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Hamiltonian Monte Carlo frames sampling from a probability distribution as a physics problem. By endowing "particles" with momentum and simulating their energy and motion through Hamilton's equations you can efficiently explore a distribution.

Alec Helbling

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168,671 views • 8 months ago •via X (Twitter)

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Langevin Monte Carlo allows you to draw samples from a probability distribution using its log gradient ∇ log p(x). By performing a sort of gradient ascent with noise you can navigate around the distribution. Langevin MC is heavily related to modern diffusion models.

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