2020-05-10 22:32:26 -07:00

130 lines
3.5 KiB
Python

import tensorflow as tf
import numpy as np
from tensorflow.python.platform import flags
flags.DEFINE_bool('proposal_debug', False, 'Print hmc acceptance raes')
FLAGS = flags.FLAGS
def kinetic_energy(velocity):
"""Kinetic energy of the current velocity (assuming a standard Gaussian)
(x dot x) / 2
Parameters
----------
velocity : tf.Variable
Vector of current velocity
Returns
-------
kinetic_energy : float
"""
return 0.5 * tf.square(velocity)
def hamiltonian(position, velocity, energy_function):
"""Computes the Hamiltonian of the current position, velocity pair
H = U(x) + K(v)
U is the potential energy and is = -log_posterior(x)
Parameters
----------
position : tf.Variable
Position or state vector x (sample from the target distribution)
velocity : tf.Variable
Auxiliary velocity variable
energy_function
Function from state to position to 'energy'
= -log_posterior
Returns
-------
hamitonian : float
"""
batch_size = tf.shape(velocity)[0]
kinetic_energy_flat = tf.reshape(kinetic_energy(velocity), (batch_size, -1))
return tf.squeeze(energy_function(position)) + tf.reduce_sum(kinetic_energy_flat, axis=[1])
def leapfrog_step(x0,
v0,
neg_log_posterior,
step_size,
num_steps):
# Start by updating the velocity a half-step
v = v0 - 0.5 * step_size * tf.gradients(neg_log_posterior(x0), x0)[0]
# Initalize x to be the first step
x = x0 + step_size * v
for i in range(num_steps):
# Compute gradient of the log-posterior with respect to x
gradient = tf.gradients(neg_log_posterior(x), x)[0]
# Update velocity
v = v - step_size * gradient
# x_clip = tf.clip_by_value(x, 0.0, 1.0)
# x = x_clip
# v_mask = 1 - 2 * tf.abs(tf.sign(x - x_clip))
# v = v * v_mask
# Update x
x = x + step_size * v
# x = tf.clip_by_value(x, -0.01, 1.01)
# x = tf.Print(x, [tf.reduce_min(x), tf.reduce_max(x), tf.reduce_mean(x)])
# Do a final update of the velocity for a half step
v = v - 0.5 * step_size * tf.gradients(neg_log_posterior(x), x)[0]
# return new proposal state
return x, v
def hmc(initial_x,
step_size,
num_steps,
neg_log_posterior):
"""Summary
Parameters
----------
initial_x : tf.Variable
Initial sample x ~ p
step_size : float
Step-size in Hamiltonian simulation
num_steps : int
Number of steps to take in Hamiltonian simulation
neg_log_posterior : str
Negative log posterior (unnormalized) for the target distribution
Returns
-------
sample :
Sample ~ target distribution
"""
v0 = tf.random_normal(tf.shape(initial_x))
x, v = leapfrog_step(initial_x,
v0,
step_size=step_size,
num_steps=num_steps,
neg_log_posterior=neg_log_posterior)
orig = hamiltonian(initial_x, v0, neg_log_posterior)
current = hamiltonian(x, v, neg_log_posterior)
prob_accept = tf.exp(orig - current)
if FLAGS.proposal_debug:
prob_accept = tf.Print(prob_accept, [tf.reduce_mean(tf.clip_by_value(prob_accept, 0, 1))])
uniform = tf.random_uniform(tf.shape(prob_accept))
keep_mask = (prob_accept > uniform)
# print(keep_mask.get_shape())
x_new = tf.where(keep_mask, x, initial_x)
return x_new