Python kullback_leibler.kl_divergence函数代码示例

  def testDomainErrorExceptions(self):

    class MyDistException(normal.Normal):
      pass

    # Register KL to a lambda that spits out the name parameter
    @kullback_leibler.RegisterKL(MyDistException, MyDistException)
    # pylint: disable=unused-argument,unused-variable
    def _kl(a, b, name=None):
      return array_ops.identity([float("nan")])

    # pylint: disable=unused-argument,unused-variable

    with self.cached_session():
      a = MyDistException(loc=0.0, scale=1.0, allow_nan_stats=False)
      kl = kullback_leibler.kl_divergence(a, a, allow_nan_stats=False)
      with self.assertRaisesOpError(
          "KL calculation between .* and .* returned NaN values"):
        self.evaluate(kl)
      with self.assertRaisesOpError(
          "KL calculation between .* and .* returned NaN values"):
        a.kl_divergence(a).eval()
      a = MyDistException(loc=0.0, scale=1.0, allow_nan_stats=True)
      kl_ok = kullback_leibler.kl_divergence(a, a)
      self.assertAllEqual([float("nan")], self.evaluate(kl_ok))
      self_kl_ok = a.kl_divergence(a)
      self.assertAllEqual([float("nan")], self.evaluate(self_kl_ok))
      cross_ok = a.cross_entropy(a)
      self.assertAllEqual([float("nan")], self.evaluate(cross_ok))

  def testKLRaises(self):
    ind1 = independent_lib.Independent(
        distribution=normal_lib.Normal(
            loc=np.float32([-1., 1]),
            scale=np.float32([0.1, 0.5])),
        reinterpreted_batch_ndims=1)
    ind2 = independent_lib.Independent(
        distribution=normal_lib.Normal(
            loc=np.float32(-1),
            scale=np.float32(0.5)),
        reinterpreted_batch_ndims=0)

    with self.assertRaisesRegexp(
        ValueError, "Event shapes do not match"):
      kullback_leibler.kl_divergence(ind1, ind2)

    ind1 = independent_lib.Independent(
        distribution=normal_lib.Normal(
            loc=np.float32([-1., 1]),
            scale=np.float32([0.1, 0.5])),
        reinterpreted_batch_ndims=1)
    ind2 = independent_lib.Independent(
        distribution=mvn_diag_lib.MultivariateNormalDiag(
            loc=np.float32([-1., 1]),
            scale_diag=np.float32([0.1, 0.5])),
        reinterpreted_batch_ndims=0)

    with self.assertRaisesRegexp(
        NotImplementedError, "different event shapes"):
      kullback_leibler.kl_divergence(ind1, ind2)

  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)

        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 testDirichletDirichletKL(self):
    conc1 = np.array([[1., 2., 3., 1.5, 2.5, 3.5],
                      [1.5, 2.5, 3.5, 4.5, 5.5, 6.5]])
    conc2 = np.array([[0.5, 1., 1.5, 2., 2.5, 3.]])

    d1 = dirichlet_lib.Dirichlet(conc1)
    d2 = dirichlet_lib.Dirichlet(conc2)
    x = d1.sample(int(1e4), seed=0)
    kl_sample = math_ops.reduce_mean(d1.log_prob(x) - d2.log_prob(x), 0)
    kl_actual = kullback_leibler.kl_divergence(d1, d2)

    kl_sample_val = self.evaluate(kl_sample)
    kl_actual_val = self.evaluate(kl_actual)

    self.assertEqual(conc1.shape[:-1], kl_actual.get_shape())

    if not special:
      return

    kl_expected = (
        special.gammaln(np.sum(conc1, -1))
        - special.gammaln(np.sum(conc2, -1))
        - np.sum(special.gammaln(conc1) - special.gammaln(conc2), -1)
        + np.sum((conc1 - conc2) * (special.digamma(conc1) - special.digamma(
            np.sum(conc1, -1, keepdims=True))), -1))

    self.assertAllClose(kl_expected, kl_actual_val, atol=0., rtol=1e-6)
    self.assertAllClose(kl_sample_val, kl_actual_val, atol=0., rtol=1e-1)

    # 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))

  def testCategoricalCategoricalKL(self):
    def np_softmax(logits):
      exp_logits = np.exp(logits)
      return exp_logits / exp_logits.sum(axis=-1, keepdims=True)

    with self.cached_session() as sess:
      for categories in [2, 10]:
        for batch_size in [1, 2]:
          p_logits = self._rng.random_sample((batch_size, categories))
          q_logits = self._rng.random_sample((batch_size, categories))
          p = onehot_categorical.OneHotCategorical(logits=p_logits)
          q = onehot_categorical.OneHotCategorical(logits=q_logits)
          prob_p = np_softmax(p_logits)
          prob_q = np_softmax(q_logits)
          kl_expected = np.sum(
              prob_p * (np.log(prob_p) - np.log(prob_q)), axis=-1)

          kl_actual = kullback_leibler.kl_divergence(p, q)
          kl_same = kullback_leibler.kl_divergence(p, p)
          x = p.sample(int(2e4), seed=0)
          x = math_ops.cast(x, dtype=dtypes.float32)
          # Compute empirical KL(p||q).
          kl_sample = math_ops.reduce_mean(p.log_prob(x) - q.log_prob(x), 0)

          [kl_sample_, kl_actual_, kl_same_] = sess.run([kl_sample, kl_actual,
                                                         kl_same])
          self.assertEqual(kl_actual.get_shape(), (batch_size,))
          self.assertAllClose(kl_same_, np.zeros_like(kl_expected))
          self.assertAllClose(kl_actual_, kl_expected, atol=0., rtol=1e-6)
          self.assertAllClose(kl_sample_, kl_expected, atol=1e-2, rtol=0.)

  def testCategoricalCategoricalKL(self):

    def np_softmax(logits):
      exp_logits = np.exp(logits)
      return exp_logits / exp_logits.sum(axis=-1, keepdims=True)

    with self.cached_session() as sess:
      for categories in [2, 4]:
        for batch_size in [1, 10]:
          a_logits = np.random.randn(batch_size, categories)
          b_logits = np.random.randn(batch_size, categories)

          a = categorical.Categorical(logits=a_logits)
          b = categorical.Categorical(logits=b_logits)

          kl = kullback_leibler.kl_divergence(a, b)
          kl_val = sess.run(kl)
          # Make sure KL(a||a) is 0
          kl_same = sess.run(kullback_leibler.kl_divergence(a, a))

          prob_a = np_softmax(a_logits)
          prob_b = np_softmax(b_logits)
          kl_expected = np.sum(prob_a * (np.log(prob_a) - np.log(prob_b)),
                               axis=-1)

          self.assertEqual(kl.get_shape(), (batch_size,))
          self.assertAllClose(kl_val, kl_expected)
          self.assertAllClose(kl_same, np.zeros_like(kl_expected))

def _kl_independent(a, b, name="kl_independent"):
  """Batched KL divergence `KL(a || b)` for Independent distributions.

  We can leverage the fact that
  ```
  KL(Independent(a) || Independent(b)) = sum(KL(a || b))
  ```
  where the sum is over the `reinterpreted_batch_ndims`.

  Args:
    a: Instance of `Independent`.
    b: Instance of `Independent`.
    name: (optional) name to use for created ops. Default "kl_independent".

  Returns:
    Batchwise `KL(a || b)`.

  Raises:
    ValueError: If the event space for `a` and `b`, or their underlying
      distributions don't match.
  """
  p = a.distribution
  q = b.distribution

  # The KL between any two (non)-batched distributions is a scalar.
  # Given that the KL between two factored distributions is the sum, i.e.
  # KL(p1(x)p2(y) || q1(x)q2(y)) = KL(p1 || q1) + KL(q1 || q2), we compute
  # KL(p || q) and do a `reduce_sum` on the reinterpreted batch dimensions.
  if a.event_shape.is_fully_defined() and b.event_shape.is_fully_defined():
    if a.event_shape == b.event_shape:
      if p.event_shape == q.event_shape:
        num_reduce_dims = a.event_shape.ndims - p.event_shape.ndims
        reduce_dims = [-i - 1 for i in range(0, num_reduce_dims)]

        return math_ops.reduce_sum(
            kullback_leibler.kl_divergence(p, q, name=name), axis=reduce_dims)
      else:
        raise NotImplementedError("KL between Independents with different "
                                  "event shapes not supported.")
    else:
      raise ValueError("Event shapes do not match.")
  else:
    with ops.control_dependencies([
        check_ops.assert_equal(a.event_shape_tensor(), b.event_shape_tensor()),
        check_ops.assert_equal(p.event_shape_tensor(), q.event_shape_tensor())
    ]):
      num_reduce_dims = (
          array_ops.shape(a.event_shape_tensor()[0]) -
          array_ops.shape(p.event_shape_tensor()[0]))
      reduce_dims = math_ops.range(-num_reduce_dims - 1, -1, 1)
      return math_ops.reduce_sum(
          kullback_leibler.kl_divergence(p, q, name=name), axis=reduce_dims)

  def test_kl_reverse_multidim(self):

    with self.test_session() as sess:
      d = 5  # Dimension

      p = mvn_full_lib.MultivariateNormalFullCovariance(
          covariance_matrix=self._tridiag(d, diag_value=1, offdiag_value=0.5))

      q = mvn_diag_lib.MultivariateNormalDiag(scale_diag=[0.5]*d)

      approx_kl = cd.monte_carlo_csiszar_f_divergence(
          f=cd.kl_reverse,
          p=p,
          q=q,
          num_draws=int(1e5),
          seed=1)

      approx_kl_self_normalized = cd.monte_carlo_csiszar_f_divergence(
          f=lambda logu: cd.kl_reverse(logu, self_normalized=True),
          p=p,
          q=q,
          num_draws=int(1e5),
          seed=1)

      exact_kl = kullback_leibler.kl_divergence(q, p)

      [approx_kl_, approx_kl_self_normalized_, exact_kl_] = sess.run([
          approx_kl, approx_kl_self_normalized, exact_kl])

      self.assertAllClose(approx_kl_, exact_kl_,
                          rtol=0.02, atol=0.)

      self.assertAllClose(approx_kl_self_normalized_, exact_kl_,
                          rtol=0.08, atol=0.)

  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(concentration=alpha0, rate=beta0)
      g1 = gamma_lib.Gamma(concentration=alpha1, rate=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_divergence(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 test_kl_reverse(self):
    with self.test_session() as sess:

      q = normal_lib.Normal(
          loc=np.ones(6),
          scale=np.array([0.5, 1.0, 1.5, 2.0, 2.5, 3.0]))

      p = normal_lib.Normal(loc=q.loc + 0.1, scale=q.scale - 0.2)

      approx_kl = cd.monte_carlo_csiszar_f_divergence(
          f=cd.kl_reverse,
          p=p,
          q=q,
          num_draws=int(1e5),
          seed=1)

      approx_kl_self_normalized = cd.monte_carlo_csiszar_f_divergence(
          f=lambda logu: cd.kl_reverse(logu, self_normalized=True),
          p=p,
          q=q,
          num_draws=int(1e5),
          seed=1)

      exact_kl = kullback_leibler.kl_divergence(q, p)

      [approx_kl_, approx_kl_self_normalized_, exact_kl_] = sess.run([
          approx_kl, approx_kl_self_normalized, exact_kl])

      self.assertAllClose(approx_kl_, exact_kl_,
                          rtol=0.07, atol=0.)

      self.assertAllClose(approx_kl_self_normalized_, exact_kl_,
                          rtol=0.02, atol=0.)

  def test_convergence_to_kl_using_sample_form_on_3dim_normal(self):
    # Test that the sample mean KL is the same as analytic when we use samples
    # to estimate every part of the KL divergence ratio.
    vector_shape = (2, 3)
    n_samples = 5000

    with self.test_session():
      q = mvn_diag_lib.MultivariateNormalDiag(
          loc=self._rng.rand(*vector_shape),
          scale_diag=self._rng.rand(*vector_shape))
      p = mvn_diag_lib.MultivariateNormalDiag(
          loc=self._rng.rand(*vector_shape),
          scale_diag=self._rng.rand(*vector_shape))

      # In this case, the log_ratio is the KL.
      sample_kl = -1 * entropy.elbo_ratio(
          log_p=p.log_prob,
          q=q,
          n=n_samples,
          form=entropy.ELBOForms.sample,
          seed=42)
      actual_kl = kullback_leibler_lib.kl_divergence(q, p)

      # Relative tolerance (rtol) chosen 2 times as large as minimim needed to
      # pass.
      self.assertEqual((2,), sample_kl.get_shape())
      self.assertAllClose(actual_kl.eval(), sample_kl.eval(), rtol=0.05)

 def testDefaultVariationalAndPrior(self):
   _, prior, variational, _, log_likelihood = mini_vae()
   elbo = vi.elbo(log_likelihood)
   expected_elbo = log_likelihood - kullback_leibler.kl_divergence(
       variational.distribution, prior)
   with self.test_session() as sess:
     sess.run(variables.global_variables_initializer())
     self.assertAllEqual(*sess.run([expected_elbo, elbo]))

  def testKLScalarToMultivariate(self):
    normal1 = normal_lib.Normal(
        loc=np.float32([-1., 1]),
        scale=np.float32([0.1, 0.5]))
    ind1 = independent_lib.Independent(
        distribution=normal1, reinterpreted_batch_ndims=1)

    normal2 = normal_lib.Normal(
        loc=np.float32([-3., 3]),
        scale=np.float32([0.3, 0.3]))
    ind2 = independent_lib.Independent(
        distribution=normal2, reinterpreted_batch_ndims=1)

    normal_kl = kullback_leibler.kl_divergence(normal1, normal2)
    ind_kl = kullback_leibler.kl_divergence(ind1, ind2)
    self.assertAllClose(
        self.evaluate(math_ops.reduce_sum(normal_kl, axis=-1)),
        self.evaluate(ind_kl))

 def testExplicitVariationalAndPrior(self):
   with self.test_session() as sess:
     _, _, variational, _, log_likelihood = mini_vae()
     prior = normal.Normal(loc=3., scale=2.)
     elbo = vi.elbo(
         log_likelihood, variational_with_prior={variational: prior})
     expected_elbo = log_likelihood - kullback_leibler.kl_divergence(
         variational.distribution, prior)
     sess.run(variables.global_variables_initializer())
     self.assertAllEqual(*sess.run([expected_elbo, elbo]))

  def testRegistration(self):

    class MyDist(normal.Normal):
      pass

    # Register KL to a lambda that spits out the name parameter
    @kullback_leibler.RegisterKL(MyDist, MyDist)
    def _kl(a, b, name=None):  # pylint: disable=unused-argument,unused-variable
      return name

    a = MyDist(loc=0.0, scale=1.0)
    self.assertEqual("OK", kullback_leibler.kl_divergence(a, a, name="OK"))