def testDirichletDirichletKL(self):
conc1 = np.array([[1., 2., 3., 1.5, 2.5, 3.5],
[1.5, 2.5, 3.5, 4.5, 5.5, 6.5]])
conc2 = np.array([[0.5, 1., 1.5, 2., 2.5, 3.]])
d1 = dirichlet_lib.Dirichlet(conc1)
d2 = dirichlet_lib.Dirichlet(conc2)
x = d1.sample(int(1e4), seed=0)
kl_sample = tf.reduce_mean(d1.log_prob(x) - d2.log_prob(x), 0)
kl_actual = kullback_leibler.kl_divergence(d1, d2)
kl_sample_val = self.evaluate(kl_sample)
kl_actual_val = self.evaluate(kl_actual)
self.assertEqual(conc1.shape[:-1], kl_actual.shape)
if not special:
return
kl_expected = (
special.gammaln(np.sum(conc1, -1)) -
special.gammaln(np.sum(conc2, -1)) -
np.sum(special.gammaln(conc1) - special.gammaln(conc2), -1) +
np.sum((conc1 - conc2) *
(special.digamma(conc1) -
special.digamma(np.sum(conc1, -1, keepdims=True))), -1))
self.assertAllClose(kl_expected, kl_actual_val, atol=0., rtol=1e-6)
self.assertAllClose(kl_sample_val, kl_actual_val, atol=0., rtol=1e-1)
# Make sure KL(d1||d1) is 0
kl_same = self.evaluate(kullback_leibler.kl_divergence(d1, d1))
self.assertAllClose(kl_same, np.zeros_like(kl_expected))
def testSimpleShapes(self):
alpha = np.random.rand(3)
dist = dirichlet_lib.Dirichlet(alpha)
self.assertEqual(3, self.evaluate(dist.event_shape_tensor()))
self.assertAllEqual([], self.evaluate(dist.batch_shape_tensor()))
self.assertEqual(tf.TensorShape([3]), dist.event_shape)
self.assertEqual(tf.TensorShape([]), dist.batch_shape)
def testComplexShapes(self):
alpha = np.random.rand(3, 2, 2)
dist = dirichlet_lib.Dirichlet(alpha)
self.assertEqual(2, self.evaluate(dist.event_shape_tensor()))
self.assertAllEqual([3, 2], self.evaluate(dist.batch_shape_tensor()))
self.assertEqual(tf.TensorShape([2]), dist.event_shape)
self.assertEqual(tf.TensorShape([3, 2]), dist.batch_shape)
def testLogPdfOnBoundaryIsFiniteWhenAlphaIsOne(self):
# Test concentration = 1. for each dimension.
concentration = 3 * np.ones((10, 10)).astype(np.float32)
concentration[range(10), range(10)] = 1.
x = 1 / 9. * np.ones((10, 10)).astype(np.float32)
x[range(10), range(10)] = 0.
dist = dirichlet_lib.Dirichlet(concentration)
log_prob = self.evaluate(dist.log_prob(x))
self.assertAllEqual(np.ones_like(log_prob, dtype=np.bool),
np.isfinite(log_prob))
# Test when concentration[k] = 1., and x is zero at various dimensions.
dist = dirichlet_lib.Dirichlet(10 * [1.])
log_prob = self.evaluate(dist.log_prob(x))
self.assertAllEqual(np.ones_like(log_prob, dtype=np.bool),
np.isfinite(log_prob))
def testPdfAlphaStretchedInBroadcastWhenSameRank(self):
alpha = [[1., 2]]
x = [[.5, .5], [.3, .7]]
dist = dirichlet_lib.Dirichlet(alpha)
pdf = dist.prob(x)
self.assertAllClose([1., 7. / 5], self.evaluate(pdf))
self.assertEqual((2), pdf.shape)
def testPdfZeroBatchesNontrivialX(self):
alpha = [1., 2]
x = [.3, .7]
dist = dirichlet_lib.Dirichlet(alpha)
pdf = dist.prob(x)
self.assertAllClose(7. / 5, self.evaluate(pdf))
self.assertEqual((), pdf.shape)
def testPdfZeroBatches(self):
alpha = [1., 2]
x = [.5, .5]
dist = dirichlet_lib.Dirichlet(alpha)
pdf = dist.prob(x)
self.assertAllClose(1., self.evaluate(pdf))
self.assertEqual((), pdf.shape)
def testMean(self):
alpha = [1., 2, 3]
dirichlet = dirichlet_lib.Dirichlet(concentration=alpha)
self.assertEqual(dirichlet.mean().shape, [3])
if not stats:
return
expected_mean = stats.dirichlet.mean(alpha)
self.assertAllClose(self.evaluate(dirichlet.mean()), expected_mean)
def testPdfUniformZeroBatches(self):
# Corresponds to a uniform distribution
alpha = [1., 1, 1]
x = [[.2, .5, .3], [.3, .4, .3]]
dist = dirichlet_lib.Dirichlet(alpha)
pdf = dist.prob(x)
self.assertAllClose([2., 2.], self.evaluate(pdf))
self.assertEqual((2), pdf.shape)
def testEntropy(self):
alpha = [1., 2, 3]
dirichlet = dirichlet_lib.Dirichlet(concentration=alpha)
self.assertEqual(dirichlet.entropy().shape, ())
if not stats:
return
expected_entropy = stats.dirichlet.entropy(alpha)
self.assertAllClose(self.evaluate(dirichlet.entropy()), expected_entropy)
def testDirichletFullyReparameterized(self):
alpha = tf.constant([1.0, 2.0, 3.0])
with backprop.GradientTape() as tape:
tape.watch(alpha)
dirichlet = dirichlet_lib.Dirichlet(alpha)
samples = dirichlet.sample(100)
grad_alpha = tape.gradient(samples, alpha)
self.assertIsNotNone(grad_alpha)
def testModeEnableAllowNanStats(self):
alpha = np.array([1., 2, 3])
dirichlet = dirichlet_lib.Dirichlet(concentration=alpha,
allow_nan_stats=True)
expected_mode = np.zeros_like(alpha) + np.nan
self.assertEqual(dirichlet.mode().shape, [3])
self.assertAllClose(self.evaluate(dirichlet.mode()), expected_mode)
def testPdfXProper(self):
alpha = [[1., 2, 3]]
dist = dirichlet_lib.Dirichlet(alpha, validate_args=True)
self.evaluate(dist.prob([.1, .3, .6]))
self.evaluate(dist.prob([.2, .3, .5]))
# Either condition can trigger.
with self.assertRaisesOpError("samples must be positive"):
self.evaluate(dist.prob([-1., 1.5, 0.5]))
with self.assertRaisesOpError("samples must be positive"):
self.evaluate(dist.prob([0., .1, .9]))
with self.assertRaisesOpError("sample last-dimension must sum to `1`"):
self.evaluate(dist.prob([.1, .2, .8]))
def testVariance(self):
alpha = [1., 2, 3]
denominator = np.sum(alpha)**2 * (np.sum(alpha) + 1)
dirichlet = dirichlet_lib.Dirichlet(concentration=alpha)
self.assertEqual(dirichlet.covariance().shape, (3, 3))
if not stats:
return
expected_covariance = np.diag(stats.dirichlet.var(alpha))
expected_covariance += [[0., -2, -3], [-2, 0, -6], [-3, -6, 0]
] / denominator
self.assertAllClose(self.evaluate(dirichlet.covariance()),
expected_covariance)
def testSample(self):
alpha = [1., 2]
dirichlet = dirichlet_lib.Dirichlet(alpha)
n = tf.constant(100000)
samples = dirichlet.sample(n)
sample_values = self.evaluate(samples)
self.assertEqual(sample_values.shape, (100000, 2))
self.assertTrue(np.all(sample_values > 0.0))
if not stats:
return
self.assertLess(
stats.kstest(
# Beta is a univariate distribution.
sample_values[:, 0],
stats.beta(a=1., b=2.).cdf)[0],
0.01)
def testCovarianceFromSampling(self):
alpha = np.array([[1., 2, 3], [2.5, 4, 0.01]], dtype=np.float32)
dist = dirichlet_lib.Dirichlet(
alpha) # batch_shape=[2], event_shape=[3]
x = dist.sample(int(250e3), seed=1)
sample_mean = tf.reduce_mean(x, 0)
x_centered = x - sample_mean[None, ...]
sample_cov = tf.reduce_mean(
tf.matmul(x_centered[..., None], x_centered[..., None, :]), 0)
sample_var = tf.matrix_diag_part(sample_cov)
sample_stddev = tf.sqrt(sample_var)
[
sample_mean_,
sample_cov_,
sample_var_,
sample_stddev_,
analytic_mean,
analytic_cov,
analytic_var,
analytic_stddev,
] = self.evaluate([
sample_mean,
sample_cov,
sample_var,
sample_stddev,
dist.mean(),
dist.covariance(),
dist.variance(),
dist.stddev(),
])
self.assertAllClose(sample_mean_, analytic_mean, atol=0.04, rtol=0.)
self.assertAllClose(sample_cov_, analytic_cov, atol=0.06, rtol=0.)
self.assertAllClose(sample_var_, analytic_var, atol=0.03, rtol=0.)
self.assertAllClose(sample_stddev_,
analytic_stddev,
atol=0.02,
rtol=0.)
def testModeInvalid(self):
alpha = np.array([1., 2, 3])
dirichlet = dirichlet_lib.Dirichlet(concentration=alpha,
allow_nan_stats=False)
with self.assertRaisesOpError("Condition x < y.*"):
self.evaluate(dirichlet.mode())
def testPdfAlphaStretchedInBroadcastWhenLowerRank(self):
alpha = [1., 2]
x = [[.5, .5], [.2, .8]]
pdf = dirichlet_lib.Dirichlet(alpha).prob(x)
self.assertAllClose([1., 8. / 5], self.evaluate(pdf))
self.assertEqual((2), pdf.shape)
def testConcentrationProperty(self):
alpha = [[1., 2, 3]]
dist = dirichlet_lib.Dirichlet(alpha)
self.assertEqual([1, 3], dist.concentration.shape)
self.assertAllClose(alpha, self.evaluate(dist.concentration))
def testPdfXStretchedInBroadcastWhenLowerRank(self):
alpha = [[1., 2], [2., 3]]
x = [.5, .5]
pdf = dirichlet_lib.Dirichlet(alpha).prob(x)
self.assertAllClose([1., 3. / 2], self.evaluate(pdf))
self.assertEqual((2), pdf.shape)
def testMode(self):
alpha = np.array([1.1, 2, 3])
expected_mode = (alpha - 1) / (np.sum(alpha) - 3)
dirichlet = dirichlet_lib.Dirichlet(concentration=alpha)
self.assertEqual(dirichlet.mode().shape, [3])
self.assertAllClose(self.evaluate(dirichlet.mode()), expected_mode)