Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Markov Chain

Chapter 18 Reinforcement learning

Chapter 18: Langevin Dynamics and Sampling — Markov Chain Monte Carlo (MCMC) (also appears in Ch. 14)

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From the book

Chapter 18: Langevin Dynamics and Sampling. In the chapter mind map this icon labels Markov Chain Monte Carlo (MCMC). The discussion below is excerpted and lightly edited from § Markov Chain Monte Carlo (MCMC) in Mathematics for AI and Machine Learning. Related material also appears in Chapter 14 (Markov Chains & Stochastic Matrices).

We now place Langevin dynamics within the broader framework of Markov Chain Monte Carlo (MCMC) methods. This provides a more general theoretical foundation and helps us understand how Langevin dynamics relates to other sampling techniques.

What this drawing shows

What you see. Two states $S_1, S_2$ with fixed transition arcs; a red token hops $S_1\!\to\!S_2$ then $S_2\!\to\!S_1$, illustrating memoryless Markov transitions.

In the mind map. Chapter 18 — Markov Chain Monte Carlo (MCMC). See From the book above for definitions, figures, and worked examples.

Also appears in Ch. 14 (Markov Chains & Stochastic Matrices).

Where to read next

Open Chapter 18 companion →

Read the full definitions, figures, and worked examples in Chapter 18: Langevin Dynamics and Sampling — see the mind-map node Markov Chain Monte Carlo (MCMC).

This concept is also referenced in Chapter 14 (Markov Chains & Stochastic Matrices).