Advanced & Applied Topics · Information Theory & Entropy

Information theory and statistical inference: Interactions and foundations

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Statistical Geometry and Divergence Measures

Overview

Topics covered

  • Introduction
  • Information Theory and Statistical Inference
  • Shannon Entropy, Differential and Axiomatic Entropy
  • 1.1 Differential Entropy: The transition to the continuum
  • Divergences of Information and Sanov's Theorem
  • 2.1 Fundamental Analytical Properties

Related concepts

Main connections

  • Calculus & differentiation
  • Maximum likelihood estimation
  • Linear algebra & matrices
  • Bayes' theorem & priors
  • Normal (Gaussian) distribution
  • Variance & standard deviation

Compatible notation

Mathematical sample in LaTeX

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

H(X)=−∑x∈𝒳p(x)logbp(x)=𝔼[logb1p(X)]
View LaTeX sourceH(X) = -\sum_{x \in \mathcal{X}} p(x) \log_b p(x) = \mathbb{E} \left[ \log_b \frac{1}{p(X)} \right]