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AI Engineering/Phase 01/Lesson 22

Stochastic Processes

Randomness with structure. The math behind random walks, Markov chains, and diffusion models.

Learn 1.3 hr Python

Prerequisites: Phase 1, Lessons 06-07 (probability, Bayes)

#Learning Objectives

  • Simulate 1D and 2D random walks and verify the sqrt(n) scaling of displacement
  • Build a Markov chain simulator and compute its stationary distribution via eigendecomposition
  • Implement Metropolis-Hastings MCMC and Langevin dynamics for sampling from target distributions
  • Connect the forward diffusion process to Brownian motion and explain how the reverse process generates data
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The text and code of this lesson are based on AI Engineering from Scratch by Rohit Ghumare, MIT licensed.