Notes

Notes for students, half-baked write-ups for myself, and probably other random maths/stats/ML texts. Certainly full of typos, comments welcome!

---

Notes indexed by categories.

---

Denoising Diffusion Probabilistic Models

• Noising and Reverse Ornstein-Uhlenbeck
• From Denoising Diffusion to ODEs
• Reverse diffusions, Score & Tweedie
• VIASM mini-course on diffusions and flows

Information Theory

• References & Readings
• Entropy and Basic Definitions
• Shannon Source Coding Theorem
• Fano’s inequality
• Shearer’s Lemma

Monte-Carlo methods

• Deriving the Langevin MCMC algorithm
• Gaussian Assimilation & the EnKF
• Ensemble Kalman Smoothers
• MCMC with deterministic proposals
• RWM & HMC on Manifolds

Probability Misc

• Auxiliary variable trick
• Sanov’s Theorem
• Wasserstein Gradients & Langevin Diffusions
• Poisson Equation & Asymptotic Variance
• Averaging and Homogenization
• Joe Doob & Change of measures on path space
• Girsanov and importance sampling
• Doob, Girsanov and Bellman
• Basic Conformal Inference