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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.

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Alec Helbling

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156,437 görüntüleme • 7 ay önce •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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Random Walks aim to explore a distribution through random perturbations. This is likely to move into low density regions, which is inefficient. Hamiltonian MC sails through a distribution much more rapidly by incorporating the distribution's structure into proposals.
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