def testDirichletMode(self):
with self.test_session():
alpha = np.array([1.1, 2, 3])
expected_mode = (alpha - 1) / (np.sum(alpha) - 3)
dirichlet = dirichlet_lib.Dirichlet(alpha=alpha)
self.assertEqual(dirichlet.mode().get_shape(), (3, ))
self.assertAllClose(dirichlet.mode().eval(), expected_mode)
def testDirichletMean(self):
with self.test_session():
alpha = [1., 2, 3]
expected_mean = stats.dirichlet.mean(alpha)
dirichlet = dirichlet_lib.Dirichlet(alpha=alpha)
self.assertEqual(dirichlet.mean().get_shape(), (3, ))
self.assertAllClose(dirichlet.mean().eval(), expected_mean)
def testDirichletEntropy(self):
with self.test_session():
alpha = [1., 2, 3]
expected_entropy = stats.dirichlet.entropy(alpha)
dirichlet = dirichlet_lib.Dirichlet(alpha=alpha)
self.assertEqual(dirichlet.entropy().get_shape(), ())
self.assertAllClose(dirichlet.entropy().eval(), expected_entropy)
def testPdfAlphaStretchedInBroadcastWhenLowerRank(self):
with self.test_session():
alpha = [1., 2]
x = [[.5, .5], [.2, .8]]
pdf = dirichlet_lib.Dirichlet(alpha).pdf(x)
self.assertAllClose([1., 8. / 5], pdf.eval())
self.assertEqual((2), pdf.get_shape())
def testPdfXStretchedInBroadcastWhenLowerRank(self):
with self.test_session():
alpha = [[1., 2], [2., 3]]
x = [.5, .5]
pdf = dirichlet_lib.Dirichlet(alpha).prob(x)
self.assertAllClose([1., 3. / 2], pdf.eval())
self.assertEqual((2), pdf.get_shape())
def testDirichletModeInvalid(self):
with self.test_session():
alpha = np.array([1., 2, 3])
dirichlet = dirichlet_lib.Dirichlet(alpha=alpha,
allow_nan_stats=False)
with self.assertRaisesOpError("Condition x < y.*"):
dirichlet.mode().eval()
def testPdfAlphaStretchedInBroadcastWhenSameRank(self):
with self.test_session():
alpha = [[1., 2]]
x = [[.5, .5], [.3, .7]]
dist = dirichlet_lib.Dirichlet(alpha)
pdf = dist.prob(x)
self.assertAllClose([1., 7. / 5], pdf.eval())
self.assertEqual((2), pdf.get_shape())
def testPdfZeroBatches(self):
with self.test_session():
alpha = [1., 2]
x = [.5, .5]
dist = dirichlet_lib.Dirichlet(alpha)
pdf = dist.prob(x)
self.assertAllClose(1., pdf.eval())
self.assertEqual((), pdf.get_shape())
def testPdfZeroBatchesNontrivialX(self):
with self.test_session():
alpha = [1., 2]
x = [.3, .7]
dist = dirichlet_lib.Dirichlet(alpha)
pdf = dist.prob(x)
self.assertAllClose(7. / 5, pdf.eval())
self.assertEqual((), pdf.get_shape())
def testSimpleShapes(self):
with self.test_session():
alpha = np.random.rand(3)
dist = dirichlet_lib.Dirichlet(alpha)
self.assertEqual(3, dist.event_shape_tensor().eval())
self.assertAllEqual([], dist.batch_shape_tensor().eval())
self.assertEqual(tensor_shape.TensorShape([3]), dist.event_shape)
self.assertEqual(tensor_shape.TensorShape([]), dist.batch_shape)
def testPdfUniformZeroBatches(self):
with self.test_session():
# 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.], pdf.eval())
self.assertEqual((2), pdf.get_shape())
def testModeEnableAllowNanStats(self):
with self.test_session():
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().get_shape(), [3])
self.assertAllClose(dirichlet.mode().eval(), expected_mode)
def testComplexShapes(self):
with self.test_session():
alpha = np.random.rand(3, 2, 2)
dist = dirichlet_lib.Dirichlet(alpha)
self.assertEqual(2, dist.event_shape().eval())
self.assertAllEqual([3, 2], dist.batch_shape().eval())
self.assertEqual(tensor_shape.TensorShape([2]),
dist.get_event_shape())
self.assertEqual(tensor_shape.TensorShape([3, 2]),
dist.get_batch_shape())
def testDirichletVariance(self):
with self.test_session():
alpha = [1., 2, 3]
denominator = np.sum(alpha)**2 * (np.sum(alpha) + 1)
expected_variance = np.diag(stats.dirichlet.var(alpha))
expected_variance += [[0., -2, -3], [-2, 0, -6], [-3, -6, 0]
] / denominator
dirichlet = dirichlet_lib.Dirichlet(alpha=alpha)
self.assertEqual(dirichlet.variance().get_shape(), (3, 3))
self.assertAllClose(dirichlet.variance().eval(), expected_variance)
def testDirichletModeEnableAllowNanStats(self):
with self.test_session():
alpha = np.array([1., 2, 3])
dirichlet = dirichlet_lib.Dirichlet(alpha=alpha,
allow_nan_stats=True)
expected_mode = (alpha - 1) / (np.sum(alpha) - 3)
expected_mode[0] = np.nan
self.assertEqual(dirichlet.mode().get_shape(), (3, ))
self.assertAllClose(dirichlet.mode().eval(), expected_mode)
def testPdfXProper(self):
alpha = [[1., 2, 3]]
with self.test_session():
dist = dirichlet_lib.Dirichlet(alpha, validate_args=True)
dist.prob([.1, .3, .6]).eval()
dist.prob([.2, .3, .5]).eval()
# Either condition can trigger.
with self.assertRaisesOpError("samples must be positive"):
dist.prob([-1., 1.5, 0.5]).eval()
with self.assertRaisesOpError("samples must be positive"):
dist.prob([0., .1, .9]).eval()
with self.assertRaisesOpError(
"sample last-dimension must sum to `1`"):
dist.prob([.1, .2, .8]).eval()
def testPdfXProper(self):
alpha = [[1., 2, 3]]
with self.test_session():
dist = dirichlet_lib.Dirichlet(alpha, validate_args=True)
dist.prob([.1, .3, .6]).eval()
dist.prob([.2, .3, .5]).eval()
# Either condition can trigger.
with self.assertRaisesOpError(
"Condition x > 0.*|Condition x < y.*"):
dist.prob([-1., 1, 1]).eval()
with self.assertRaisesOpError("Condition x > 0.*"):
dist.prob([0., .1, .9]).eval()
with self.assertRaisesOpError("Condition x ~= y.*"):
dist.prob([.1, .2, .8]).eval()
def testDirichletSample(self):
with self.test_session():
alpha = [1., 2]
dirichlet = dirichlet_lib.Dirichlet(alpha)
n = constant_op.constant(100000)
samples = dirichlet.sample(n)
sample_values = samples.eval()
self.assertEqual(sample_values.shape, (100000, 2))
self.assertTrue(np.all(sample_values > 0.0))
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)
with self.test_session() as sess:
dist = dirichlet_lib.Dirichlet(
alpha) # batch_shape=[2], event_shape=[3]
x = dist.sample(int(250e3), seed=1)
sample_mean = math_ops.reduce_mean(x, 0)
x_centered = x - sample_mean[None, ...]
sample_cov = math_ops.reduce_mean(
math_ops.matmul(x_centered[..., None], x_centered[...,
None, :]), 0)
sample_var = array_ops.matrix_diag_part(sample_cov)
sample_stddev = math_ops.sqrt(sample_var)
[
sample_mean_,
sample_cov_,
sample_var_,
sample_stddev_,
analytic_mean,
analytic_cov,
analytic_var,
analytic_stddev,
] = sess.run([
sample_mean,
sample_cov,
sample_var,
sample_stddev,
dist.mean(),
dist.covariance(),
dist.variance(),
dist.stddev(),
])
self.assertAllClose(sample_mean_,
analytic_mean,
atol=0.,
rtol=0.04)
self.assertAllClose(sample_cov_, analytic_cov, atol=0., rtol=0.06)
self.assertAllClose(sample_var_, analytic_var, atol=0., rtol=0.03)
self.assertAllClose(sample_stddev_,
analytic_stddev,
atol=0.,
rtol=0.02)
def testAlphaProperty(self):
alpha = [[1., 2, 3]]
with self.test_session():
dist = dirichlet_lib.Dirichlet(alpha)
self.assertEqual([1, 3], dist.alpha.get_shape())
self.assertAllClose(alpha, dist.alpha.eval())
