Markov Jump Hamiltonian Monte Carlo

Python implementation of Markov Jump HMC

Markov Jump HMC is described in the paper

A. Berger, M. Mudigonda, M. R. DeWeese and J. Sohl-Dickstein
A Markov Jump Process for More Efficient Hamiltonian Monte Carlo
arXiv preprint arXiv:1509.03808, 2015

Example Python Code

from mjhmc.samplers.markov_jump_hmc import MarkovJumpHMC
from mjhmc.misc.distributions import LambdaDistribution
import numpy as np

# Define the energy function and gradient
def E(X, sigma=1.):
    """ Energy function for isotropic Gaussian """
    return np.sum(X**2, axis=0).reshape((1,-1))/2./sigma**2

def dEdX(X, sigma=1.):
    """ Energy function gradient for isotropic Gaussian """
    return X/sigma**2

# Create a good initalization for the sampling particle locations -- 2 dimensions, 100 indepedent sampling particles
Xinit = np.random.randn(2,100)

# Initialize an anonymous distribution object
anonymous_gaussian = LambdaDistribution(energy_func=E, energy_grad_func=dEdX, init=Xinit, name='IsotropicGaussian')

# Initialize the sampler
mjhmc = MarkovJumpHMC(distribution=anonymous_gaussian)
# Perform 10 sampling steps for all 100 particles
# Returns an array of samples with shape (ndims, num_steps * num_particles), in this case (2, 1000)
X = mjhmc.sample(num_steps = 10)

Dependencies

Required

• numpy
• scipy

Optional

• matplotlib
• nosetests
• seaborn (for making pretty plots)
• spearmint (for hyperparameter optimization)
• pandas (needed for some plots)