def testMeanHigherDimension(self, dtype):
testee_lkj = tfd.LKJ(dimension=6,
concentration=dtype([1., 3., 5.]),
validate_args=True)
num_samples = 20000
results = testee_lkj.sample(sample_shape=[num_samples],
seed=test_util.test_seed())
mean = testee_lkj.mean()
self.assertEqual(mean.shape, [3, 6, 6])
# tfd.LKJ has some small numerical issues, so we allow for some amount of
# numerical tolerance when testing means.
numerical_tolerance = 1e-5
check1 = st.assert_true_mean_in_interval_by_dkwm(
samples=results,
low=-1.,
high=1.,
expected_low=mean - numerical_tolerance,
expected_high=mean + numerical_tolerance,
false_fail_rate=1e-6)
check2 = assert_util.assert_less(
st.min_discrepancy_of_true_means_detectable_by_dkwm(
num_samples,
low=-1.,
high=1.,
# Smaller false fail rate because of different batch sizes between
# these two checks.
false_fail_rate=1e-7,
false_pass_rate=1e-6),
# 4% relative error
0.08)
self.evaluate([check1, check2])
def test_dkwm_mean_in_interval_one_sample_assertion(self):
rng = np.random.RandomState(seed=0)
num_samples = 5000
# Test that the test assertion agrees that the mean of the standard
# uniform distribution is between 0.4 and 0.6.
samples = rng.uniform(size=num_samples).astype(np.float32)
self.evaluate(st.assert_true_mean_in_interval_by_dkwm(
samples, 0., 1.,
expected_low=0.4, expected_high=0.6, false_fail_rate=1e-6))
# Test that the test assertion confirms that the mean of the
# standard uniform distribution is not between 0.2 and 0.4.
with self.assertRaisesOpError("true mean greater than expected"):
self.evaluate(st.assert_true_mean_in_interval_by_dkwm(
samples, 0., 1.,
expected_low=0.2, expected_high=0.4, false_fail_rate=1e-6))
# Test that the test assertion confirms that the mean of the
# standard uniform distribution is not between 0.6 and 0.8.
with self.assertRaisesOpError("true mean smaller than expected"):
self.evaluate(st.assert_true_mean_in_interval_by_dkwm(
samples, 0., 1.,
expected_low=0.6, expected_high=0.8, false_fail_rate=1e-6))
def test_dkwm_mean_in_interval_one_sample_assertion(self):
rng = np.random.RandomState(seed=0)
num_samples = 5000
# Test that the test assertion agrees that the mean of the standard
# uniform distribution is between 0.4 and 0.6.
samples = rng.uniform(size=num_samples).astype(np.float32)
self.evaluate(
st.assert_true_mean_in_interval_by_dkwm(samples,
0.,
1.,
expected_low=0.4,
expected_high=0.6,
false_fail_rate=1e-6))
# Test that the test assertion confirms that the mean of the
# standard uniform distribution is not between 0.2 and 0.4.
with self.assertRaisesOpError("true mean greater than expected"):
self.evaluate(
st.assert_true_mean_in_interval_by_dkwm(samples,
0.,
1.,
expected_low=0.2,
expected_high=0.4,
false_fail_rate=1e-6))
# Test that the test assertion confirms that the mean of the
# standard uniform distribution is not between 0.6 and 0.8.
with self.assertRaisesOpError("true mean smaller than expected"):
self.evaluate(
st.assert_true_mean_in_interval_by_dkwm(samples,
0.,
1.,
expected_low=0.6,
expected_high=0.8,
false_fail_rate=1e-6))
def _testSampleConsistentLogProbInterval(self,
concentrations,
det_bounds,
dim,
num_samples=int(1e5),
dtype=np.float32,
false_fail_rate=1e-6,
target_discrepancy=0.1,
seed=42):
# Consider the set M of dim x dim correlation matrices whose
# determinant exceeds some bound (rationale for bound forthwith).
# - This is a (convex!) shape in dim * (dim - 1) / 2 dimensions
# (because a correlation matrix is determined by its lower
# triangle, and the main diagonal is all 1s).
# - Further, M is contained entirely in the [-1,1] cube,
# because no correlation can fall outside that interval.
#
# We have two different ways to estimate the volume of M:
# - Importance sampling from the LKJ distribution
# - Importance sampling from the uniform distribution on the cube
#
# This test checks that these two methods agree. However, because
# the uniform proposal leads to many rejections (thus slowness),
# those volumes are computed offline and the confidence intervals
# are presented to this test procedure in the "volume_bounds"
# table.
#
# Why place a lower bound on the determinant? Because for eta > 1,
# the density of LKJ approaches 0 as the determinant approaches 0.
# However, the test methodology requires an upper bound on the
# improtance weights produced. Rejecting matrices with too-small
# determinant (from both methods) allows me to supply that bound.
#
# I considered several alternative regions whose volume I might
# know analytically (without having to do rejection).
# - Option a: Some hypersphere guaranteed to be contained inside M.
# - Con: I don't know a priori how to find a radius for it.
# - Con: I still need a lower bound on the determinants that appear
# in this sphere, and I don't know how to compute it.
# - Option b: Some trapezoid given as the convex hull of the
# nearly-extreme correlation matrices (i.e., those that partition
# the variables into two strongly anti-correclated groups).
# - Con: Would have to dig up n-d convex hull code to implement this.
# - Con: Need to compute the volume of that convex hull.
# - Con: Need a bound on the determinants of the matrices in that hull.
# - Option c: Same thing, but with the matrices that make a single pair
# of variables strongly correlated (or anti-correlated), and leaves
# the others uncorrelated.
# - Same cons, except that there is a determinant bound (which
# felt pretty loose).
lows = [dtype(volume_bounds[dim][db][0]) for db in det_bounds]
highs = [dtype(volume_bounds[dim][db][1]) for db in det_bounds]
concentration = np.array(concentrations, dtype=dtype)
det_bounds = np.array(det_bounds, dtype=dtype)
# Due to possible numerical inaccuracies while lower bounding the
# determinant, the maximum of the importance weights may exceed the
# theoretical maximum (importance_maxima). We add a tolerance to guard
# against this. An alternative would have been to add a threshold while
# filtering in _det_ok_mask, but that would affect the mean as well.
high_tolerance = 1e-6
testee_lkj = tfd.LKJ(dimension=dim,
concentration=concentration,
validate_args=True)
x = testee_lkj.sample(num_samples, seed=seed)
importance_weights = (tf.exp(-testee_lkj.log_prob(x)) *
_det_ok_mask(x, det_bounds))
importance_maxima = (1. / det_bounds)**(concentration - 1) * tf.exp(
testee_lkj._log_normalization())
check1 = st.assert_true_mean_in_interval_by_dkwm(
samples=importance_weights,
low=0.,
high=importance_maxima + high_tolerance,
expected_low=lows,
expected_high=highs,
false_fail_rate=false_fail_rate)
check2 = tf.assert_less(
st.min_discrepancy_of_true_means_detectable_by_dkwm(
num_samples,
low=0.,
high=importance_maxima + high_tolerance,
false_fail_rate=false_fail_rate,
false_pass_rate=false_fail_rate), dtype(target_discrepancy))
self.evaluate([check1, check2])
def _testSampleConsistentLogProbInterval(
self, concentrations, det_bounds, dim, num_samples=int(1e5),
dtype=np.float32, false_fail_rate=1e-6, target_discrepancy=0.1, seed=42):
# Consider the set M of dim x dim correlation matrices whose
# determinant exceeds some bound (rationale for bound forthwith).
# - This is a (convex!) shape in dim * (dim - 1) / 2 dimensions
# (because a correlation matrix is determined by its lower
# triangle, and the main diagonal is all 1s).
# - Further, M is contained entirely in the [-1,1] cube,
# because no correlation can fall outside that interval.
#
# We have two different ways to estimate the volume of M:
# - Importance sampling from the LKJ distribution
# - Importance sampling from the uniform distribution on the cube
#
# This test checks that these two methods agree. However, because
# the uniform proposal leads to many rejections (thus slowness),
# those volumes are computed offline and the confidence intervals
# are presented to this test procedure in the "volume_bounds"
# table.
#
# Why place a lower bound on the determinant? Because for eta > 1,
# the density of LKJ approaches 0 as the determinant approaches 0.
# However, the test methodology requires an upper bound on the
# improtance weights produced. Rejecting matrices with too-small
# determinant (from both methods) allows me to supply that bound.
#
# I considered several alternative regions whose volume I might
# know analytically (without having to do rejection).
# - Option a: Some hypersphere guaranteed to be contained inside M.
# - Con: I don't know a priori how to find a radius for it.
# - Con: I still need a lower bound on the determinants that appear
# in this sphere, and I don't know how to compute it.
# - Option b: Some trapezoid given as the convex hull of the
# nearly-extreme correlation matrices (i.e., those that partition
# the variables into two strongly anti-correclated groups).
# - Con: Would have to dig up n-d convex hull code to implement this.
# - Con: Need to compute the volume of that convex hull.
# - Con: Need a bound on the determinants of the matrices in that hull.
# - Option c: Same thing, but with the matrices that make a single pair
# of variables strongly correlated (or anti-correlated), and leaves
# the others uncorrelated.
# - Same cons, except that there is a determinant bound (which
# felt pretty loose).
lows = [dtype(volume_bounds[dim][db][0]) for db in det_bounds]
highs = [dtype(volume_bounds[dim][db][1]) for db in det_bounds]
concentration = np.array(concentrations, dtype=dtype)
det_bounds = np.array(det_bounds, dtype=dtype)
# Due to possible numerical inaccuracies while lower bounding the
# determinant, the maximum of the importance weights may exceed the
# theoretical maximum (importance_maxima). We add a tolerance to guard
# against this. An alternative would have been to add a threshold while
# filtering in _det_ok_mask, but that would affect the mean as well.
high_tolerance = 1e-6
testee_lkj = tfd.LKJ(
dimension=dim, concentration=concentration, validate_args=True)
x = testee_lkj.sample(num_samples, seed=seed)
importance_weights = (
tf.exp(-testee_lkj.log_prob(x)) * _det_ok_mask(x, det_bounds))
importance_maxima = (1. / det_bounds) ** (concentration - 1) * tf.exp(
testee_lkj._log_normalization())
check1 = st.assert_true_mean_in_interval_by_dkwm(
samples=importance_weights,
low=0.,
high=importance_maxima + high_tolerance,
expected_low=lows,
expected_high=highs,
false_fail_rate=false_fail_rate)
check2 = tf.assert_less(
st.min_discrepancy_of_true_means_detectable_by_dkwm(
num_samples,
low=0.,
high=importance_maxima + high_tolerance,
false_fail_rate=false_fail_rate,
false_pass_rate=false_fail_rate),
dtype(target_discrepancy))
self.evaluate([check1, check2])
