Gradient-based traversal through parameter space.
This implementation of the HMC algorithm uses
lens as a means to operate over
generic indexed traversable functors, so you can expect it to work if your
target function takes a list, vector, map, sequence, etc. as its argument.
If you don't want to calculate your gradients by hand you can use the handy ad library for automatic differentiation.
mcmc function that prints a trace to stdout, a
for collecting results in memory, and a
hamiltonian transition operator
that can be used more generally.
import Numeric.AD (grad) import Numeric.MCMC.Hamiltonian target :: RealFloat a => [a] -> a target [x0, x1] = negate ((x0 + 2 * x1 - 7) ^ 2 + (2 * x0 + x1 - 5) ^ 2) gTarget :: [Double] -> [Double] gTarget = grad target booth :: Target [Double] booth = Target target (Just gTarget) main :: IO () main = withSystemRandom . asGenIO $ mcmc 10000 0.05 20 [0, 0] booth