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Mental map of Markov Chain Monte Carlo (MCMC) algorithms, and analogous machine learning (ML) algorithms [dashed = especially loose analogy]. Grey boxes are basic tools, and each arrow is annotated with the "delta" between algorithms.

Keenan Crane

39,219 subscribers

100,691 просмотров • 1 год назад •via X (Twitter)

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Комментарии: 10

Фото профиля Keenan Crane

Keenan Crane1 год назад

I'm developing this "map" as part of a new course on Monte Carlo Methods and Applications, taught at @CarnegieMellon this fall: (See also last year's offering:

Фото профиля Keenan Crane

Keenan Crane1 год назад

Very glad to hear from seasoned travelers about errors in my cartography! Likewise glad to know about papers that make some of the MCMC <=> ML connections precise/rigorous. I know a bunch that touch on these connections, like Welling & Teh 2011:

Фото профиля Keenan Crane

Keenan Crane1 год назад

(For related posts, see the tag #MCMA2023.)

Фото профиля Kyle Cranmer

Kyle Cranmer1 год назад

Recently, there are MCMC (and importance sampling) algorithms that use neural density estimation to act as a good proposal distribution.

Фото профиля Artur Chakhvadze

Artur Chakhvadze1 год назад

Is there a good derivation of Langevin Monte-Carlo from first principles which is independent from Hamiltonian Dynamics? The only one I know is “We just do one-step HMC and by making step sizes smaller over time we make sure that acceptance probability approaches 1”

Фото профиля Keenan Crane

Keenan Crane1 год назад

Yeah, definitely. You don't need the symplectic picture do develop LMC: just "gradient descent plus noise" (more or less). If you don't want it to totally fall out of the sky, you can use motivation from physics. The tough part is proving it *works*, which takes 1/2 a semester!

Фото профиля Amit Patel

Amit Patel1 год назад

I'd love a non-animated version of this so I can read it before the animation resets ;)

Фото профиля Keenan Crane

Keenan Crane1 год назад

I think if you fullscreen it you may get a pause button. (But I totally hear you!)

Фото профиля Bassel Mabsout

Bassel Mabsout1 год назад

I can see how the cooling schedule captures the essence of simulated annealing, but it's supposed to be a gradientless metaheuristic, is there some more general definition of simulated annealing that can be considered the global optimizer in conjunction with some local optimizer?

Фото профиля Keenan Crane

Keenan Crane1 год назад

Yeah, that’s actually a good point. That box should probably be something like Simulated Annealing with Langevin Sampling. It’s indeed important that simulated annealing (e.g., with Metropolis/normal proposals) can be applied without derivatives.

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