def testSampleProbConsistentBroadcastMixNonStandardBase(self):
with self.test_session() as sess:
dims = 4
vdm = vector_diffeomixture_lib.VectorDiffeomixture(
mix_loc=[[0.], [1.]],
mix_scale=[1.],
distribution=normal_lib.Normal(1., 1.5),
loc=[
None,
np.float32([2.] * dims),
],
scale=[
linop_identity_lib.LinearOperatorScaledIdentity(
num_rows=dims,
multiplier=np.float32(1.1),
is_positive_definite=True),
linop_diag_lib.LinearOperatorDiag(
diag=np.linspace(2.5, 3.5, dims, dtype=np.float32),
is_positive_definite=True),
],
validate_args=True)
# Ball centered at component0's mean.
self.run_test_sample_consistent_log_prob(sess,
vdm,
radius=2.,
center=1.,
rtol=0.006)
# Larger ball centered at component1's mean.
self.run_test_sample_consistent_log_prob(sess,
vdm,
radius=4.,
center=3.,
rtol=0.009)
def testSampleProbConsistentBroadcastMixBatch(self):
with self.cached_session() as sess:
dims = 4
vdm = vdm_lib.VectorDiffeomixture(
mix_loc=[[0.], [1.]],
temperature=[1.],
distribution=normal_lib.Normal(0., 1.),
loc=[
None,
np.float32([2.]*dims),
],
scale=[
linop_identity_lib.LinearOperatorScaledIdentity(
num_rows=dims,
multiplier=[np.float32(1.1)],
is_positive_definite=True),
linop_diag_lib.LinearOperatorDiag(
diag=np.stack([
np.linspace(2.5, 3.5, dims, dtype=np.float32),
np.linspace(2.75, 3.25, dims, dtype=np.float32),
]),
is_positive_definite=True),
],
quadrature_size=8,
validate_args=True)
# Ball centered at component0's mean.
self.run_test_sample_consistent_log_prob(
sess.run, vdm, radius=2., center=0., rtol=0.01)
# Larger ball centered at component1's mean.
self.run_test_sample_consistent_log_prob(
sess.run, vdm, radius=4., center=2., rtol=0.01)
def testMeanCovarianceBatch(self):
with self.test_session() as sess:
dims = 3
vdm = vector_diffeomixture_lib.VectorDiffeomixture(
mix_loc=[[0.], [4.]],
mix_scale=[10.],
distribution=normal_lib.Normal(0., 1.),
loc=[
np.float32([[-2.]]),
None,
],
scale=[
linop_identity_lib.LinearOperatorScaledIdentity(
num_rows=dims,
multiplier=[np.float32(1.5)],
is_positive_definite=True),
linop_diag_lib.LinearOperatorDiag(
diag=np.stack([
np.linspace(2.5, 3.5, dims, dtype=np.float32),
np.linspace(0.5, 1.5, dims, dtype=np.float32),
]),
is_positive_definite=True),
],
validate_args=True)
self.run_test_sample_consistent_mean_covariance(sess,
vdm,
rtol=0.02,
cov_rtol=0.06)
def testSampleProbConsistentBroadcastMixTwoBatchDims(self):
dims = 4
loc_1 = rng.randn(2, 3, dims).astype(np.float32)
with self.cached_session() as sess:
vdm = vdm_lib.VectorDiffeomixture(
mix_loc=(rng.rand(2, 3, 1) - 0.5).astype(np.float32),
temperature=[1.],
distribution=normal_lib.Normal(0., 1.),
loc=[
None,
loc_1,
],
scale=[
linop_identity_lib.LinearOperatorScaledIdentity(
num_rows=dims,
multiplier=[np.float32(1.1)],
is_positive_definite=True),
] * 2,
validate_args=True)
# Ball centered at component0's mean.
self.run_test_sample_consistent_log_prob(
sess.run, vdm, radius=2., center=0., rtol=0.01)
# Larger ball centered at component1's mean.
self.run_test_sample_consistent_log_prob(
sess.run, vdm, radius=3., center=loc_1, rtol=0.02)
def testConcentrationLocControlsHowMuchWeightIsOnEachComponent(self):
with self.test_session() as sess:
dims = 1
vdm = vdm_lib.VectorDiffeomixture(
mix_loc=[[-1.], [0.], [1.]],
temperature=[0.5],
distribution=normal_lib.Normal(0., 1.),
loc=[
np.float32([-2.]),
np.float32([2.]),
],
scale=[
linop_identity_lib.LinearOperatorScaledIdentity(
num_rows=dims,
multiplier=np.float32(0.5),
is_positive_definite=True),
] * 2, # Use the same scale for each component.
quadrature_size=8,
validate_args=True)
samps = vdm.sample(10000)
self.assertAllEqual((10000, 3, 1), samps.shape)
samps_ = sess.run(samps).reshape(10000,
3) # Make scalar event shape.
# One characteristic of putting more weight on a component is that the
# mean is closer to that component's mean.
# Get the mean for each batch member, the names signify the value of
# concentration for that batch member.
mean_neg1, mean_0, mean_1 = samps_.mean(axis=0)
# Since concentration is the concentration for component 0,
# concentration = -1 ==> more weight on component 1, which has mean = 2
# concentration = 0 ==> equal weight
# concentration = 1 ==> more weight on component 0, which has mean = -2
self.assertLess(-2, mean_1)
self.assertLess(mean_1, mean_0)
self.assertLess(mean_0, mean_neg1)
self.assertLess(mean_neg1, 2)
# Run this test as well, just because we can.
self.run_test_sample_consistent_mean_covariance(sess.run,
vdm,
rtol=0.02,
cov_rtol=0.08)
def testSampleProbConsistentDynamicQuadrature(self):
with self.test_session() as sess:
qgrid = array_ops.placeholder(dtype=dtypes.float32)
qprobs = array_ops.placeholder(dtype=dtypes.float32)
g, p = np.polynomial.hermite.hermgauss(deg=8)
dims = 4
vdm = vector_diffeomixture_lib.VectorDiffeomixture(
mix_loc=[[0.], [1.]],
mix_scale=[1.],
distribution=normal_lib.Normal(0., 1.),
loc=[
None,
np.float32([2.] * dims),
],
scale=[
linop_identity_lib.LinearOperatorScaledIdentity(
num_rows=dims,
multiplier=np.float32(1.1),
is_positive_definite=True),
linop_diag_lib.LinearOperatorDiag(
diag=np.linspace(2.5, 3.5, dims, dtype=np.float32),
is_positive_definite=True),
],
quadrature_grid_and_probs=(g, p),
validate_args=True)
# Ball centered at component0's mean.
sess_run_fn = lambda x: sess.run(x,
feed_dict={
qgrid: g,
qprobs: p
})
self.run_test_sample_consistent_log_prob(sess_run_fn,
vdm,
radius=2.,
center=0.,
rtol=0.005)
# Larger ball centered at component1's mean.
self.run_test_sample_consistent_log_prob(sess_run_fn,
vdm,
radius=4.,
center=2.,
rtol=0.005)
def testTemperatureControlsHowMuchThisLooksLikeDiscreteMixture(self):
# As temperature decreases, this should approach a mixture of normals, with
# components at -2, 2.
with self.test_session() as sess:
dims = 1
vdm = vdm_lib.VectorDiffeomixture(
mix_loc=[0.],
temperature=[[2.], [1.], [0.2]],
distribution=normal_lib.Normal(0., 1.),
loc=[
np.float32([-2.]),
np.float32([2.]),
],
scale=[
linop_identity_lib.LinearOperatorScaledIdentity(
num_rows=dims,
multiplier=np.float32(0.5),
is_positive_definite=True),
] * 2, # Use the same scale for each component.
quadrature_size=8,
validate_args=True)
samps = vdm.sample(10000)
self.assertAllEqual((10000, 3, 1), samps.shape)
samps_ = sess.run(samps).reshape(10000,
3) # Make scalar event shape.
# One characteristic of a discrete mixture (as opposed to a "smear") is
# that more weight is put near the component centers at -2, 2, and thus
# less weight is put near the origin.
prob_of_being_near_origin = (np.abs(samps_) < 1).mean(axis=0)
self.assertGreater(prob_of_being_near_origin[0],
prob_of_being_near_origin[1])
self.assertGreater(prob_of_being_near_origin[1],
prob_of_being_near_origin[2])
# Run this test as well, just because we can.
self.run_test_sample_consistent_mean_covariance(sess.run,
vdm,
rtol=0.02,
cov_rtol=0.08)
def testMeanCovarianceNoBatchUncenteredNonStandardBase(self):
with self.test_session() as sess:
dims = 3
vdm = vector_diffeomixture_lib.VectorDiffeomixture(
mix_loc=[[0.], [4.]],
mix_scale=[10.],
distribution=normal_lib.Normal(-1., 1.5),
loc=[
np.float32([-2.]),
np.float32([0.]),
],
scale=[
linop_identity_lib.LinearOperatorScaledIdentity(
num_rows=dims,
multiplier=np.float32(1.5),
is_positive_definite=True),
linop_diag_lib.LinearOperatorDiag(
diag=np.linspace(2.5, 3.5, dims, dtype=np.float32),
is_positive_definite=True),
],
validate_args=True)
self.run_test_sample_consistent_mean_covariance(
sess, vdm, num_samples=int(1e6), rtol=0.01, cov_atol=0.025)