Notes

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

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Notes indexed by categories.

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Denoising Diffusion Probabilistic Models

• Noising and Reverse Ornstein-Uhlenbeck
• From Denoising Diffusion to ODEs
• Reverse diffusions, Score & Tweedie

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