def testGammaGammaSampleConcentrationCausesBroadcast(self):
gg = tfd.GammaGamma(concentration=[1., 2.],
mixing_concentration=1.,
mixing_rate=1.)
n = 3
samples = self.evaluate(gg.sample(n, seed=tfp_test_util.test_seed()))
self.assertAllEqual((n, 2), samples.shape)
def testGammaGammaLogPDF(self):
batch_size = 5
alpha = tf.constant([2.] * batch_size, dtype=np.float32)
alpha0 = tf.constant([3.] * batch_size, dtype=np.float32)
beta0 = tf.constant([4.] * batch_size, dtype=np.float32)
x = np.array([6.] * batch_size, dtype=np.float32)
# Let
# alpha = concentration = 2.
# alpha0 = mixing_concentration = 3.,
# beta0 = mixing_rate = 4.
#
# See the PDF derivation in formula (1) of
# http://www.brucehardie.com/notes/025/gamma_gamma.pdf.
#
# x**(alpha - 1) * beta0**alpha0
# prob(x=6) = ------------------------------------------------
# B(alpha, alpha0) * (x + beta0)**(alpha + alpha0)
#
# 6 * 4**3
# = --------------- = 0.04608
# B(2, 3) * 10**5
#
# log_prob(x=6) = -3.077376
expected_log_pdf = [-3.077376] * batch_size
gg = tfd.GammaGamma(concentration=alpha,
mixing_concentration=alpha0,
mixing_rate=beta0)
log_pdf = gg.log_prob(x)
self.assertEqual(log_pdf.shape, (5, ))
self.assertAllClose(self.evaluate(log_pdf), expected_log_pdf)
def testAssertValidSample(self):
gg = tfd.GammaGamma(concentration=2.,
mixing_concentration=.1,
mixing_rate=3.,
validate_args=True)
with self.assertRaisesOpError('Sample must be non-negative.'):
self.evaluate(gg.log_prob(-.1))
def testGammaGammaLogPDFAtZero(self):
# When concentration = 1., the log pdf should be finite.
gg = tfd.GammaGamma(concentration=1.,
mixing_concentration=[0.01, 0.1, 2, 3],
mixing_rate=[0.01, 0.1, 2, 3])
log_pdf = self.evaluate(gg.log_prob(0.))
self.assertAllEqual(np.ones_like(log_pdf, dtype=np.bool),
np.isfinite(log_pdf))
def testSupportBijectorOutsideRange(self):
dist = tfd.GammaGamma(concentration=[3., 2., 5.4],
mixing_concentration=2.,
mixing_rate=1.,
validate_args=True)
with self.assertRaisesOpError('must be greater than or equal to 0'):
dist.experimental_default_event_space_bijector().inverse(
[-4.2, -0.3, -1e-6])
def testGammaGammaShape(self):
gg = tfd.GammaGamma(concentration=[[2.], [4.]],
mixing_concentration=[1., 2., 3.],
mixing_rate=0.5)
self.assertAllEqual(self.evaluate(gg.batch_shape_tensor()), [2, 3])
self.assertEqual(gg.batch_shape, tf.TensorShape([2, 3]))
self.assertAllEqual(self.evaluate(gg.event_shape_tensor()), [])
self.assertEqual(gg.event_shape, tf.TensorShape([]))
def testGammaGammaLogPDFAtZero(self):
# When concentration = 1., the log pdf should be finite.
gg = tfd.GammaGamma(concentration=1.,
mixing_concentration=[0.01, 0.1, 2, 3],
mixing_rate=[0.01, 0.1, 2, 3],
validate_args=True)
log_pdf = self.evaluate(gg.log_prob(0.))
self.assertAllEqual(np.ones_like(log_pdf, dtype=np.bool_),
np.isfinite(log_pdf))
gg = tfd.GammaGamma(concentration=2.,
mixing_concentration=[0.01, 0.1, 2, 3],
mixing_rate=[0.01, 0.1, 2, 3],
validate_args=True)
log_pdf = self.evaluate(gg.log_prob(0.))
self.assertAllNegativeInf(log_pdf)
pdf = self.evaluate(gg.prob(0.))
self.assertAllEqual(pdf, np.zeros_like(pdf))
def testGammaGammaMeanAllDefined(self):
alpha_v = np.array([2., 4.])
alpha0_v = np.array([3., 6.])
beta0_v = np.array([4., 8.])
expected_mean = alpha_v * beta0_v / (alpha0_v - 1.)
gg = tfd.GammaGamma(concentration=alpha_v,
mixing_concentration=alpha0_v,
mixing_rate=beta0_v)
self.assertEqual(gg.mean().shape, (2, ))
self.assertAllClose(self.evaluate(gg.mean()), expected_mean)
def testGammaGammaLogPDFMultidimensionalBroadcasting(self):
batch_size = 6
alpha = tf.constant([[2., 4.]] * batch_size)
alpha0 = tf.constant(3.0)
beta0 = tf.constant([4., 8.])
x = np.array([[2.5, 2.5, 4.0, 0.1, 1.0, 2.0]], dtype=np.float32).T
gg = tfd.GammaGamma(
concentration=alpha, mixing_concentration=alpha0, mixing_rate=beta0)
log_pdf = gg.log_prob(x)
self.assertEqual(log_pdf.shape, (6, 2))
def testGammaGammaMeanNanStats(self):
# Mean will not be defined for the first entry.
alpha_v = np.array([2., 4.])
alpha0_v = np.array([1., 6.])
beta0_v = np.array([4., 8.])
expected_mean = np.array([np.nan, 6.4])
gg = tfd.GammaGamma(concentration=alpha_v,
mixing_concentration=alpha0_v,
mixing_rate=beta0_v)
self.assertEqual(gg.mean().shape, (2, ))
self.assertAllClose(self.evaluate(gg.mean()), expected_mean)
def testGammaGammaMeanAllowNanStats(self):
# Mean will not be defined for the first entry.
alpha_v = np.array([2., 4.])
alpha0_v = np.array([1., 6.])
beta0_v = np.array([4., 8.])
gg = tfd.GammaGamma(concentration=alpha_v,
mixing_concentration=alpha0_v,
mixing_rate=beta0_v,
allow_nan_stats=False)
with self.assertRaisesOpError('x < y'):
self.evaluate(gg.mean())
def testGammaGammaInvalidArgs(self):
with self.assertRaisesOpError('`concentration` must be positive'):
gg = tfd.GammaGamma(concentration=-1.,
mixing_concentration=2.,
mixing_rate=0.5,
validate_args=True)
self.evaluate(gg.mean())
with self.assertRaisesOpError(
'`mixing_concentration` must be positive'):
gg = tfd.GammaGamma(concentration=1.,
mixing_concentration=-2.,
mixing_rate=0.5,
validate_args=True)
self.evaluate(gg.mean())
with self.assertRaisesOpError('`mixing_rate` must be positive'):
gg = tfd.GammaGamma(concentration=1.,
mixing_concentration=2.,
mixing_rate=-0.5,
validate_args=True)
self.evaluate(gg.mean())
def testGammaGammaSample(self):
alpha_v = 2.0
alpha0_v = 3.0
beta0_v = 5.0
n = 100000
gg = tfd.GammaGamma(concentration=alpha_v,
mixing_concentration=alpha0_v,
mixing_rate=beta0_v)
samples = gg.sample(n, seed=tfp_test_util.test_seed())
sample_values = self.evaluate(samples)
self.assertEqual(samples.shape, (n, ))
self.assertEqual(sample_values.shape, (n, ))
self.assertAllClose(sample_values.mean(),
self.evaluate(gg.mean()),
rtol=.02)
def testGammaGammaSampleMultidimensional(self):
alpha_v = np.array([np.arange(5, 25, 2, dtype=np.float32)]) # 1 x 10
alpha0_v = 5.
beta0_v = np.array([np.arange(5, 15, 2, dtype=np.float32)]).T # 5 x 1
n = 75000
gg = tfd.GammaGamma(
concentration=alpha_v,
mixing_concentration=alpha0_v,
mixing_rate=beta0_v)
samples = gg.sample(n, seed=tfp_test_util.test_seed())
sample_values = self.evaluate(samples)
expected_shape = (n, beta0_v.shape[0], alpha_v.shape[-1])
self.assertEqual(samples.shape, expected_shape)
self.assertEqual(sample_values.shape, expected_shape)
self.assertAllClose(
self.evaluate(gg.variance()), sample_values.var(axis=0), rtol=.6)
self.assertAllClose(
self.evaluate(gg.mean()), sample_values.mean(axis=0), rtol=.02)
