^{-1} X^T y