e5983061d3
An implementation involving continued fractions is used. The continued fraction for this function can be seen at http://dlmf.nist.gov/8.17.v PiperOrigin-RevId: 277327138 Change-Id: Icb8527af344b629806fd7e4880072d05e2530cd2
388 lines
14 KiB
Python
388 lines
14 KiB
Python
# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
|
|
#
|
|
# Licensed under the Apache License, Version 2.0 (the "License");
|
|
# you may not use this file except in compliance with the License.
|
|
# You may obtain a copy of the License at
|
|
#
|
|
# http://www.apache.org/licenses/LICENSE-2.0
|
|
#
|
|
# Unless required by applicable law or agreed to in writing, software
|
|
# distributed under the License is distributed on an "AS IS" BASIS,
|
|
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
# See the License for the specific language governing permissions and
|
|
# limitations under the License.
|
|
# ==============================================================================
|
|
from __future__ import absolute_import
|
|
from __future__ import division
|
|
from __future__ import print_function
|
|
|
|
import importlib
|
|
|
|
import numpy as np
|
|
|
|
from tensorflow.python.eager import backprop
|
|
from tensorflow.python.framework import constant_op
|
|
from tensorflow.python.framework import random_seed
|
|
from tensorflow.python.framework import tensor_shape
|
|
from tensorflow.python.framework import test_util
|
|
from tensorflow.python.ops import math_ops
|
|
from tensorflow.python.ops import nn_ops
|
|
from tensorflow.python.ops.distributions import beta as beta_lib
|
|
from tensorflow.python.ops.distributions import kullback_leibler
|
|
from tensorflow.python.platform import test
|
|
from tensorflow.python.platform import tf_logging
|
|
|
|
|
|
def try_import(name): # pylint: disable=invalid-name
|
|
module = None
|
|
try:
|
|
module = importlib.import_module(name)
|
|
except ImportError as e:
|
|
tf_logging.warning("Could not import %s: %s" % (name, str(e)))
|
|
return module
|
|
|
|
|
|
special = try_import("scipy.special")
|
|
stats = try_import("scipy.stats")
|
|
|
|
|
|
@test_util.run_all_in_graph_and_eager_modes
|
|
class BetaTest(test.TestCase):
|
|
|
|
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 testComplexShapes(self):
|
|
a = np.random.rand(3, 2, 2)
|
|
b = np.random.rand(3, 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 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 testAlphaProperty(self):
|
|
a = [[1., 2, 3]]
|
|
b = [[2., 4, 3]]
|
|
dist = beta_lib.Beta(a, b)
|
|
self.assertEqual([1, 3], dist.concentration1.get_shape())
|
|
self.assertAllClose(a, self.evaluate(dist.concentration1))
|
|
|
|
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))
|
|
|
|
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 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 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 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 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 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 testPdfXStretchedInBroadcastWhenSameRank(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 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 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 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 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 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 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 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 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 testBetaSample(self):
|
|
a = 1.
|
|
b = 2.
|
|
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,))
|
|
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 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)
|
|
|
|
# Test that sampling with the same seed twice gives the same results.
|
|
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 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 testBetaCdf(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(beta_lib.Beta(a, b).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=9e-3, atol=5e-6)
|
|
|
|
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=3e-3, atol=2e-5)
|
|
|
|
def testBetaWithSoftplusConcentration(self):
|
|
a, b = -4.2, -9.1
|
|
dist = beta_lib.BetaWithSoftplusConcentration(a, b)
|
|
self.assertAllClose(
|
|
self.evaluate(nn_ops.softplus(a)), self.evaluate(dist.concentration1))
|
|
self.assertAllClose(
|
|
self.evaluate(nn_ops.softplus(b)), self.evaluate(dist.concentration0))
|
|
|
|
def testBetaBetaKL(self):
|
|
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 = self.evaluate(kl)
|
|
self.assertEqual(kl.get_shape(), shape)
|
|
self.assertAllClose(kl_val, kl_expected)
|
|
|
|
# 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))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
test.main()
|