Advanced & Applied Topics · Information Theory & Entropy

Information Theory: Asymptotic Behavior and Data Compression

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Rigorous Reference Technical Treatise

Overview

Topics covered

  • Introduction
  • Information Theory and Asymptotic Behavior
  • Fundamental measures of information and mathematical entropy
  • 1.1 Shannon entropy for a discrete variable
  • 1.2 Joint, conditional entropy and the chain rule
  • 1.3 Mutual information and Kullback-Leibler divergence

Related concepts

Main connections

  • Calculus & differentiation
  • Mean & expected value
  • Linear algebra & matrices
  • Mathematical expectation & moments
  • Variance & standard deviation
  • Markov chain Monte Carlo (MCMC)

Compatible notation

Mathematical sample in LaTeX

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

H(X)=−∑x∈𝒳p(x)logbp(x)
View LaTeX sourceH(X) = -\sum_{x \in \mathcal{X}} p(x) \log_b p(x)