Advanced & Applied Topics · High-Dimensional Statistics & Sparsity

FDR: Introduction to high dimensionality and geometric phenomena

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction // High Density Multivariate Inference

Overview

Topics covered

  • Introduction
  • FDR: High Dimensionality and Geometric Phenomena
  • The High Dimensionality Paradigm ( )
  • Geometry of High Dimensional Spaces
  • The Volume of the Hypersphere and the Hypercube
  • Concentration of Volume in the Cortex (The Empty Space Phenomenon)

Related concepts

Main connections

  • Multiple testing & FWER/FDR
  • p-value & significance
  • Linear algebra & matrices
  • Hypothesis testing
  • Variance & standard deviation
  • Regularization (Lasso / Ridge / Elastic Net)

Compatible notation

Mathematical sample in LaTeX

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

Vol(Bd(R))=πd/2Γ(d2+1)Rd
View LaTeX source\text{Vol}(B_d(R)) = \frac{\pi^{d/2}}{\Gamma\left(\frac{d}{2} + 1\right)} R^d