Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Entropy

Chapter 14 Probability & information

Chapter 14: Information Theory — Entropy

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Entropy — high-resolution mind-map icon

From the book

Chapter 14: Information Theory. In the chapter mind map this icon labels Entropy: $H(X) = -\sum p_i \log p_i$. The discussion below is excerpted and lightly edited from § Definition: Entropy (Discrete) in Mathematics for AI and Machine Learning.

For a discrete random variable $X$ with probability mass function $p(x) = P(X = x)$, the entropy is defined as the expected information content:

where the sum is over all possible values of $X$, and we use the convention $0 \log 0 = 0$.

What this drawing shows

What you see. Represents uncertainty, spread, or information content in a probability distribution.

In the mind map. Chapter 14 — Entropy. See From the book above for definitions, figures, and worked examples.

Where to read next

Open Chapter 14 companion →

Read the full definitions, figures, and worked examples in Chapter 14: Information Theory — see the mind-map node Entropy.