def testBetaModeInvalid(self):
a = np.array([1., 2, 3])
b = np.array([2., 4, 1.2])
dist = beta_lib.Beta(a, b, allow_nan_stats=False)
with self.assertRaisesOpError("Condition x < y.*"):
self.evaluate(dist.mode())
a = np.array([2., 2, 3])
b = np.array([1., 4, 1.2])
dist = beta_lib.Beta(a, b, allow_nan_stats=False)
with self.assertRaisesOpError("Condition x < y.*"):
self.evaluate(dist.mode())
def testPdfAlphaStretchedInBroadcastWhenLowerRank(self): a = [1., 2] b = [1., 2] x = [[.5, .5], [.2, .8]] pdf = beta_lib.Beta(a, b).prob(x) self.assertAllClose([[1., 3. / 2], [1., 24. / 25]], self.evaluate(pdf)) self.assertEqual((2, 2), pdf.get_shape())
def testBetaMode(self): a = np.array([1.1, 2, 3]) b = np.array([2., 4, 1.2]) expected_mode = (a - 1) / (a + b - 2) dist = beta_lib.Beta(a, b) self.assertEqual(dist.mode().get_shape(), (3,)) self.assertAllClose(expected_mode, self.evaluate(dist.mode()))
def testBetaProperty(self):
a = [[1., 2, 3]]
b = [[2., 4, 3]]
with self.test_session():
dist = beta_lib.Beta(a, b)
self.assertEqual([1, 3], dist.concentration0.get_shape())
self.assertAllClose(b, dist.concentration0.eval())
def testBetaSampleMultipleTimes(self):
a_val = 1.
b_val = 2.
n_val = 100
random_seed.set_random_seed(654321)
beta1 = beta_lib.Beta(
concentration1=a_val, concentration0=b_val, name="beta1")
samples1 = self.evaluate(beta1.sample(n_val, seed=123456))
random_seed.set_random_seed(654321)
beta2 = beta_lib.Beta(
concentration1=a_val, concentration0=b_val, name="beta2")
samples2 = self.evaluate(beta2.sample(n_val, seed=123456))
self.assertAllClose(samples1, samples2)
def testBetaSample(self):
with self.test_session():
a = 1.
b = 2.
beta = beta_lib.Beta(a, b)
n = constant_op.constant(100000)
samples = beta.sample(n)
sample_values = samples.eval()
self.assertEqual(sample_values.shape, (100000, ))
self.assertFalse(np.any(sample_values < 0.0))
if not stats:
return
self.assertLess(
stats.kstest(
# Beta is a univariate distribution.
sample_values,
stats.beta(a=1., b=2.).cdf)[0],
0.01)
# The standard error of the sample mean is 1 / (sqrt(18 * n))
self.assertAllClose(sample_values.mean(axis=0),
stats.beta.mean(a, b),
atol=1e-2)
self.assertAllClose(np.cov(sample_values, rowvar=0),
stats.beta.var(a, b),
atol=1e-1)
def testPdfXStretchedInBroadcastWhenLowerRank(self): a = [[1., 2], [2., 3]] b = [[1., 2], [2., 3]] x = [.5, .5] pdf = beta_lib.Beta(a, b).prob(x) self.assertAllClose([[1., 3. / 2], [3. / 2, 15. / 8]], self.evaluate(pdf)) self.assertEqual((2, 2), pdf.get_shape())
def testPdfTwoBatchesNontrivialX(self): a = [1., 2] b = [1., 2] x = [.3, .7] dist = beta_lib.Beta(a, b) pdf = dist.prob(x) self.assertAllClose([1, 63. / 50], self.evaluate(pdf)) self.assertEqual((2,), pdf.get_shape())
def testPdfTwoBatches(self): a = [1., 2] b = [1., 2] x = [.5, .5] dist = beta_lib.Beta(a, b) pdf = dist.prob(x) self.assertAllClose([1., 3. / 2], self.evaluate(pdf)) self.assertEqual((2,), pdf.get_shape())
def testComplexShapesBroadcast(self): a = np.random.rand(3, 2, 2) b = np.random.rand(2, 2) dist = beta_lib.Beta(a, b) self.assertAllEqual([], self.evaluate(dist.event_shape_tensor())) self.assertAllEqual([3, 2, 2], self.evaluate(dist.batch_shape_tensor())) self.assertEqual(tensor_shape.TensorShape([]), dist.event_shape) self.assertEqual(tensor_shape.TensorShape([3, 2, 2]), dist.batch_shape)
def testPdfXStretchedInBroadcastWhenSameRank(self):
with self.test_session():
a = [[1., 2], [2., 3]]
b = [[1., 2], [2., 3]]
x = [[.5, .5]]
pdf = beta_lib.Beta(a, b).prob(x)
self.assertAllClose([[1., 3. / 2], [3. / 2, 15. / 8]], pdf.eval())
self.assertEqual((2, 2), pdf.get_shape())
def testSimpleShapes(self): a = np.random.rand(3) b = np.random.rand(3) dist = beta_lib.Beta(a, b) self.assertAllEqual([], self.evaluate(dist.event_shape_tensor())) self.assertAllEqual([3], self.evaluate(dist.batch_shape_tensor())) self.assertEqual(tensor_shape.TensorShape([]), dist.event_shape) self.assertEqual(tensor_shape.TensorShape([3]), dist.batch_shape)
def testPdfAlphaStretchedInBroadcastWhenSameRank(self): a = [[1., 2]] b = [[1., 2]] x = [[.5, .5], [.3, .7]] dist = beta_lib.Beta(a, b) pdf = dist.prob(x) self.assertAllClose([[1., 3. / 2], [1., 63. / 50]], self.evaluate(pdf)) self.assertEqual((2, 2), pdf.get_shape())
def testBetaEntropy(self):
a = [1., 2, 3]
b = [2., 4, 1.2]
dist = beta_lib.Beta(a, b)
self.assertEqual(dist.entropy().get_shape(), (3,))
if not stats:
return
expected_entropy = stats.beta.entropy(a, b)
self.assertAllClose(expected_entropy, self.evaluate(dist.entropy()))
def testBetaVariance(self):
a = [1., 2, 3]
b = [2., 4, 1.2]
dist = beta_lib.Beta(a, b)
self.assertEqual(dist.variance().get_shape(), (3,))
if not stats:
return
expected_variance = stats.beta.var(a, b)
self.assertAllClose(expected_variance, self.evaluate(dist.variance()))
def testBetaModeEnableAllowNanStats(self):
a = np.array([1., 2, 3])
b = np.array([2., 4, 1.2])
dist = beta_lib.Beta(a, b, allow_nan_stats=True)
expected_mode = (a - 1) / (a + b - 2)
expected_mode[0] = np.nan
self.assertEqual((3,), dist.mode().get_shape())
self.assertAllClose(expected_mode, self.evaluate(dist.mode()))
a = np.array([2., 2, 3])
b = np.array([1., 4, 1.2])
dist = beta_lib.Beta(a, b, allow_nan_stats=True)
expected_mode = (a - 1) / (a + b - 2)
expected_mode[0] = np.nan
self.assertEqual((3,), dist.mode().get_shape())
self.assertAllClose(expected_mode, self.evaluate(dist.mode()))
def testBetaMean(self):
a = [1., 2, 3]
b = [2., 4, 1.2]
dist = beta_lib.Beta(a, b)
self.assertEqual(dist.mean().get_shape(), (3,))
if not stats:
return
expected_mean = stats.beta.mean(a, b)
self.assertAllClose(expected_mean, self.evaluate(dist.mean()))
def testPdfUniformZeroBatch(self): # This is equivalent to a uniform distribution a = 1. b = 1. x = np.array([.1, .2, .3, .5, .8], dtype=np.float32) dist = beta_lib.Beta(a, b) pdf = dist.prob(x) self.assertAllClose([1.] * 5, self.evaluate(pdf)) self.assertEqual((5,), pdf.get_shape())
def testComplexShapes(self):
with self.test_session():
a = np.random.rand(3, 2, 2)
b = np.random.rand(3, 2, 2)
dist = beta_lib.Beta(a, b)
self.assertAllEqual([], dist.event_shape_tensor().eval())
self.assertAllEqual([3, 2, 2], dist.batch_shape_tensor().eval())
self.assertEqual(tensor_shape.TensorShape([]), dist.event_shape)
self.assertEqual(tensor_shape.TensorShape([3, 2, 2]),
dist.batch_shape)
def testBetaFullyReparameterized(self):
a = constant_op.constant(1.0)
b = constant_op.constant(2.0)
with backprop.GradientTape() as tape:
tape.watch(a)
tape.watch(b)
beta = beta_lib.Beta(a, b)
samples = beta.sample(100)
grad_a, grad_b = tape.gradient(samples, [a, b])
self.assertIsNotNone(grad_a)
self.assertIsNotNone(grad_b)
def testBetaLogCdf(self):
shape = (30, 40, 50)
for dt in (np.float32, np.float64):
a = 10. * np.random.random(shape).astype(dt)
b = 10. * np.random.random(shape).astype(dt)
x = np.random.random(shape).astype(dt)
actual = self.evaluate(math_ops.exp(beta_lib.Beta(a, b).log_cdf(x)))
self.assertAllEqual(np.ones(shape, dtype=np.bool), 0. <= x)
self.assertAllEqual(np.ones(shape, dtype=np.bool), 1. >= x)
if not stats:
return
self.assertAllClose(stats.beta.cdf(x, a, b), actual, rtol=1e-4, atol=0)
def testBetaBetaKL(self):
with self.test_session() as sess:
for shape in [(10, ), (4, 5)]:
a1 = 6.0 * np.random.random(size=shape) + 1e-4
b1 = 6.0 * np.random.random(size=shape) + 1e-4
a2 = 6.0 * np.random.random(size=shape) + 1e-4
b2 = 6.0 * np.random.random(size=shape) + 1e-4
# Take inverse softplus of values to test BetaWithSoftplusConcentration
a1_sp = np.log(np.exp(a1) - 1.0)
b1_sp = np.log(np.exp(b1) - 1.0)
a2_sp = np.log(np.exp(a2) - 1.0)
b2_sp = np.log(np.exp(b2) - 1.0)
d1 = beta_lib.Beta(concentration1=a1, concentration0=b1)
d2 = beta_lib.Beta(concentration1=a2, concentration0=b2)
d1_sp = beta_lib.BetaWithSoftplusConcentration(
concentration1=a1_sp, concentration0=b1_sp)
d2_sp = beta_lib.BetaWithSoftplusConcentration(
concentration1=a2_sp, concentration0=b2_sp)
if not special:
return
kl_expected = (special.betaln(a2, b2) -
special.betaln(a1, b1) +
(a1 - a2) * special.digamma(a1) +
(b1 - b2) * special.digamma(b1) +
(a2 - a1 + b2 - b1) * special.digamma(a1 + b1))
for dist1 in [d1, d1_sp]:
for dist2 in [d2, d2_sp]:
kl = kullback_leibler.kl_divergence(dist1, dist2)
kl_val = sess.run(kl)
self.assertEqual(kl.get_shape(), shape)
self.assertAllClose(kl_val, kl_expected)
# Make sure KL(d1||d1) is 0
kl_same = sess.run(kullback_leibler.kl_divergence(d1, d1))
self.assertAllClose(kl_same, np.zeros_like(kl_expected))
def testPdfXProper(self):
a = [[1., 2, 3]]
b = [[2., 4, 3]]
with self.test_session():
dist = beta_lib.Beta(a, b, validate_args=True)
dist.prob([.1, .3, .6]).eval()
dist.prob([.2, .3, .5]).eval()
# Either condition can trigger.
with self.assertRaisesOpError("sample must be positive"):
dist.prob([-1., 0.1, 0.5]).eval()
with self.assertRaisesOpError("sample must be positive"):
dist.prob([0., 0.1, 0.5]).eval()
with self.assertRaisesOpError("sample must be no larger than `1`"):
dist.prob([.1, .2, 1.2]).eval()
def testBetaSampleMultidimensional(self):
a = np.random.rand(3, 2, 2).astype(np.float32)
b = np.random.rand(3, 2, 2).astype(np.float32)
beta = beta_lib.Beta(a, b)
n = constant_op.constant(100000)
samples = beta.sample(n)
sample_values = self.evaluate(samples)
self.assertEqual(sample_values.shape, (100000, 3, 2, 2))
self.assertFalse(np.any(sample_values < 0.0))
if not stats:
return
self.assertAllClose(sample_values[:, 1, :].mean(axis=0),
stats.beta.mean(a, b)[1, :],
atol=1e-1)
def testPdfXProper(self):
a = [[1., 2, 3]]
b = [[2., 4, 3]]
dist = beta_lib.Beta(a, b, validate_args=True)
self.evaluate(dist.prob([.1, .3, .6]))
self.evaluate(dist.prob([.2, .3, .5]))
# Either condition can trigger.
with self.assertRaisesOpError("sample must be positive"):
self.evaluate(dist.prob([-1., 0.1, 0.5]))
with self.assertRaisesOpError("sample must be positive"):
self.evaluate(dist.prob([0., 0.1, 0.5]))
with self.assertRaisesOpError("sample must be less than `1`"):
self.evaluate(dist.prob([.1, .2, 1.2]))
with self.assertRaisesOpError("sample must be less than `1`"):
self.evaluate(dist.prob([.1, .2, 1.0]))
def testBetaCdf(self):
with self.test_session():
shape = (30, 40, 50)
for dt in (np.float32, np.float64):
a = 10. * np.random.random(shape).astype(dt)
b = 10. * np.random.random(shape).astype(dt)
x = np.random.random(shape).astype(dt)
actual = beta_lib.Beta(a, b).cdf(x).eval()
self.assertAllEqual(np.ones(shape, dtype=np.bool), 0. <= x)
self.assertAllEqual(np.ones(shape, dtype=np.bool), 1. >= x)
if not stats:
return
self.assertAllClose(stats.beta.cdf(x, a, b),
actual,
rtol=1e-4,
atol=0)
def testLogPdfOnBoundaryIsFiniteWhenAlphaIsOne(self):
b = [[0.01, 0.1, 1., 2], [5., 10., 2., 3]]
pdf = self.evaluate(beta_lib.Beta(1., b).prob(0.))
self.assertAllEqual(np.ones_like(pdf, dtype=np.bool), np.isfinite(pdf))
def testBetaProperty(self): a = [[1., 2, 3]] b = [[2., 4, 3]] dist = beta_lib.Beta(a, b) self.assertEqual([1, 3], dist.concentration0.get_shape()) self.assertAllClose(b, self.evaluate(dist.concentration0))
