def test_sample_from_1D_gaussian(self):
energy_norm_cst = 0.5 * np.log(2 * 3.141592)
U = lambda q: energy_norm_cst + (q ** 2).sum() / 2
grad_U = lambda q: q.sum()
# This won't work as well with epsilon = 1.e-3
# or with L = 10. It'll get something close, but
# the histogram plot will look difform.
epsilon = 0.1
L = 10
N = 100000
N_accepted_counter = 0
X = np.zeros((N, 1))
# starts at the origin with X[0,:]
for n in np.arange(1, N):
X[n, :] = hmc.one_step_update(U, grad_U, epsilon, L, X[n - 1, :])
if X[n, :] != X[n - 1, :]:
N_accepted_counter = N_accepted_counter + 1
sample_mean = X.mean()
sample_var = X.var()
self.assertTrue(abs(sample_mean) < 0.01)
self.assertTrue(abs(sample_var - 1.0) < 0.01)
if False:
print "sample mean : %0.6f" % sample_mean
print "sample var : %0.6f" % sample_var
print "acceptance ration : %0.6f" % (N_accepted_counter * 1.0 / N,)
import matplotlib
matplotlib.use("Agg")
import pylab
import os
pylab.hist(X[:, 0], 50)
pylab.draw()
pylab.savefig(os.path.join("/u/alaingui/umontreal/cae.py/plots/", "debug_HMC.png"), dpi=300)
pylab.close()
def perform_one_update(the_dae,
X,
noise_stddev,
L,
epsilon,
simulate_only=False):
# We'll format the parameters of the DAE so that they
# fit into the mold of hamiltonian_monte_carlo.one_step_update,
# we'll call that function and then reformat the parameters.
#
# In particular, this means that we'll transform (W, b, c)
# into the vector of position for the Hamiltonian Monte Carlo.
# Helper functions. One being the opposite of the other.
def serialize_params_as_q(W, b, c):
return np.hstack((W.reshape((-1, )), b.reshape(
(-1, )), c.reshape((-1, )))).reshape((-1, ))
def read_params_from_q(q, n_inputs, n_hiddens):
n_elems_W = n_inputs * n_hiddens
n_elems_b = n_inputs
n_elems_c = n_hiddens
W = q[0:n_elems_W].reshape((n_inputs, n_hiddens)).copy()
b = q[n_elems_W:n_elems_W + n_elems_b].reshape((n_elems_b, )).copy()
c = q[n_elems_W + n_elems_b:n_elems_W + n_elems_b + n_elems_c].reshape(
(n_elems_c, )).copy()
return (W, b, c)
# We'll reuse the same perturbed_X for all the evaluations
# of the potential during the leapfrog.
if noise_stddev > 0.0:
perturbed_X = X + np.random.normal(scale=noise_stddev, size=X.shape)
else:
perturbed_X = X.copy()
def U(q):
# the dataset X is baked into the definition of U(q)
(W, b, c) = read_params_from_q(q, the_dae.n_inputs, the_dae.n_hiddens)
(loss, _, _) = the_dae.theano_loss(W, b, c, perturbed_X, X)
return loss.sum()
def grad_U(q):
(W, b, c) = read_params_from_q(q, the_dae.n_inputs, the_dae.n_hiddens)
(grad_W, grad_b,
grad_c) = the_dae.theano_gradients(W, b, c, perturbed_X, X)
# We can use the same function to spin the gradients into the
# momentum vector. This works well because
# grad_W.shape == W.shape
# grad_b.shape == b.shape
# grad_c.shape == c.shape
return serialize_params_as_q(grad_W, grad_b, grad_c)
current_q = serialize_params_as_q(the_dae.W, the_dae.b, the_dae.c)
updated_q = hmc.one_step_update(U,
grad_U,
epsilon,
L,
current_q,
verbose=True)
if the_dae.logging.has_key('hmc'):
if np.any(current_q != updated_q):
# it would make more sense to store the acceptance likelihood
# instead, but right now we don't pass it as extra returned value
the_dae.logging['hmc']['acceptance_history'].append(1)
else:
the_dae.logging['hmc']['acceptance_history'].append(0)
else:
the_dae.logging['hmc'] = {}
the_dae.logging['hmc']['acceptance_history'] = []
# Our function U(q) is mutating the dae in a way that makes
# it necessary that we rewrite the parameters values at the
# end even if current_q == updated_q.
(the_dae.W, the_dae.b,
the_dae.c) = read_params_from_q(updated_q, the_dae.n_inputs,
the_dae.n_hiddens)
def perform_one_update(the_dae, X, noise_stddev, L, epsilon, simulate_only = False):
# We'll format the parameters of the DAE so that they
# fit into the mold of hamiltonian_monte_carlo.one_step_update,
# we'll call that function and then reformat the parameters.
#
# In particular, this means that we'll transform (W, b, c)
# into the vector of position for the Hamiltonian Monte Carlo.
# Helper functions. One being the opposite of the other.
def serialize_params_as_q(W, b, c):
return np.hstack((W.reshape((-1,)),
b.reshape((-1,)),
c.reshape((-1,)))).reshape((-1,))
def read_params_from_q(q, n_inputs, n_hiddens):
n_elems_W = n_inputs * n_hiddens
n_elems_b = n_inputs
n_elems_c = n_hiddens
W = q[0 : n_elems_W].reshape((n_inputs, n_hiddens)).copy()
b = q[n_elems_W : n_elems_W + n_elems_b].reshape((n_elems_b,)).copy()
c = q[n_elems_W + n_elems_b : n_elems_W + n_elems_b + n_elems_c].reshape((n_elems_c,)).copy()
return (W, b, c)
# We'll reuse the same perturbed_X for all the evaluations
# of the potential during the leapfrog.
if noise_stddev > 0.0:
perturbed_X = X + np.random.normal(scale=noise_stddev, size=X.shape)
else:
perturbed_X = X.copy()
def U(q):
# the dataset X is baked into the definition of U(q)
(W, b, c) = read_params_from_q(q, the_dae.n_inputs, the_dae.n_hiddens)
(loss, _, _) = the_dae.theano_loss(W, b, c, perturbed_X, X)
return loss.sum()
def grad_U(q):
(W, b, c) = read_params_from_q(q, the_dae.n_inputs, the_dae.n_hiddens)
(grad_W, grad_b, grad_c) = the_dae.theano_gradients(W, b, c, perturbed_X, X)
# We can use the same function to spin the gradients into the
# momentum vector. This works well because
# grad_W.shape == W.shape
# grad_b.shape == b.shape
# grad_c.shape == c.shape
return serialize_params_as_q(grad_W, grad_b, grad_c)
current_q = serialize_params_as_q(the_dae.W, the_dae.b, the_dae.c)
updated_q = hmc.one_step_update(U, grad_U, epsilon, L, current_q, verbose=True)
if the_dae.logging.has_key('hmc'):
if np.any(current_q != updated_q):
# it would make more sense to store the acceptance likelihood
# instead, but right now we don't pass it as extra returned value
the_dae.logging['hmc']['acceptance_history'].append(1)
else:
the_dae.logging['hmc']['acceptance_history'].append(0)
else:
the_dae.logging['hmc'] = {}
the_dae.logging['hmc']['acceptance_history'] = []
# Our function U(q) is mutating the dae in a way that makes
# it necessary that we rewrite the parameters values at the
# end even if current_q == updated_q.
(the_dae.W, the_dae.b, the_dae.c) = read_params_from_q(updated_q, the_dae.n_inputs, the_dae.n_hiddens)