def testGammaGammaKL(self):
alpha0 = np.array([3.])
beta0 = np.array([1., 2., 3., 1.5, 2.5, 3.5])
alpha1 = np.array([0.4])
beta1 = np.array([0.5, 1., 1.5, 2., 2.5, 3.])
# Build graph.
with self.test_session() as sess:
g0 = gamma_lib.Gamma(alpha=alpha0, beta=beta0)
g1 = gamma_lib.Gamma(alpha=alpha1, beta=beta1)
x = g0.sample(int(1e4), seed=0)
kl_sample = math_ops.reduce_mean(
g0.log_prob(x) - g1.log_prob(x), 0)
kl_actual = kullback_leibler.kl(g0, g1)
# Execute graph.
[kl_sample_, kl_actual_] = sess.run([kl_sample, kl_actual])
kl_expected = ((alpha0 - alpha1) * special.digamma(alpha0) +
special.gammaln(alpha1) - special.gammaln(alpha0) +
alpha1 * np.log(beta0) - alpha1 * np.log(beta1) +
alpha0 * (beta1 / beta0 - 1.))
self.assertEqual(beta0.shape, kl_actual.get_shape())
self.assertAllClose(kl_expected, kl_actual_, atol=0., rtol=1e-6)
self.assertAllClose(kl_sample_, kl_actual_, atol=0., rtol=1e-2)
def testGammaNonPositiveInitializationParamsRaises(self):
with self.test_session():
alpha_v = constant_op.constant(0.0, name="alpha")
beta_v = constant_op.constant(1.0, name="beta")
gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v, validate_args=True)
with self.assertRaisesOpError("alpha"):
gamma.mean().eval()
alpha_v = constant_op.constant(1.0, name="alpha")
beta_v = constant_op.constant(0.0, name="beta")
gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v, validate_args=True)
with self.assertRaisesOpError("beta"):
gamma.mean().eval()
def testGammaPdfOfSampleMultiDims(self):
with session.Session() as sess:
gamma = gamma_lib.Gamma(alpha=[7., 11.], beta=[[5.], [6.]])
num = 50000
samples = gamma.sample(num, seed=137)
pdfs = gamma.pdf(samples)
sample_vals, pdf_vals = sess.run([samples, pdfs])
self.assertEqual(samples.get_shape(), (num, 2, 2))
self.assertEqual(pdfs.get_shape(), (num, 2, 2))
self.assertAllClose(stats.gamma.mean(
[[7., 11.], [7., 11.]],
scale=1 / np.array([[5., 5.], [6., 6.]])),
sample_vals.mean(axis=0),
atol=.1)
self.assertAllClose(stats.gamma.var(
[[7., 11.], [7., 11.]],
scale=1 / np.array([[5., 5.], [6., 6.]])),
sample_vals.var(axis=0),
atol=.1)
self._assertIntegral(sample_vals[:, 0, 0],
pdf_vals[:, 0, 0],
err=0.02)
self._assertIntegral(sample_vals[:, 0, 1],
pdf_vals[:, 0, 1],
err=0.02)
self._assertIntegral(sample_vals[:, 1, 0],
pdf_vals[:, 1, 0],
err=0.02)
self._assertIntegral(sample_vals[:, 1, 1],
pdf_vals[:, 1, 1],
err=0.02)
def testGammaSampleMultiDimensional(self):
with session.Session():
alpha_v = np.array([np.arange(1, 101,
dtype=np.float32)]) # 1 x 100
beta_v = np.array([np.arange(1, 11, dtype=np.float32)]).T # 10 x 1
gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v)
n = 10000
samples = gamma.sample(n, seed=137)
sample_values = samples.eval()
self.assertEqual(samples.get_shape(), (n, 10, 100))
self.assertEqual(sample_values.shape, (n, 10, 100))
zeros = np.zeros_like(alpha_v + beta_v) # 10 x 100
alpha_bc = alpha_v + zeros
beta_bc = beta_v + zeros
self.assertAllClose(sample_values.mean(axis=0),
stats.gamma.mean(alpha_bc, scale=1 / beta_bc),
rtol=.035)
self.assertAllClose(sample_values.var(axis=0),
stats.gamma.var(alpha_bc, scale=1 / beta_bc),
atol=4.5)
fails = 0
trials = 0
for ai, a in enumerate(np.reshape(alpha_v, [-1])):
for bi, b in enumerate(np.reshape(beta_v, [-1])):
s = sample_values[:, bi, ai]
trials += 1
fails += 0 if self._kstest(a, b, s) else 1
self.assertLess(fails, trials * 0.03)
def testDocstringExample(self):
with self.test_session():
exp_gamma_distribution = (
transformed_distribution_lib.TransformedDistribution(
distribution=gamma_lib.Gamma(concentration=1., rate=2.),
bijector=bijectors.Invert(bijectors.Exp())))
self.assertAllEqual(
[], array_ops.shape(exp_gamma_distribution.sample()).eval())
def testGammaEntropy(self):
with self.test_session():
alpha_v = np.array([1.0, 3.0, 2.5])
beta_v = np.array([1.0, 4.0, 5.0])
expected_entropy = stats.gamma.entropy(alpha_v, scale=1 / beta_v)
gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v)
self.assertEqual(gamma.entropy().get_shape(), (3, ))
self.assertAllClose(gamma.entropy().eval(), expected_entropy)
def testGammaStd(self):
with self.test_session():
alpha_v = np.array([1.0, 3.0, 2.5])
beta_v = np.array([1.0, 4.0, 5.0])
gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v)
expected_stddev = stats.gamma.std(alpha_v, scale=1. / beta_v)
self.assertEqual(gamma.stddev().get_shape(), (3, ))
self.assertAllClose(gamma.stddev().eval(), expected_stddev)
def testGammaVariance(self):
with self.test_session():
alpha_v = np.array([1.0, 3.0, 2.5])
beta_v = np.array([1.0, 4.0, 5.0])
gamma = gamma_lib.Gamma(concentration=alpha_v, rate=beta_v)
expected_variances = stats.gamma.var(alpha_v, scale=1 / beta_v)
self.assertEqual(gamma.variance().get_shape(), (3,))
self.assertAllClose(gamma.variance().eval(), expected_variances)
def testGammaModeAllowNanStatsIsFalseWorksWhenAllBatchMembersAreDefined(self):
with self.test_session():
alpha_v = np.array([5.5, 3.0, 2.5])
beta_v = np.array([1.0, 4.0, 5.0])
gamma = gamma_lib.Gamma(concentration=alpha_v, rate=beta_v)
expected_modes = (alpha_v - 1) / beta_v
self.assertEqual(gamma.mode().get_shape(), (3,))
self.assertAllClose(gamma.mode().eval(), expected_modes)
def testGammaModeAllowNanStatsFalseRaisesForUndefinedBatchMembers(self):
with self.test_session():
# Mode will not be defined for the first entry.
alpha_v = np.array([0.5, 3.0, 2.5])
beta_v = np.array([1.0, 4.0, 5.0])
gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v, allow_nan_stats=False)
with self.assertRaisesOpError("x < y"):
gamma.mode().eval()
def testGammaShape(self):
with self.test_session():
alpha = constant_op.constant([3.0] * 5)
beta = constant_op.constant(11.0)
gamma = gamma_lib.Gamma(concentration=alpha, rate=beta)
self.assertEqual(gamma.batch_shape_tensor().eval(), (5,))
self.assertEqual(gamma.batch_shape, tensor_shape.TensorShape([5]))
self.assertAllEqual(gamma.event_shape_tensor().eval(), [])
self.assertEqual(gamma.event_shape, tensor_shape.TensorShape([]))
def testGammaModeAllowNanStatsIsTrueReturnsNaNforUndefinedBatchMembers(self):
with self.test_session():
# Mode will not be defined for the first entry.
alpha_v = np.array([0.5, 3.0, 2.5])
beta_v = np.array([1.0, 4.0, 5.0])
gamma = gamma_lib.Gamma(alpha=alpha_v, beta=beta_v, allow_nan_stats=True)
expected_modes = (alpha_v - 1) / beta_v
expected_modes[0] = np.nan
self.assertEqual(gamma.mode().get_shape(), (3,))
self.assertAllClose(gamma.mode().eval(), expected_modes)
def testGammaCDF(self):
with self.test_session():
batch_size = 6
alpha = constant_op.constant([2.0] * batch_size)
beta = constant_op.constant([3.0] * batch_size)
alpha_v = 2.0
beta_v = 3.0
x = np.array([2.5, 2.5, 4.0, 0.1, 1.0, 2.0], dtype=np.float32)
gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
expected_cdf = stats.gamma.cdf(x, alpha_v, scale=1 / beta_v)
cdf = gamma.cdf(x)
self.assertEqual(cdf.get_shape(), (6, ))
self.assertAllClose(cdf.eval(), expected_cdf)
def testGammaLogPDF(self):
with self.test_session():
batch_size = 6
alpha = constant_op.constant([2.0] * batch_size)
beta = constant_op.constant([3.0] * batch_size)
alpha_v = 2.0
beta_v = 3.0
x = np.array([2.5, 2.5, 4.0, 0.1, 1.0, 2.0], dtype=np.float32)
gamma = gamma_lib.Gamma(concentration=alpha, rate=beta)
expected_log_pdf = stats.gamma.logpdf(x, alpha_v, scale=1 / beta_v)
log_pdf = gamma.log_prob(x)
self.assertEqual(log_pdf.get_shape(), (6,))
self.assertAllClose(log_pdf.eval(), expected_log_pdf)
pdf = gamma.prob(x)
self.assertEqual(pdf.get_shape(), (6,))
self.assertAllClose(pdf.eval(), np.exp(expected_log_pdf))
def testGammaLogPDFMultidimensionalBroadcasting(self):
with self.test_session():
batch_size = 6
alpha = constant_op.constant([[2.0, 4.0]] * batch_size)
beta = constant_op.constant(3.0)
alpha_v = np.array([2.0, 4.0])
beta_v = 3.0
x = np.array([[2.5, 2.5, 4.0, 0.1, 1.0, 2.0]], dtype=np.float32).T
gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
expected_log_pdf = stats.gamma.logpdf(x, alpha_v, scale=1 / beta_v)
log_pdf = gamma.log_pdf(x)
log_pdf_values = log_pdf.eval()
self.assertEqual(log_pdf.get_shape(), (6, 2))
self.assertAllClose(log_pdf_values, expected_log_pdf)
pdf = gamma.pdf(x)
pdf_values = pdf.eval()
self.assertEqual(pdf.get_shape(), (6, 2))
self.assertAllClose(pdf_values, np.exp(expected_log_pdf))
def testGammaSample(self):
with session.Session():
alpha_v = 4.0
beta_v = 3.0
alpha = constant_op.constant(alpha_v)
beta = constant_op.constant(beta_v)
n = 100000
gamma = gamma_lib.Gamma(alpha=alpha, beta=beta)
samples = gamma.sample(n, seed=137)
sample_values = samples.eval()
self.assertEqual(samples.get_shape(), (n, ))
self.assertEqual(sample_values.shape, (n, ))
self.assertAllClose(sample_values.mean(),
stats.gamma.mean(alpha_v, scale=1 / beta_v),
atol=.01)
self.assertAllClose(sample_values.var(),
stats.gamma.var(alpha_v, scale=1 / beta_v),
atol=.15)
self.assertTrue(self._kstest(alpha_v, beta_v, sample_values))
