path: root/tensorflow/python/kernel_tests/distributions/beta_test.py

# 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.client import session
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import random_seed
from tensorflow.python.framework import tensor_shape
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")


class BetaTest(test.TestCase):

  def testSimpleShapes(self):
    with self.test_session():
      a = np.random.rand(3)
      b = np.random.rand(3)
      dist = beta_lib.Beta(a, b)
      self.assertAllEqual([], dist.event_shape_tensor().eval())
      self.assertAllEqual([3], dist.batch_shape_tensor().eval())
      self.assertEqual(tensor_shape.TensorShape([]), dist.event_shape)
      self.assertEqual(tensor_shape.TensorShape([3]), dist.batch_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 testComplexShapesBroadcast(self):
    with self.test_session():
      a = np.random.rand(3, 2, 2)
      b = np.random.rand(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 testAlphaProperty(self):
    a = [[1., 2, 3]]
    b = [[2., 4, 3]]
    with self.test_session():
      dist = beta_lib.Beta(a, b)
      self.assertEqual([1, 3], dist.concentration1.get_shape())
      self.assertAllClose(a, dist.concentration1.eval())

  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 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 less than `1`"):
        dist.prob([.1, .2, 1.2]).eval()
      with self.assertRaisesOpError("sample must be less than `1`"):
        dist.prob([.1, .2, 1.0]).eval()

  def testPdfTwoBatches(self):
    with self.test_session():
      a = [1., 2]
      b = [1., 2]
      x = [.5, .5]
      dist = beta_lib.Beta(a, b)
      pdf = dist.prob(x)
      self.assertAllClose([1., 3. / 2], pdf.eval())
      self.assertEqual((2,), pdf.get_shape())

  def testPdfTwoBatchesNontrivialX(self):
    with self.test_session():
      a = [1., 2]
      b = [1., 2]
      x = [.3, .7]
      dist = beta_lib.Beta(a, b)
      pdf = dist.prob(x)
      self.assertAllClose([1, 63. / 50], pdf.eval())
      self.assertEqual((2,), pdf.get_shape())

  def testPdfUniformZeroBatch(self):
    with self.test_session():
      # 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, pdf.eval())
      self.assertEqual((5,), pdf.get_shape())

  def testPdfAlphaStretchedInBroadcastWhenSameRank(self):
    with self.test_session():
      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]], pdf.eval())
      self.assertEqual((2, 2), pdf.get_shape())

  def testPdfAlphaStretchedInBroadcastWhenLowerRank(self):
    with self.test_session():
      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]], pdf.eval())
      self.assertEqual((2, 2), pdf.get_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 testPdfXStretchedInBroadcastWhenLowerRank(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 testBetaMean(self):
    with session.Session():
      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, dist.mean().eval())

  def testBetaVariance(self):
    with session.Session():
      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, dist.variance().eval())

  def testBetaMode(self):
    with session.Session():
      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, dist.mode().eval())

  def testBetaModeInvalid(self):
    with session.Session():
      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.*"):
        dist.mode().eval()

      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.*"):
        dist.mode().eval()

  def testBetaModeEnableAllowNanStats(self):
    with session.Session():
      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, dist.mode().eval())

      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, dist.mode().eval())

  def testBetaEntropy(self):
    with session.Session():
      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, dist.entropy().eval())

  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)

  # Test that sampling with the same seed twice gives the same results.
  def testBetaSampleMultipleTimes(self):
    with self.test_session():
      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 = beta1.sample(n_val, seed=123456).eval()

      random_seed.set_random_seed(654321)
      beta2 = beta_lib.Beta(concentration1=a_val,
                            concentration0=b_val,
                            name="beta2")
      samples2 = beta2.sample(n_val, seed=123456).eval()

      self.assertAllClose(samples1, samples2)

  def testBetaSampleMultidimensional(self):
    with self.test_session():
      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 = samples.eval()
      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):
    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 testBetaLogCdf(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 = math_ops.exp(beta_lib.Beta(a, b).log_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 testBetaWithSoftplusConcentration(self):
    with self.test_session():
      a, b = -4.2, -9.1
      dist = beta_lib.BetaWithSoftplusConcentration(a, b)
      self.assertAllClose(nn_ops.softplus(a).eval(), dist.concentration1.eval())
      self.assertAllClose(nn_ops.softplus(b).eval(), dist.concentration0.eval())

  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))


if __name__ == "__main__":
  test.main()