def _parameter_control_dependencies(self, is_init):
assertions = []
logits = self._logits
probs = self._probs
param, name = (probs, 'probs') if logits is None else (logits, 'logits')
# In init, we can always build shape and dtype checks because
# we assume shape doesn't change for Variable backed args.
if is_init:
if not dtype_util.is_floating(param.dtype):
raise TypeError('Argument `{}` must having floating type.'.format(name))
msg = 'Argument `{}` must have rank at least 1.'.format(name)
shape_static = tensorshape_util.dims(param.shape)
if shape_static is not None:
if len(shape_static) < 1:
raise ValueError(msg)
elif self.validate_args:
param = tf.convert_to_tensor(param)
assertions.append(
assert_util.assert_rank_at_least(param, 1, message=msg))
with tf.control_dependencies(assertions):
param = tf.identity(param)
msg1 = 'Argument `{}` must have final dimension >= 1.'.format(name)
msg2 = 'Argument `{}` must have final dimension <= {}.'.format(
name, dtype_util.max(tf.int32))
event_size = shape_static[-1] if shape_static is not None else None
if event_size is not None:
if event_size < 1:
raise ValueError(msg1)
if event_size > dtype_util.max(tf.int32):
raise ValueError(msg2)
elif self.validate_args:
param = tf.convert_to_tensor(param)
assertions.append(assert_util.assert_greater_equal(
tf.shape(param)[-1], 1, message=msg1))
# NOTE: For now, we leave out a runtime assertion that
# `tf.shape(param)[-1] <= tf.int32.max`. An earlier `tf.shape` call
# will fail before we get to this point.
if not self.validate_args:
assert not assertions # Should never happen.
return []
if probs is not None:
probs = param # reuse tensor conversion from above
if is_init != tensor_util.is_ref(probs):
probs = tf.convert_to_tensor(probs)
one = tf.ones([], dtype=probs.dtype)
assertions.extend([
assert_util.assert_non_negative(probs),
assert_util.assert_less_equal(probs, one),
assert_util.assert_near(
tf.reduce_sum(probs, axis=-1), one,
message='Argument `probs` must sum to 1.'),
])
return assertions
def test_assert_all_finite_input_finite(self):
minval = tf.constant(dtype_util.min(self.dtype), dtype=self.dtype)
maxval = tf.constant(dtype_util.max(self.dtype), dtype=self.dtype)
# This tests if the minimum value for the dtype is detected as finite.
self.assertAllFinite(minval)
# This tests if the maximum value for the dtype is detected as finite.
self.assertAllFinite(maxval)
# This tests if a rank 3 `Tensor` with entries in the range
# [0.4*minval, 0.4*maxval] is detected as finite.
# The choice of range helps to avoid overflows or underflows
# in tf.linspace calculations.
num_elem = 1000
shape = (10, 10, 10)
a = tf.reshape(tf.linspace(0.4*minval, 0.4*maxval, num_elem), shape)
self.assertAllFinite(a)
def testMax(self, dtype, expected_maxval): self.assertEqual(dtype_util.max(dtype), expected_maxval)
def _sample_n(self, n, seed=None):
power = tf.convert_to_tensor(self.power)
shape = ps.concat([[n], ps.shape(power)], axis=0)
numpy_dtype = dtype_util.as_numpy_dtype(power.dtype)
seed = samplers.sanitize_seed(seed, salt='zipf')
# Because `_hat_integral` is montonically decreasing, the bounds for u will
# switch.
# Compute the hat_integral explicitly here since we can calculate the log of
# the inputs statically in float64 with numpy.
maxval_u = tf.math.exp(-(power - 1.) * numpy_dtype(np.log1p(0.5)) -
tf.math.log(power - 1.)) + 1.
minval_u = tf.math.exp(
-(power - 1.) *
numpy_dtype(np.log1p(dtype_util.max(self.dtype) - 0.5)) -
tf.math.log(power - 1.))
def loop_body(should_continue, k, seed):
"""Resample the non-accepted points."""
u_seed, next_seed = samplers.split_seed(seed)
# Uniform variates must be sampled from the open-interval `(0, 1)` rather
# than `[0, 1)`. To do so, we use
# `np.finfo(dtype_util.as_numpy_dtype(self.dtype)).tiny`
# because it is the smallest, positive, 'normal' number. A 'normal' number
# is such that the mantissa has an implicit leading 1. Normal, positive
# numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
# this case, a subnormal number (i.e., np.nextafter) can cause us to
# sample 0.
u = samplers.uniform(
shape,
minval=np.finfo(dtype_util.as_numpy_dtype(power.dtype)).tiny,
maxval=numpy_dtype(1.),
dtype=power.dtype,
seed=u_seed)
# We use (1 - u) * maxval_u + u * minval_u rather than the other way
# around, since we want to draw samples in (minval_u, maxval_u].
u = maxval_u + (minval_u - maxval_u) * u
# set_shape needed here because of b/139013403
tensorshape_util.set_shape(u, should_continue.shape)
# Sample the point X from the continuous density h(x) \propto x^(-power).
x = self._hat_integral_inverse(u, power=power)
# Rejection-inversion requires a `hat` function, h(x) such that
# \int_{k - .5}^{k + .5} h(x) dx >= pmf(k + 1) for points k in the
# support. A natural hat function for us is h(x) = x^(-power).
#
# After sampling X from h(x), suppose it lies in the interval
# (K - .5, K + .5) for integer K. Then the corresponding K is accepted if
# if lies to the left of x_K, where x_K is defined by:
# \int_{x_k}^{K + .5} h(x) dx = H(x_K) - H(K + .5) = pmf(K + 1),
# where H(x) = \int_x^inf h(x) dx.
# Solving for x_K, we find that x_K = H_inverse(H(K + .5) + pmf(K + 1)).
# Or, the acceptance condition is X <= H_inverse(H(K + .5) + pmf(K + 1)).
# Since X = H_inverse(U), this simplifies to U <= H(K + .5) + pmf(K + 1).
# Update the non-accepted points.
# Since X \in (K - .5, K + .5), the sample K is chosen as floor(X + 0.5).
k = tf.where(should_continue, tf.floor(x + 0.5), k)
accept = (u <= self._hat_integral(k + .5, power=power) +
tf.exp(self._log_prob(k + 1, power=power)))
return [should_continue & (~accept), k, next_seed]
should_continue, samples, _ = tf.while_loop(
cond=lambda should_continue, *ignore: tf.reduce_any(should_continue
),
body=loop_body,
loop_vars=[
tf.ones(shape, dtype=tf.bool), # should_continue
tf.zeros(shape, dtype=power.dtype), # k
seed, # seed
],
maximum_iterations=self.sample_maximum_iterations,
)
samples = samples + 1.
if self.validate_args and dtype_util.is_integer(self.dtype):
samples = distribution_util.embed_check_integer_casting_closed(
samples, target_dtype=self.dtype, assert_positive=True)
samples = tf.cast(samples, self.dtype)
if self.validate_args:
npdt = dtype_util.as_numpy_dtype(self.dtype)
v = npdt(
dtype_util.min(npdt) if dtype_util.is_integer(npdt) else np.nan
)
samples = tf.where(should_continue, v, samples)
return samples
def _sample_n(self, n, seed=None):
power = tf.convert_to_tensor(self.power)
shape = tf.concat([[n], tf.shape(power)], axis=0)
has_seed = seed is not None
seed = SeedStream(seed, salt='zipf')
minval_u = self._hat_integral(0.5, power=power) + 1.
maxval_u = self._hat_integral(dtype_util.max(tf.int64) - 0.5,
power=power)
def loop_body(should_continue, k):
"""Resample the non-accepted points."""
# The range of U is chosen so that the resulting sample K lies in
# [0, tf.int64.max). The final sample, if accepted, is K + 1.
u = tf.random.uniform(shape,
minval=minval_u,
maxval=maxval_u,
dtype=power.dtype,
seed=seed())
# Sample the point X from the continuous density h(x) \propto x^(-power).
x = self._hat_integral_inverse(u, power=power)
# Rejection-inversion requires a `hat` function, h(x) such that
# \int_{k - .5}^{k + .5} h(x) dx >= pmf(k + 1) for points k in the
# support. A natural hat function for us is h(x) = x^(-power).
#
# After sampling X from h(x), suppose it lies in the interval
# (K - .5, K + .5) for integer K. Then the corresponding K is accepted if
# if lies to the left of x_K, where x_K is defined by:
# \int_{x_k}^{K + .5} h(x) dx = H(x_K) - H(K + .5) = pmf(K + 1),
# where H(x) = \int_x^inf h(x) dx.
# Solving for x_K, we find that x_K = H_inverse(H(K + .5) + pmf(K + 1)).
# Or, the acceptance condition is X <= H_inverse(H(K + .5) + pmf(K + 1)).
# Since X = H_inverse(U), this simplifies to U <= H(K + .5) + pmf(K + 1).
# Update the non-accepted points.
# Since X \in (K - .5, K + .5), the sample K is chosen as floor(X + 0.5).
k = tf.where(should_continue, tf.floor(x + 0.5), k)
accept = (u <= self._hat_integral(k + .5, power=power) +
tf.exp(self._log_prob(k + 1, power=power)))
return [should_continue & (~accept), k]
should_continue, samples = tf.while_loop(
cond=lambda should_continue, *ignore: tf.reduce_any(should_continue
),
body=loop_body,
loop_vars=[
tf.ones(shape, dtype=tf.bool), # should_continue
tf.zeros(shape, dtype=power.dtype), # k
],
parallel_iterations=1 if has_seed else 10,
maximum_iterations=self.sample_maximum_iterations,
)
samples = samples + 1.
if self.validate_args and dtype_util.is_integer(self.dtype):
samples = distribution_util.embed_check_integer_casting_closed(
samples, target_dtype=self.dtype, assert_positive=True)
samples = tf.cast(samples, self.dtype)
if self.validate_args:
npdt = dtype_util.as_numpy_dtype(self.dtype)
v = npdt(
dtype_util.min(npdt) if dtype_util.is_integer(npdt) else np.nan
)
samples = tf.where(should_continue, v, samples)
return samples
