Gradient-based traversal through parameter space.
This implementation of 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
<https://hackage.haskell.org/package/ad ad> library for automatic
Exports a 'mcmc' function that prints a trace to stdout, a 'chain' function 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.