https://github.com/Sohl-Dickstein/LAHMC

Look Ahead Hamiltonian Monte Carlo
https://github.com/Sohl-Dickstein/LAHMC

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Look Ahead Hamiltonian Monte Carlo

• Host: GitHub
• URL: https://github.com/Sohl-Dickstein/LAHMC
• Owner: Sohl-Dickstein
• Created: 2014-01-09T02:14:12.000Z (almost 11 years ago)
• Default Branch: master
• Last Pushed: 2015-03-29T04:35:12.000Z (over 9 years ago)
• Last Synced: 2024-08-01T16:49:04.225Z (3 months ago)
• Language: Matlab
• Size: 232 KB
• Stars: 30
• Watchers: 5
• Forks: 12
• Open Issues: 1
• Metadata Files:
  • Readme: README.md

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README

        
Look Ahead Hamiltonian Monte Carlo

==================================

Implements Look Ahead Hamiltonian Monte Carlo (LAHMC) and standard Hamiltonian Monte Carlo (HMC) in both Python and MATLAB.

LAHMC is described in the paper:


> Sohl-Dickstein, Jascha and Mudigonda, Mayur and DeWeese, Michael R.


> Hamiltonian Monte Carlo Without Detailed Balance.


> International Conference on Machine Learning. 2014


> http://arxiv.org/abs/1409.5191

## Example Python Code

The following code draws samples from an isotropic Gaussian distribution using LAHMC.

```python

from LAHMC import LAHMC

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

# Initialize the sample locations -- 2 dimensions, 100 particles

Xinit = np.random.randn(2,100)

# initialize the sampler.

sampler = LAHMC(Xinit, E, dEdX, epsilon=0.1, beta=0.1, kwargs={'sigma':0.1})

# perform 10 sampling steps for all 100 particles

X = sampler.sample(num_steps = 10)

# perform another 10 sampling steps

X = sampler.sample(num_steps = 10)

```

More detailed documentation, and additional options, can be found in **python/LAHMC.py**

## Example MATLAB Code

The following code draws samples from an isotropic Gaussian distribution using LAHMC.

```MATLAB

% opts holds all parameters which will be passed to the sampler

opts = [];

opts.epsilon = 0.1;

opts.beta = 0.1;

% number of sampling steps

opts.T = 10;

% energy function and gradient

opts.E = @E_gauss;

opts.dEdX = @dEdX_gauss;

% state will hold the particle positions and velocities between

% sampler calls, as well as counters for the number of transitions

% and function evaluations

state = []

% Initialize sample locations -- 2 dimensions, 100 particles

opts.Xinit = randn(2,100);

% Gaussian coupling matrix expected by E_gauss and dEdX_gauss

J = eye(2)*100;

% perform 10 sampling steps for all 100 particles

[X, state] = LAHMC(opts, state, J);

% perform another 10 sampling steps

[X, state] = LAHMC(opts, state, J);

```

More detailed documentation, and additional options, can be found in **matlab/LAHMC.m**.

## Reproduce Figure from the Paper

Code reproducing Figure 2 and Table 1 of the paper, and demonstrating usage of the sampler, can be found in **python/generate_figure_2.py** and **matlab/generate_figure_2.m**.  The exact plots appearing in the paper were generated using the MATLAB version of the code.