def test_region_est_ellipsoid(self):
"""
Tests that region_est_ellipsoid works.
"""
dist = MultivariateNormalDistribution(self.MEAN, self.COV)
u = ParticleDistribution(
particle_locations = dist.sample(self.N_PARTICLES),
particle_weights = np.ones(self.N_PARTICLES)/self.N_PARTICLES
)
# ask for a confidence level of 0.5
A, c = u.region_est_ellipsoid(level=0.5)
# center of ellipse should be the mean of the multinormal
assert_almost_equal(np.round(c), self.MEAN, 1)
# finally, the principal lengths of the ellipsoid
# should be the same as COV
_, QA, _ = np.linalg.svd(A)
_, QC, _ = np.linalg.svd(self.COV)
QA, QC = np.sqrt(QA), np.sqrt(QC)
assert_almost_equal(
QA / np.linalg.norm(QA),
QC / np.linalg.norm(QC),
1
)
def test_est_credible_region(self):
"""
Tests that est_credible_region doesn't fail miserably
"""
dist = MultivariateNormalDistribution(self.MEAN, self.COV)
u = ParticleDistribution(
particle_locations = dist.sample(self.N_PARTICLES),
particle_weights = np.ones(self.N_PARTICLES)/self.N_PARTICLES
)
# first check that 0.95 confidence points consume 0.9 confidence points
points1 = u.est_credible_region(level=0.95)
points2 = u.est_credible_region(level=0.9)
assert_almost_equal(
np.sort(unique_rows(np.concatenate([points1, points2])), axis=0),
np.sort(points1, axis=0)
)
# do the same thing with different slice
points1 = u.est_credible_region(level=0.95, modelparam_slice=self.SLICE)
points2 = u.est_credible_region(level=0.9, modelparam_slice=self.SLICE)
assert_almost_equal(
np.sort(unique_rows(np.concatenate([points1, points2])), axis=0),
np.sort(points1, axis=0)
)
def test_region_est_hull(self):
"""
Tests that test_region_est_hull works
"""
dist = MultivariateNormalDistribution(self.MEAN, self.COV)
u = ParticleDistribution(
particle_locations = dist.sample(self.N_PARTICLES),
particle_weights = np.ones(self.N_PARTICLES)/self.N_PARTICLES
)
faces, vertices = u.region_est_hull(level=0.95)
# In this multinormal case, the convex hull surface
# should be centered at MEAN
assert_almost_equal(
np.round(np.mean(vertices, axis=0)),
np.round(self.MEAN)
)
# And a lower level should result in a smaller hull
# and therefore smaller sample variance
faces2, vertices2 = u.region_est_hull(level=0.2)
assert_array_less(np.var(vertices2, axis=0), np.var(vertices, axis=0))
def test_in_credible_region(self):
"""
Tests that in_credible_region works.
"""
dist = MultivariateNormalDistribution(self.MEAN, self.COV)
u = ParticleDistribution(
particle_locations = dist.sample(self.N_PARTICLES),
particle_weights = np.ones(self.N_PARTICLES)/self.N_PARTICLES
)
# some points to test with
test_points = np.random.multivariate_normal(self.MEAN, self.COV, self.N_PARTICLES)
# method='pce'
results = [
u.in_credible_region(test_points, level=0.9, method='pce'),
u.in_credible_region(test_points, level=0.84, method='pce'),
u.in_credible_region(test_points, level=0.5, method='pce'),
]
assert_almost_equal(
np.array([np.mean(x.astype('float')) for x in results]),
np.array([0.9, 0.84, 0.5]),
3
)
# method='hpd-hull'
results1 = [
u.in_credible_region(test_points, level=0.9, method='hpd-hull'),
u.in_credible_region(test_points, level=0.84, method='hpd-hull'),
u.in_credible_region(test_points, level=0.5, method='hpd-hull'),
]
assert_array_less(
np.array([0.9, 0.84, 0.5]),
np.array([np.mean(x.astype('float')) for x in results1])
)
# method='hpd-mvee'
results2 = [
u.in_credible_region(test_points, level=0.9, method='hpd-mvee'),
u.in_credible_region(test_points, level=0.84, method='hpd-mvee'),
u.in_credible_region(test_points, level=0.5, method='hpd-mvee'),
]
assert_array_less(
np.array([0.9, 0.84, 0.5]),
np.array([np.mean(x.astype('float')) for x in results2])
)
# the mvee should be bigger than the convex hull.
# this passes iff all points in the ellipses are
# also in the hulls.
assert_array_less(
np.hstack([x.astype('float') for x in results1]),
np.hstack([x.astype('float') for x in results2]) + 0.5
)
# check for no failures with slices.
u.in_credible_region(test_points[:100,self.SLICE], level=0.9, method='pce', modelparam_slice=self.SLICE)
u.in_credible_region(test_points[:100,self.SLICE], level=0.9, method='hpd-hull', modelparam_slice=self.SLICE)
u.in_credible_region(test_points[:100,self.SLICE], level=0.9, method='hpd-mvee', modelparam_slice=self.SLICE)
# check for no failures with single inputs
assert(u.in_credible_region(test_points[0,:], level=0.9, method='pce').size == 1)
assert(u.in_credible_region(test_points[0,:], level=0.9, method='hpd-hull').size == 1)
assert(u.in_credible_region(test_points[0,:], level=0.9, method='hpd-mvee').size == 1)
def __call__(self,
model,
particle_dist,
n_particles=None,
precomputed_mean=None,
precomputed_cov=None):
"""
Resample the particles according to algorithm given in
[LW01]_.
"""
# Possibly recompute moments, if not provided.
if precomputed_mean is None:
mean = particle_dist.est_mean()
else:
mean = precomputed_mean
if precomputed_cov is None:
cov = particle_dist.est_covariance_mtx()
else:
cov = precomputed_cov
if n_particles is None:
if self._default_n_particles is None:
n_particles = particle_dist.n_particles
else:
n_particles = self._default_n_particles
# parameters in the Liu and West algorithm
a, h = self._a, self._h
if la.norm(cov, 'fro') == 0:
# The norm of the square root of S is literally zero, such that
# the error estimated in the next step will not make sense.
# We fix that by adding to the covariance a tiny bit of the
# identity.
warnings.warn(
"Covariance has zero norm; adding in small covariance in "
"resampler. Consider increasing n_particles to improve covariance "
"estimates.", ResamplerWarning)
cov = self._zero_cov_comp * np.eye(cov.shape[0])
S, S_err = sqrtm_psd(cov)
if not np.isfinite(S_err):
raise ResamplerError(
"Infinite error in computing the square root of the "
"covariance matrix. Check that n_ess is not too small.")
S = np.real(h * S)
# Give shorter names to weights, locations, and nr. of random variables
w = particle_dist.particle_weights
l = particle_dist.particle_locations
n_rvs = particle_dist.n_rvs
new_locs = np.empty((n_particles, n_rvs))
cumsum_weights = np.cumsum(w)
idxs_to_resample = np.arange(n_particles, dtype=int)
# Loop as long as there are any particles left to resample.
n_iters = 0
# Draw j with probability self.particle_weights[j].
# We do this by drawing random variates uniformly on the interval
# [0, 1], then see where they belong in the CDF.
js = cumsum_weights.searchsorted(np.random.random(
(idxs_to_resample.size, )),
side='right')
# Set mu_i to a x_j + (1 - a) mu.
# FIXME This should use particle_dist.particle_mean
mus = a * l[js, :] + (1 - a) * mean
while idxs_to_resample.size and n_iters < self._maxiter:
# Keep track of how many iterations we used.
n_iters += 1
# Draw x_i from N(mu_i, S).
new_locs[idxs_to_resample, :] = mus + np.dot(
S, self._kernel(n_rvs, mus.shape[0])).T
# Now we remove from the list any valid models.
# We write it out in a longer form than is strictly necessary so
# that we can validate assertions as we go. This is helpful for
# catching models that may not hold to the expected postconditions.
resample_locs = new_locs[idxs_to_resample, :]
if self._postselect:
valid_mask = model.are_models_valid(resample_locs)
else:
valid_mask = np.ones((resample_locs.shape[0], ), dtype=bool)
assert valid_mask.ndim == 1, "are_models_valid returned tensor, expected vector."
n_invalid = np.sum(np.logical_not(valid_mask))
if self._debug and n_invalid > 0:
logger.debug(
"LW resampler found {} invalid particles; repeating.".
format(n_invalid))
assert ((len(valid_mask.shape) == 1 or len(valid_mask.shape) == 2
and valid_mask.shape[-1] == 1)
and valid_mask.shape[0] == resample_locs.shape[0]), (
"are_models_valid returned wrong shape {} "
"for input of shape {}.").format(
valid_mask.shape, resample_locs.shape)
idxs_to_resample = idxs_to_resample[np.nonzero(
np.logical_not(valid_mask))[0]]
# This may look a little weird, but it should delete the unused
# elements of js, so that we don't need to reallocate.
js = js[np.logical_not(valid_mask)]
mus = mus[:idxs_to_resample.size, :]
if idxs_to_resample.size:
# We failed to force all models to be valid within maxiter attempts.
# This means that we could be propagating out invalid models, and
# so we should warn about that.
warnings.warn(
("Liu-West resampling failed to find valid models for {} "
"particles within {} iterations.").format(
idxs_to_resample.size, self._maxiter), ResamplerWarning)
if self._debug:
logger.debug(
"LW resampling completed in {} iterations.".format(n_iters))
# Now we reset the weights to be uniform, letting the density of
# particles represent the information that used to be stored in the
# weights. This is done by SMCUpdater, and so we simply need to return
# the new locations here.
new_weights = np.ones((n_particles, )) / n_particles
return ParticleDistribution(particle_locations=new_locs,
particle_weights=new_weights)