Numeric.MCMC.Anneal

Transition operators can easily be tweaked to operate over an annealed parameter space, which can be useful when sampling from bumpy landscapes with isolated modes.

This library exports a single anneal function that allows one to run a declarative-compatible transition operator over a space that has been annealed to a specified temperature.

import Numeric.MCMC

annealingTransition = do
  anneal 0.70 (metropolis 1)
  anneal 0.05 (metropolis 1)
  anneal 0.05 (metropolis 1)
  anneal 0.70 (metropolis 1)
  metropolis 1

These annealed operators can then just be used like any other:

himmelblau :: Target [Double]
himmelblau = Target lHimmelblau Nothing where
  lHimmelblau :: [Double] -> Double
  lHimmelblau [x0, x1] =
    (-1) * ((x0 * x0 + x1 - 11) ^ 2 + (x0 + x1 * x1 - 7) ^ 2)

main :: IO ()
main = withSystemRandom . asGenIO $
  mcmc 10000 [0, 0] annealingTransition himmelblau

Documentation

anneal :: (Monad m, Functor f) => Double -> Transition m (Chain (f Double) b) -> Transition m (Chain (f Double) b)

An annealing transformer.

When executed, the supplied transition operator will execute over the parameter space annealed to the supplied inverse temperature.

let annealedTransition = anneal 0.30 (slice 0.5)