class SingleBanana(object):
"""Creates the log_target as in [WKB09]
:param dim:
integer; the dimension
"""
def __init__(self, dim, twistdim):
assert dim >= 2
assert twistdim < dim - 1
self.dim = dim
self.twistdim = twistdim
# kilbinger_params:
self.sigma1_squared = 100.0
self.p = 10.0
self.b = 0.03
self.mean = np.zeros(dim)
self.cov = np.eye(dim)
self.cov[twistdim, twistdim] = self.sigma1_squared
self.underlying_gauss = Gauss(self.mean, self.cov)
def __call__(self, x):
x = np.array(x)
x[1 + self.twistdim] += self.b * (x[0 + self.twistdim] * x[0 + self.twistdim] - self.sigma1_squared)
return self.underlying_gauss.evaluate(x)
class LogTarget(object):
"""Creates the log_target as in [WKB09]
:param dim:
integer; the dimension
"""
def __init__(self, dim):
assert dim >= 2
self.dim = dim
# kilbinger_params:
self.sigma1_squared = 100.
self.p = 10.
self.b = .03
self.mean = np.zeros(dim)
self.cov = np.diag([self.sigma1_squared] + [1. for i in range(dim-1)])
self.underlying_gauss = Gauss(self.mean, self.cov)
def __call__(self, x):
x1 = np.array(x)
x1[1] += 5.
x1[2] -= 5.
x1[1] += self.b * (x1[0]*x1[0] - self.sigma1_squared)
x2 = np.array(x)
x2[1] -= 5.
x2[2] += 5.
x2[2] += self.b * (x2[0]*x2[0] - self.sigma1_squared)
return np.log( .5 * np.exp( self.underlying_gauss.evaluate(x1) )
+ .5 * np.exp( self.underlying_gauss.evaluate(x2) ) )
def __init__(self, dim):
assert dim >= 2
self.dim = dim
# kilbinger_params:
self.sigma1_squared = 100.
self.p = 10.
self.b = .03
self.mean = np.zeros(dim)
self.cov = np.diag([self.sigma1_squared] + [1. for i in range(dim-1)])
self.underlying_gauss = Gauss(self.mean, self.cov)
def __init__(self, dim, twistdim):
assert dim >= 2
assert twistdim < dim - 1
self.dim = dim
self.twistdim = twistdim
# kilbinger_params:
self.sigma1_squared = 100.0
self.p = 10.0
self.b = 0.03
self.mean = np.zeros(dim)
self.cov = np.eye(dim)
self.cov[twistdim, twistdim] = self.sigma1_squared
self.underlying_gauss = Gauss(self.mean, self.cov)
def run_iter(
self,
num_gauss_samples=400,
max_ncalls=100000,
min_ess=400,
max_improvement_loops=4,
heavytail_laplaceapprox=True,
verbose=True,
):
"""
Iterative version of run(). See documentation there.
Returns current samples on each iteration.
"""
paramnames = self.paramnames
loglike = self.loglike
transform = self.transform
ndim = len(paramnames)
optu, cov, invcov = self.optu, self.cov, self.invcov
# for numerical stability, use 1e260, so that we can go down be 1e-100,
# but up by 1e600
self.Loffset = self.optL #+ 600
# first iteration: create a single gaussian and importance-sample
if self.log:
self.logger.info("Initiating gaussian importance sampler")
def log_target(u):
""" log-posterior to sample from """
if (u > 1).any() or (u < 0).any():
return -np.inf
p = transform(u)
L = loglike(p)
return L - self.Loffset
if not heavytail_laplaceapprox:
initial_proposal = Gauss(optu, cov)
else:
# make a few gaussians, in case the fit errors were too narrow
means, covs, weights = _make_initial_proposal(optu, cov)
initial_proposal = create_gaussian_mixture(means, covs, weights)
mixes = [initial_proposal]
N = num_gauss_samples
Nhere = N // self.mpi_size
if self.mpi_size > 1:
SequentialIS = ImportanceSampler
from pypmc.tools.parallel_sampler import MPISampler
sampler = MPISampler(SequentialIS,
target=log_target,
proposal=initial_proposal,
prealloc=Nhere)
else:
sampler = ImportanceSampler(target=log_target,
proposal=initial_proposal,
prealloc=Nhere)
if self.log:
self.logger.info(" sampling %d ..." % N)
np.seterr(over="warn")
sampler.run(Nhere)
self.ncall += Nhere * self.mpi_size
samples, weights = self._collect_samples(sampler)
assert weights.sum() > 0, 'All samples have weight zero.'
vbmix = None
for it in range(max_improvement_loops):
ess_fraction = ess(weights)
if self.log:
self.logger.info(" sampling efficiency: %.3f%%" %
(ess_fraction * 100))
if it % 3 == 0:
if self.log:
self.logger.info("Optimizing proposal (from scratch) ...")
mix = _make_proposal(samples, weights, optu, cov, invcov)
vb = GaussianInference(samples,
weights=weights,
initial_guess=mix,
W0=np.eye(ndim) * 1e10)
vb_prune = 0.5 * len(vb.data) / vb.K
else:
if self.log:
self.logger.info("Optimizing proposal (from previous) ...")
prior_for_proposal_update = vb.posterior2prior()
prior_for_proposal_update.pop('alpha0')
vb = GaussianInference(samples,
initial_guess=vbmix,
weights=weights,
**prior_for_proposal_update)
if self.log:
self.logger.info(' running variational Bayes ...')
vb.run(1000,
rel_tol=1e-8,
abs_tol=1e-5,
prune=vb_prune,
verbose=False)
vbmix = vb.make_mixture()
if self.log:
self.logger.info(' reduced from %d to %d components' %
(len(mix.components), len(vbmix.components)))
sampler.proposal = vbmix
if self.log:
self.logger.info("Importance sampling %d ..." % N)
sampler.run(N // self.mpi_size)
self.ncall += (N // self.mpi_size) * self.mpi_size
mixes.append(vbmix)
samples, weights = self._collect_samples(sampler)
ess_fraction = ess(weights)
if self.log:
self.logger.debug(" sampling efficiency: %.3f%%" %
(ess_fraction * 100))
self.logger.debug(" obtained %.0f new effective samples" %
(ess_fraction * len(weights)))
samples, weights = self._collect_samples(sampler,
all=True,
mixes=mixes)
ess_fraction = ess(weights)
Ndone = ess_fraction * len(weights)
result = self._update_results(samples, weights)
if Ndone >= min_ess:
if self.log:
self.logger.info(
"Status: Have %d total effective samples, done." %
Ndone)
yield result
break
elif self.ncall > max_ncalls:
if self.log:
self.logger.info(
"Status: Have %d total effective samples, reached max number of calls."
% Ndone)
yield result
break
else:
N = int(1.4 * min(max_ncalls - self.ncall, N))
if self.log:
self.logger.info(
"Status: Have %d total effective samples, sampling %d next."
% (Ndone, N))
yield result