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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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Alec Helbling

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32,767 次观看 • 1 年前 •via X (Twitter)

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One of the simplest algorithms for sampling from a probability distribution is Random Walk Metropolis-Hastings. It proposes new samples by taking Gaussian-distributed steps, accepting or rejecting them to maintain the target distribution. I call this pdf the "fidget spinner".
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One of the simplest algorithms for sampling from a probability distribution is Random Walk Metropolis-Hastings. It proposes new samples by taking Gaussian-distributed steps, accepting or rejecting them to maintain the target distribution. I call this pdf the "fidget spinner".

Alec Helbling

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A basic strategy for drawing from a random distribution is to first generate uniformly-distributed points, then "warp" these points so they're spread out according to the target distribution. For example, the Box-Muller transform takes uniform points to normally-distributed ones
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A basic strategy for drawing from a random distribution is to first generate uniformly-distributed points, then "warp" these points so they're spread out according to the target distribution. For example, the Box-Muller transform takes uniform points to normally-distributed ones

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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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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.

Alec Helbling

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Did you know you can create the Maxwell-Boltzmann distribution with just some balls and a motor? I built this simple device to illustrate it. This is how it works: A spinning agitator pumps energy into ~400 balls, so they bounce around and collide like gas particles in a box. They escape one at a time through a tiny hole, then fall a fixed gap into bins below. Since the hole is so small, every ball leaves with no vertical speed and takes the same time to fall. Constant fall time means how far a ball flies sideways is set purely by its speed. A faster ball goes into a further bin. So each bin is really a speed. Tally all 400 and you get the Maxwell-Boltzmann distribution.
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Did you know you can create the Maxwell-Boltzmann distribution with just some balls and a motor? I built this simple device to illustrate it. This is how it works: A spinning agitator pumps energy into ~400 balls, so they bounce around and collide like gas particles in a box. They escape one at a time through a tiny hole, then fall a fixed gap into bins below. Since the hole is so small, every ball leaves with no vertical speed and takes the same time to fall. Constant fall time means how far a ball flies sideways is set purely by its speed. A faster ball goes into a further bin. So each bin is really a speed. Tally all 400 and you get the Maxwell-Boltzmann distribution.

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50 websites that can turn a “5-minute break” into hours of exploring 🌐 1. — Discover fascinating websites at random 2. — Search the old-school web 3. — Find hidden internet gems 4. — Human-curated useful tools 5. — Random weird & wonderful websites 6. — Explore live radio around the world 7. — Drive through cities with local radio 8. — Geography games with real locations 9. — Guess cities from walking videos 10. — Explore the world through clues 11. — Street-level imagery from around the world 12. — Turn historical maps into interactive maps 13. — Browse historical maps 14. — Explore detailed interactive game maps 15. — Watch global winds & weather 16. — Visualize weather across the planet 17. — Explore Earth’s atmosphere in motion 18. — Travel through music by country & decade 19. — Discover music through connections 20. — Explore thousands of music genres 21. — Explore concert setlists from around the world 22. — Discover live music history 23. — Explore movies through people & lists 24. — Find movies by describing them 25. — Explore movie frames 26. — Search movies by visual composition 27. — Travel through the old internet 28. — Explore a massive web archive 29. — Explore Australia’s digital archives 30. — Search New Zealand’s cultural collections 31. — Explore Europe’s digital heritage 32. — Explore millions of digital objects 33. — Explore design history 34. — Explore American art collections 35. — Explore historic biology books 36. — Explore biodiversity data 37. — Explore species data worldwide 38. — Identify & explore species around you 39. — Watch ships move around the world 40. — Track flights worldwide 41. — Explore detailed satellite imagery 42. — Explore global population data 43. — Explore data about countries & cities 44. — Play with global development data 45. — Explore computational answers 46. — Jump between radio stations worldwide 47. — One click into internet chaos 48. — Find a random person pointing at your cursor 49. — Look through windows around the world 50. — Weird, clever & addictive interactive experiments The internet is still full of places most people never discover. 🔖 Save this list. following You’ll definitely come back to it. Follow Amelia hazel for more hidden websites, useful tools & AI discoveries.

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Extrusion is a common method for producing bricks, where a clay mixture is forced through a die to create a continuous column of clay, which is then cut into individual bricks.

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