Advanced & Applied Topics · High-Dimensional Statistics & Sparsity

FDR and dimensionality reduction in high dimensions

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Chart from the original guide

Overview

Topics covered

  • Introduction
  • FDR and High Dimensional Inference
  • The problem of high dimension and the curse of dimensionality
  • 1. Concentration of the measurement in high-dimensional spaces
  • 2. Spurious correlations and noise accumulation
  • 3. The Sparsity Paradigm

Related concepts

Main connections

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

Compatible notation

Mathematical sample in LaTeX

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

Vp(R)=πp/2Γ(p/2+1)Rp
View LaTeX sourceV_p(R) = \frac{\pi^{p/2}}{\Gamma(p/2 + 1)} R^p