def rhmc_worker_beta(comm, block_width, start, y, template, theta, mu, sigmasq,
region_types, prop_df=5., eps=0.01, n_steps=100,
sigmasq_p=1., adj=2., verbose=0):
# Compute needed data properties
chrom_length = y.size
w = template.size/2 + 1
# Calculate subset of data to work on
end = min(chrom_length, start + block_width)
block = slice(max(start-w, 0), min(end+w, chrom_length))
size_block = block.stop - block.start
original = slice(start-block.start, size_block - (block.stop-end))
subset = slice(w*(start!=0)+start-block.start,
size_block-w*(end!=chrom_length) - (block.stop-end))
size_subset = subset.stop - subset.start
beta_block = np.exp(theta[:size_block])
beta_subset = beta_block[subset]
# Setup initial return value
ret_val = np.empty(block_width)
# Calculate diagonal of Hessian if requested (by setting sigma.p to None)
if sigmasq_p is None:
result = lib.deconvolve(lib.loglik_convolve, lib.dloglik_convolve,
y[block], region_types[block], template,
mu, sigmasq,
subset=subset, theta0=beta_block,
log=False,
messages=0)
sigmasq_p = lib.ddloglik_diag_convolve(theta=result[0], y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq,
theta0=beta_block,
subset=subset, log=False)
sigma_p = np.sqrt(sigmasq_p)
## Repeat leapfrog process until valid result is obtained
#leapfrog_done = False
#
#while not leapfrog_done:
# Draw momentum variables
p = np.random.randn(size_subset)*sigma_p
p_0 = p.copy()
# Initialize new draw of theta
beta_draw = beta_subset.copy()
# Initial gradient computation
grad = lib.dloglik_convolve(theta=beta_draw, y=y[block],
region_types=region_types[block],
template=template, mu=mu, sigmasq=sigmasq,
theta0=beta_block, subset=subset, log=False)
# Run leapfrog iterations
for i in xrange(n_steps):
# Half step for momentum
p -= eps*grad/2.
# Full step for position
beta_draw += eps*p/sigmasq_p
# Reflect to satisfy constraints
p[beta_draw <= 0] *= -1.
beta_draw[beta_draw <= 0] *= -1.
# Update gradient
grad = lib.dloglik_convolve(theta=beta_draw, y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, theta0=beta_block,
subset=subset, log=False)
# Half step for momentum after reflection
p -= eps*grad/2.
# Reverse momentum at end of trajectory to make the proposal symmetric.
p *= -1.
# Construct complete proposal for theta
beta_prop = beta_block.copy()
beta_prop[subset] = beta_draw
# Compute log target and kinetic energy differences
log_target_ratio = -lib.loglik_convolve(theta=beta_prop, y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, subset=None,
theta0=beta_prop, log=False)
log_target_ratio -= -lib.loglik_convolve(theta=beta_block, y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, subset=None,
theta0=beta_block, log=False)
log_kinetic_diff = 0.5*np.sum((p**2 - p_0**2)/sigmasq_p)
# Execute MH step
log_accept_prob = log_target_ratio - log_kinetic_diff
if np.log(np.random.uniform()) < log_accept_prob:
accept = 1
ret_val[:end-start] = np.log(beta_prop[original])
else:
accept = 0
ret_val[:end-start] = np.log(beta_block[original])
if verbose > 0:
print np.mean(sigma_p), np.std(sigma_p), eps, log_accept_prob, accept, start, end
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
def rhmc_worker_theta(comm, block_width, start, y, template, theta, mu, sigmasq,
region_types, prop_df=5., eps_max=0.1, eps_min=0.001,
n_steps=100, sigmasq_p=1., adj=10, verbose=0):
# Compute needed data properties
chrom_length = y.size
w = template.size/2 + 1
# Calculate subset of data to work on
end = min(chrom_length, start + block_width)
block = slice(max(start-w, 0), min(end+w, chrom_length))
size_block = block.stop - block.start
original = slice(start-block.start, size_block - (block.stop-end))
subset = slice(w*(start!=0)+start-block.start,
size_block-w*(end!=chrom_length) - (block.stop-end))
size_subset = subset.stop - subset.start
theta_block = theta[:size_block]
theta_subset = theta_block[subset]
# Setup initial return value
ret_val = np.empty(block_width)
# Calculate diagonal of Hessian if requested (by setting sigma.p to None)
if sigmasq_p is None:
result = lib.deconvolve(lib.loglik_convolve, lib.dloglik_convolve,
y[block], region_types[block], template,
mu, sigmasq,
subset=subset, theta0=theta_block,
log=True,
messages=0)
sigmasq_p = lib.ddloglik_diag_convolve(theta=result[0], y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq,
theta0=theta_block,
subset=subset, log=True)
sigma_p = np.sqrt(sigmasq_p)
# Draw momentum variables
p = np.random.randn(size_subset)*sigma_p
p_0 = p.copy()
# Repeat leapfrog process until valid result is obtained
leapfrog_done = False
eps = np.random.uniform(eps_min, eps_max)
while not leapfrog_done:
# Initialize new draw of theta
theta_draw = theta_subset.copy()
# Run leapfrog iterations
grad = lib.dloglik_convolve(theta=theta_draw, y=y[block],
region_types=region_types[block],
template=template, mu=mu, sigmasq=sigmasq,
theta0=theta_block, subset=subset, log=True)
# Start with half step for momentum
p -= eps*grad / 2.
# Alternate full steps for position and momentum
for i in xrange(n_steps):
# Full step for position
theta_draw += eps*p/sigmasq_p
# Update gradient
grad = lib.dloglik_convolve(theta=theta_draw, y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, theta0=theta_block,
subset=subset, log=True)
# Full step for momentum, except at the end of the trajectory
if i<(n_steps - 1): p -= eps*grad
# Half step for momentum at the end
p -= eps*grad/2.
if np.min(np.isfinite(theta_draw)):
leapfrog_done = True
else:
# Restart with smaller step size
eps /= adj
p[:] = p_0
theta_draw[:] = theta_subset
# Reverse momentum at end of trajectory to make the proposal symmetric.
p = -p
# Construct complete proposal for theta
theta_prop = theta_block.copy()
theta_prop[subset] = theta_draw
# Compute log target and kinetic energy differences
log_target_ratio = -lib.loglik_convolve(theta=theta_prop, y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, subset=None,
theta0=theta_prop, log=True)
log_target_ratio -= -lib.loglik_convolve(theta=theta_block, y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, subset=None,
theta0=theta_block, log=True)
log_kinetic_diff = 0.5*np.sum((p**2 - p_0**2)/sigmasq_p)
# Execute MH step
log_accept_prob = log_target_ratio - log_kinetic_diff
if np.log(np.random.uniform()) < log_accept_prob:
accept = 1
ret_val[:end-start] = theta_prop[original]
else:
accept = 0
ret_val[:end-start] = theta_block[original]
if verbose > 0:
print np.mean(sigma_p), np.std(sigma_p), eps, log_accept_prob, accept, start, end
if verbose > 1 and np.isnan(log_accept_prob):
print sigmasq_p.min(), sigmasq_p.mean(), sigmasq_p.max(), sigmasq_p.std()
print >> sys.stderr, -lib.loglik_convolve(theta=theta_prop, y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, subset=None,
theta0=theta_prop, log=True)
print >> sys.stderr, -lib.loglik_convolve(theta=theta_block, y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, subset=None,
theta0=theta_block, log=True)
print >> sys.stderr, log_kinetic_diff
print >> sys.stderr, log_target_ratio
print >> sys.stderr, log_accept_prob, accept
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
def rmh_worker_theta(comm, block_width, start, y, template, theta, mu, sigmasq,
region_types, prop_df=5.):
# Compute needed data properties
chrom_length = y.size
w = template.size/2 + 1
# Calculate subset of data to work on
end = min(chrom_length, start + block_width)
block = slice(max(start-w, 0), min(end+w, chrom_length))
size_block = block.stop - block.start
subset = slice(w*(start!=0)+start-block.start,
size_block-w*(end!=chrom_length) - (block.stop-end))
size_subset = subset.stop - subset.start
original = slice(start-block.start, size_block - (block.stop-end))
theta_block = theta[block]
theta_subset = theta_block[subset]
# Setup initial return value
ret_val = np.empty(block_width)
# Run optimization to obtain conditional posterior mode
theta_hat = lib.deconvolve(lib.loglik_convolve,
lib.dloglik_convolve,
y[block], region_types[block], template,
mu, sigmasq,
subset=subset, theta0=theta_block,
log=True,
messages=0)[0]
# Compute (sparse) conditional observed information
X = sparse.spdiags((np.ones((template.size,size_block)).T *
template).T, diags=range(-w+1, w),
m=size_block, n=size_block, format='csr')
info = lib.ddloglik(theta=theta_hat,
theta0=theta_block,
X=X, Xt=X, y=y[block],
mu=mu, sigmasq=sigmasq,
region_types=region_types[block],
subset=subset, log=True)
info = info[subset,:]
info = info.tocsc()
info = info[:,subset]
# Propose from multivariate t distribution
try:
info_factor = cholmod.cholesky(info)
except:
# Always reject for these cases
accept = 0
ret_val[:end-start] = theta_block[original]
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
return
L, D = info_factor.L_D()
D = D.diagonal()
#
z = np.random.standard_t(df=prop_df, size=size_subset)
#
theta_draw = info_factor.solve_Lt(z / np.sqrt(D))
theta_draw = info_factor.solve_Pt(theta_draw)
theta_draw = theta_draw.flatten()
theta_draw += theta_hat
#
theta_prop = theta_block.copy()
theta_prop[subset] = theta_draw
# Check for overflow issues
if np.max(theta_prop) >= np.log(np.finfo(np.float).max)/2.:
# Always reject for these cases
accept = 0
ret_val[:end-start] = theta_block[original]
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
return
# Demean and decorrelate previous draw
z_prev = L.T * info_factor.solve_P(theta_subset-theta_hat)
z_prev = z_prev.flatten()
z_prev *= np.sqrt(D)
# Compute log target and proposal ratios
log_target_ratio = -lib.loglik_convolve(theta=theta_prop,
y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, subset=None,
theta0=theta_prop, log=True)
log_target_ratio -= -lib.loglik_convolve(theta=theta_block,
y=y[block],
region_types=region_types[block],
template=template, mu=mu,
sigmasq=sigmasq, subset=None,
theta0=theta_block, log=True)
log_prop_ratio = -0.5*(prop_df+1)*np.sum(np.log(1. + z**2/prop_df)-
np.log(1. + z_prev**2/prop_df))
# Execute MH step
log_accept_prob = log_target_ratio - log_prop_ratio
#print block, log_target_ratio, log_prop_ratio, log_accept_prob
if np.log(np.random.uniform()) < log_accept_prob:
accept = 1
ret_val[:end-start] = theta_prop[original]
else:
accept = 0
ret_val[:end-start] = theta_block[original]
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
def rhmc_worker_beta(comm,
block_width,
start,
y,
template,
theta,
mu,
sigmasq,
region_types,
prop_df=5.,
eps=0.01,
n_steps=100,
sigmasq_p=1.,
adj=2.,
verbose=0):
# Compute needed data properties
chrom_length = y.size
w = template.size / 2 + 1
# Calculate subset of data to work on
end = min(chrom_length, start + block_width)
block = slice(max(start - w, 0), min(end + w, chrom_length))
size_block = block.stop - block.start
original = slice(start - block.start, size_block - (block.stop - end))
subset = slice(w * (start != 0) + start - block.start,
size_block - w * (end != chrom_length) - (block.stop - end))
size_subset = subset.stop - subset.start
beta_block = np.exp(theta[:size_block])
beta_subset = beta_block[subset]
# Setup initial return value
ret_val = np.empty(block_width)
# Calculate diagonal of Hessian if requested (by setting sigma.p to None)
if sigmasq_p is None:
result = lib.deconvolve(lib.loglik_convolve,
lib.dloglik_convolve,
y[block],
region_types[block],
template,
mu,
sigmasq,
subset=subset,
theta0=beta_block,
log=False,
messages=0)
sigmasq_p = lib.ddloglik_diag_convolve(
theta=result[0],
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
theta0=beta_block,
subset=subset,
log=False)
sigma_p = np.sqrt(sigmasq_p)
## Repeat leapfrog process until valid result is obtained
#leapfrog_done = False
#
#while not leapfrog_done:
# Draw momentum variables
p = np.random.randn(size_subset) * sigma_p
p_0 = p.copy()
# Initialize new draw of theta
beta_draw = beta_subset.copy()
# Initial gradient computation
grad = lib.dloglik_convolve(theta=beta_draw,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
theta0=beta_block,
subset=subset,
log=False)
# Run leapfrog iterations
for i in xrange(n_steps):
# Half step for momentum
p -= eps * grad / 2.
# Full step for position
beta_draw += eps * p / sigmasq_p
# Reflect to satisfy constraints
p[beta_draw <= 0] *= -1.
beta_draw[beta_draw <= 0] *= -1.
# Update gradient
grad = lib.dloglik_convolve(theta=beta_draw,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
theta0=beta_block,
subset=subset,
log=False)
# Half step for momentum after reflection
p -= eps * grad / 2.
# Reverse momentum at end of trajectory to make the proposal symmetric.
p *= -1.
# Construct complete proposal for theta
beta_prop = beta_block.copy()
beta_prop[subset] = beta_draw
# Compute log target and kinetic energy differences
log_target_ratio = -lib.loglik_convolve(theta=beta_prop,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
subset=None,
theta0=beta_prop,
log=False)
log_target_ratio -= -lib.loglik_convolve(theta=beta_block,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
subset=None,
theta0=beta_block,
log=False)
log_kinetic_diff = 0.5 * np.sum((p**2 - p_0**2) / sigmasq_p)
# Execute MH step
log_accept_prob = log_target_ratio - log_kinetic_diff
if np.log(np.random.uniform()) < log_accept_prob:
accept = 1
ret_val[:end - start] = np.log(beta_prop[original])
else:
accept = 0
ret_val[:end - start] = np.log(beta_block[original])
if verbose > 0:
print np.mean(sigma_p), np.std(
sigma_p), eps, log_accept_prob, accept, start, end
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
def rhmc_worker_theta(comm,
block_width,
start,
y,
template,
theta,
mu,
sigmasq,
region_types,
prop_df=5.,
eps_max=0.1,
eps_min=0.001,
n_steps=100,
sigmasq_p=1.,
adj=10,
verbose=0):
# Compute needed data properties
chrom_length = y.size
w = template.size / 2 + 1
# Calculate subset of data to work on
end = min(chrom_length, start + block_width)
block = slice(max(start - w, 0), min(end + w, chrom_length))
size_block = block.stop - block.start
original = slice(start - block.start, size_block - (block.stop - end))
subset = slice(w * (start != 0) + start - block.start,
size_block - w * (end != chrom_length) - (block.stop - end))
size_subset = subset.stop - subset.start
theta_block = theta[:size_block]
theta_subset = theta_block[subset]
# Setup initial return value
ret_val = np.empty(block_width)
# Calculate diagonal of Hessian if requested (by setting sigma.p to None)
if sigmasq_p is None:
result = lib.deconvolve(lib.loglik_convolve,
lib.dloglik_convolve,
y[block],
region_types[block],
template,
mu,
sigmasq,
subset=subset,
theta0=theta_block,
log=True,
messages=0)
sigmasq_p = lib.ddloglik_diag_convolve(
theta=result[0],
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
theta0=theta_block,
subset=subset,
log=True)
sigma_p = np.sqrt(sigmasq_p)
# Draw momentum variables
p = np.random.randn(size_subset) * sigma_p
p_0 = p.copy()
# Repeat leapfrog process until valid result is obtained
leapfrog_done = False
eps = np.random.uniform(eps_min, eps_max)
while not leapfrog_done:
# Initialize new draw of theta
theta_draw = theta_subset.copy()
# Run leapfrog iterations
grad = lib.dloglik_convolve(theta=theta_draw,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
theta0=theta_block,
subset=subset,
log=True)
# Start with half step for momentum
p -= eps * grad / 2.
# Alternate full steps for position and momentum
for i in xrange(n_steps):
# Full step for position
theta_draw += eps * p / sigmasq_p
# Update gradient
grad = lib.dloglik_convolve(theta=theta_draw,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
theta0=theta_block,
subset=subset,
log=True)
# Full step for momentum, except at the end of the trajectory
if i < (n_steps - 1): p -= eps * grad
# Half step for momentum at the end
p -= eps * grad / 2.
if np.min(np.isfinite(theta_draw)):
leapfrog_done = True
else:
# Restart with smaller step size
eps /= adj
p[:] = p_0
theta_draw[:] = theta_subset
# Reverse momentum at end of trajectory to make the proposal symmetric.
p = -p
# Construct complete proposal for theta
theta_prop = theta_block.copy()
theta_prop[subset] = theta_draw
# Compute log target and kinetic energy differences
log_target_ratio = -lib.loglik_convolve(theta=theta_prop,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
subset=None,
theta0=theta_prop,
log=True)
log_target_ratio -= -lib.loglik_convolve(theta=theta_block,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
subset=None,
theta0=theta_block,
log=True)
log_kinetic_diff = 0.5 * np.sum((p**2 - p_0**2) / sigmasq_p)
# Execute MH step
log_accept_prob = log_target_ratio - log_kinetic_diff
if np.log(np.random.uniform()) < log_accept_prob:
accept = 1
ret_val[:end - start] = theta_prop[original]
else:
accept = 0
ret_val[:end - start] = theta_block[original]
if verbose > 0:
print np.mean(sigma_p), np.std(
sigma_p), eps, log_accept_prob, accept, start, end
if verbose > 1 and np.isnan(log_accept_prob):
print sigmasq_p.min(), sigmasq_p.mean(), sigmasq_p.max(
), sigmasq_p.std()
print >> sys.stderr, -lib.loglik_convolve(
theta=theta_prop,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
subset=None,
theta0=theta_prop,
log=True)
print >> sys.stderr, -lib.loglik_convolve(
theta=theta_block,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
subset=None,
theta0=theta_block,
log=True)
print >> sys.stderr, log_kinetic_diff
print >> sys.stderr, log_target_ratio
print >> sys.stderr, log_accept_prob, accept
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
def rmh_worker_theta(comm,
block_width,
start,
y,
template,
theta,
mu,
sigmasq,
region_types,
prop_df=5.):
# Compute needed data properties
chrom_length = y.size
w = template.size / 2 + 1
# Calculate subset of data to work on
end = min(chrom_length, start + block_width)
block = slice(max(start - w, 0), min(end + w, chrom_length))
size_block = block.stop - block.start
subset = slice(w * (start != 0) + start - block.start,
size_block - w * (end != chrom_length) - (block.stop - end))
size_subset = subset.stop - subset.start
original = slice(start - block.start, size_block - (block.stop - end))
theta_block = theta[block]
theta_subset = theta_block[subset]
# Setup initial return value
ret_val = np.empty(block_width)
# Run optimization to obtain conditional posterior mode
theta_hat = lib.deconvolve(lib.loglik_convolve,
lib.dloglik_convolve,
y[block],
region_types[block],
template,
mu,
sigmasq,
subset=subset,
theta0=theta_block,
log=True,
messages=0)[0]
# Compute (sparse) conditional observed information
X = sparse.spdiags((np.ones((template.size, size_block)).T * template).T,
diags=range(-w + 1, w),
m=size_block,
n=size_block,
format='csr')
info = lib.ddloglik(theta=theta_hat,
theta0=theta_block,
X=X,
Xt=X,
y=y[block],
mu=mu,
sigmasq=sigmasq,
region_types=region_types[block],
subset=subset,
log=True)
info = info[subset, :]
info = info.tocsc()
info = info[:, subset]
# Propose from multivariate t distribution
try:
info_factor = cholmod.cholesky(info)
except:
# Always reject for these cases
accept = 0
ret_val[:end - start] = theta_block[original]
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
return
L, D = info_factor.L_D()
D = D.diagonal()
#
z = np.random.standard_t(df=prop_df, size=size_subset)
#
theta_draw = info_factor.solve_Lt(z / np.sqrt(D))
theta_draw = info_factor.solve_Pt(theta_draw)
theta_draw = theta_draw.flatten()
theta_draw += theta_hat
#
theta_prop = theta_block.copy()
theta_prop[subset] = theta_draw
# Check for overflow issues
if np.max(theta_prop) >= np.log(np.finfo(np.float).max) / 2.:
# Always reject for these cases
accept = 0
ret_val[:end - start] = theta_block[original]
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)
return
# Demean and decorrelate previous draw
z_prev = L.T * info_factor.solve_P(theta_subset - theta_hat)
z_prev = z_prev.flatten()
z_prev *= np.sqrt(D)
# Compute log target and proposal ratios
log_target_ratio = -lib.loglik_convolve(theta=theta_prop,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
subset=None,
theta0=theta_prop,
log=True)
log_target_ratio -= -lib.loglik_convolve(theta=theta_block,
y=y[block],
region_types=region_types[block],
template=template,
mu=mu,
sigmasq=sigmasq,
subset=None,
theta0=theta_block,
log=True)
log_prop_ratio = -0.5 * (prop_df + 1) * np.sum(
np.log(1. + z**2 / prop_df) - np.log(1. + z_prev**2 / prop_df))
# Execute MH step
log_accept_prob = log_target_ratio - log_prop_ratio
#print block, log_target_ratio, log_prop_ratio, log_accept_prob
if np.log(np.random.uniform()) < log_accept_prob:
accept = 1
ret_val[:end - start] = theta_prop[original]
else:
accept = 0
ret_val[:end - start] = theta_block[original]
# Transmit result
comm.Send(ret_val, dest=MPIROOT, tag=accept)