"Refactoring probability distributions, part 2: Random sampling" by Eric

Tue, 27 Feb 2007 10:44:23 +0000

I suspect that newtype-deriving will work quite nicely. Thanks!

It might also be desirable to use the Rand monad from the Haskell wiki, or perhaps the splittable version (which might make it feasible to run sampling computations in parallel?).

"Refactoring probability distributions, part 2: Random sampling" by David House

Tue, 27 Feb 2007 10:05:28 +0000

Couldn’t you just use newtype-deriving to make Rand a monad, like you did for making Prob an instance of Num in the first part? Also, sequence (replicate f xs) is just replicateM f xs.

Great articles, by the way!

Refactoring probability distributions, part 2: Random sampling

Eric Kidd — Wed, 21 Feb 2007 23:53:00 +0000

In Part 1, we cloned PFP, a library for computing with probability distributions. PFP represents a distribution as a list of possible values, each with an associated probability.

But in the real world, things aren’t always so easy. What if we wanted to pick a random number between 0 and 1? Our previous implementation would break, because there’s an infinite number of values between 0 and 1—they don’t exactly fit in a list.

As it turns out, Sungwoo Park and colleagues found an elegant solution to this problem. They represented probability distributions as sampling functions, resulting in something called the λ_◯ calculus. (I have no idea how to pronounce this!)

With a little bit of hacking, we can use their sampling functions as a drop-in replacement for PFP.

A common interface

Since we will soon have two ways to represent probability distributions, we need to define a common interface.

type Weight = Float

class (Functor d, Monad d) => Dist d where
  weighted :: [(a, Weight)] -> d a

uniform :: Dist d => [a] -> d a
uniform = weighted . map (\x -> (x, 1))

The function uniform will create an equally-weighted distribution from a list of values. Using this API, we can represent a two-child family as follows:

data Child = Girl | Boy
  deriving (Show, Eq, Ord)

child :: Dist d => d Child
child = uniform [Girl, Boy]

family :: Dist d => d [Child]
family = do
  child1 <- child
  child2 <- child
  return [child1, child2]

Now, we need to implement this API two different ways: Once with lists, and a second time with sampling functions.

Random Hacks: Refactoring probability distributions, part 2: Random sampling

"Refactoring probability distributions, part 2: Random sampling" by Eric

"Refactoring probability distributions, part 2: Random sampling" by David House

Refactoring probability distributions, part 2: Random sampling

A common interface