def random_gamma(shape,
alpha,
beta=None,
dtype=dtypes.float32,
seed=None,
name=None):
"""Draws `shape` samples from each of the given Gamma distribution(s).
`alpha` is the shape parameter describing the distribution(s), and `beta` is
the inverse scale parameter(s).
Note: Because internal calculations are done using `float64` and casting has
`floor` semantics, we must manually map zero outcomes to the smallest
possible positive floating-point value, i.e., `np.finfo(dtype).tiny`. This
means that `np.finfo(dtype).tiny` occurs more frequently than it otherwise
should. This bias can only happen for small values of `alpha`, i.e.,
`alpha << 1` or large values of `beta`, i.e., `beta >> 1`.
The samples are differentiable w.r.t. alpha and beta.
The derivatives are computed using the approach described in the paper
[Michael Figurnov, Shakir Mohamed, Andriy Mnih.
Implicit Reparameterization Gradients, 2018](https://arxiv.org/abs/1805.08498)
Example:
```python
samples = tf.random_gamma([10], [0.5, 1.5])
# samples has shape [10, 2], where each slice [:, 0] and [:, 1] represents
# the samples drawn from each distribution
samples = tf.random_gamma([7, 5], [0.5, 1.5])
# samples has shape [7, 5, 2], where each slice [:, :, 0] and [:, :, 1]
# represents the 7x5 samples drawn from each of the two distributions
alpha = tf.constant([[1.],[3.],[5.]])
beta = tf.constant([[3., 4.]])
samples = tf.random_gamma([30], alpha=alpha, beta=beta)
# samples has shape [30, 3, 2], with 30 samples each of 3x2 distributions.
loss = tf.reduce_mean(tf.square(samples))
dloss_dalpha, dloss_dbeta = tf.gradients(loss, [alpha, beta])
# unbiased stochastic derivatives of the loss function
alpha.shape == dloss_dalpha.shape # True
beta.shape == dloss_dbeta.shape # True
```
Args:
shape: A 1-D integer Tensor or Python array. The shape of the output samples
to be drawn per alpha/beta-parameterized distribution.
alpha: A Tensor or Python value or N-D array of type `dtype`. `alpha`
provides the shape parameter(s) describing the gamma distribution(s) to
sample. Must be broadcastable with `beta`.
beta: A Tensor or Python value or N-D array of type `dtype`. Defaults to 1.
`beta` provides the inverse scale parameter(s) of the gamma
distribution(s) to sample. Must be broadcastable with `alpha`.
dtype: The type of alpha, beta, and the output: `float16`, `float32`, or
`float64`.
seed: A Python integer. Used to create a random seed for the distributions.
See
`tf.set_random_seed`
for behavior.
name: Optional name for the operation.
Returns:
samples: a `Tensor` of shape
`tf.concat([shape, tf.shape(alpha + beta)], axis=0)` with values of type
`dtype`.
"""
with ops.name_scope(name, "random_gamma", [shape, alpha, beta]):
shape = ops.convert_to_tensor(shape, name="shape", dtype=dtypes.int32)
alpha = ops.convert_to_tensor(alpha, name="alpha", dtype=dtype)
beta = ops.convert_to_tensor(
beta if beta is not None else 1, name="beta", dtype=dtype)
alpha_broadcast = alpha + array_ops.zeros_like(beta)
seed1, seed2 = random_seed.get_seed(seed)
return math_ops.maximum(
np.finfo(dtype.as_numpy_dtype).tiny,
gen_random_ops.random_gamma(
shape, alpha_broadcast, seed=seed1, seed2=seed2) / beta)
def random_gamma(shape,
alpha,
beta=None,
dtype=dtypes.float32,
seed=None,
name=None):
"""Draws `shape` samples from each of the given Gamma distribution(s).
`alpha` is the shape parameter describing the distribution(s), and `beta` is
the inverse scale parameter(s).
Note: Because internal calculations are done using `float64` and casting has
`floor` semantics, we must manually map zero outcomes to the smallest
possible positive floating-point value, i.e., `np.finfo(dtype).tiny`. This
means that `np.finfo(dtype).tiny` occurs more frequently than it otherwise
should. This bias can only happen for small values of `alpha`, i.e.,
`alpha << 1` or large values of `beta`, i.e., `beta >> 1`.
The samples are differentiable w.r.t. alpha and beta.
The derivatives are computed using the approach described in the paper
[Michael Figurnov, Shakir Mohamed, Andriy Mnih.
Implicit Reparameterization Gradients, 2018](https://arxiv.org/abs/1805.08498)
Example:
```python
samples = tf.random_gamma([10], [0.5, 1.5])
# samples has shape [10, 2], where each slice [:, 0] and [:, 1] represents
# the samples drawn from each distribution
samples = tf.random_gamma([7, 5], [0.5, 1.5])
# samples has shape [7, 5, 2], where each slice [:, :, 0] and [:, :, 1]
# represents the 7x5 samples drawn from each of the two distributions
alpha = tf.constant([[1.],[3.],[5.]])
beta = tf.constant([[3., 4.]])
samples = tf.random_gamma([30], alpha=alpha, beta=beta)
# samples has shape [30, 3, 2], with 30 samples each of 3x2 distributions.
loss = tf.reduce_mean(tf.square(samples))
dloss_dalpha, dloss_dbeta = tf.gradients(loss, [alpha, beta])
# unbiased stochastic derivatives of the loss function
alpha.shape == dloss_dalpha.shape # True
beta.shape == dloss_dbeta.shape # True
```
Args:
shape: A 1-D integer Tensor or Python array. The shape of the output samples
to be drawn per alpha/beta-parameterized distribution.
alpha: A Tensor or Python value or N-D array of type `dtype`. `alpha`
provides the shape parameter(s) describing the gamma distribution(s) to
sample. Must be broadcastable with `beta`.
beta: A Tensor or Python value or N-D array of type `dtype`. Defaults to 1.
`beta` provides the inverse scale parameter(s) of the gamma
distribution(s) to sample. Must be broadcastable with `alpha`.
dtype: The type of alpha, beta, and the output: `float16`, `float32`, or
`float64`.
seed: A Python integer. Used to create a random seed for the distributions.
See
`tf.set_random_seed`
for behavior.
name: Optional name for the operation.
Returns:
samples: a `Tensor` of shape
`tf.concat([shape, tf.shape(alpha + beta)], axis=0)` with values of type
`dtype`.
"""
with ops.name_scope(name, "random_gamma", [shape, alpha, beta]):
shape = ops.convert_to_tensor(shape, name="shape", dtype=dtypes.int32)
alpha = ops.convert_to_tensor(alpha, name="alpha", dtype=dtype)
beta = ops.convert_to_tensor(
beta if beta is not None else 1, name="beta", dtype=dtype)
alpha_broadcast = alpha + array_ops.zeros_like(beta)
seed1, seed2 = random_seed.get_seed(seed)
return math_ops.maximum(
np.finfo(dtype.as_numpy_dtype).tiny,
gen_random_ops.random_gamma(
shape, alpha_broadcast, seed=seed1, seed2=seed2) / beta)
def random_gamma(shape,
alpha,
beta=None,
dtype=dtypes.float32,
seed=None,
name=None):
"""Draws `shape` samples from each of the given Gamma distribution(s).
`alpha` is the shape parameter describing the distribution(s), and `beta` is
the inverse scale parameter(s).
Example:
samples = tf.random_gamma([10], [0.5, 1.5])
# samples has shape [10, 2], where each slice [:, 0] and [:, 1] represents
# the samples drawn from each distribution
samples = tf.random_gamma([7, 5], [0.5, 1.5])
# samples has shape [7, 5, 2], where each slice [:, :, 0] and [:, :, 1]
# represents the 7x5 samples drawn from each of the two distributions
samples = tf.random_gamma([30], [[1.],[3.],[5.]], beta=[[3., 4.]])
# samples has shape [30, 3, 2], with 30 samples each of 3x2 distributions.
Note: Because internal calculations are done using `float64` and casting has
`floor` semantics, we must manually map zero outcomes to the smallest
possible positive floating-point value, i.e., `np.finfo(dtype).tiny`. This
means that `np.finfo(dtype).tiny` occurs more frequently than it otherwise
should. This bias can only happen for small values of `alpha`, i.e.,
`alpha << 1` or large values of `beta`, i.e., `beta >> 1`.
Args:
shape: A 1-D integer Tensor or Python array. The shape of the output samples
to be drawn per alpha/beta-parameterized distribution.
alpha: A Tensor or Python value or N-D array of type `dtype`. `alpha`
provides the shape parameter(s) describing the gamma distribution(s) to
sample. Must be broadcastable with `beta`.
beta: A Tensor or Python value or N-D array of type `dtype`. Defaults to 1.
`beta` provides the inverse scale parameter(s) of the gamma
distribution(s) to sample. Must be broadcastable with `alpha`.
dtype: The type of alpha, beta, and the output: `float16`, `float32`, or
`float64`.
seed: A Python integer. Used to create a random seed for the distributions.
See
@{tf.set_random_seed}
for behavior.
name: Optional name for the operation.
Returns:
samples: a `Tensor` of shape `tf.concat(shape, tf.shape(alpha + beta))`
with values of type `dtype`.
"""
with ops.name_scope(name, "random_gamma", [shape, alpha, beta]):
shape = ops.convert_to_tensor(shape, name="shape", dtype=dtypes.int32)
alpha = ops.convert_to_tensor(alpha, name="alpha", dtype=dtype)
beta = ops.convert_to_tensor(
beta if beta is not None else 1, name="beta", dtype=dtype)
alpha_broadcast = alpha + array_ops.zeros_like(beta)
seed1, seed2 = random_seed.get_seed(seed)
return math_ops.maximum(
np.finfo(dtype.as_numpy_dtype).tiny,
gen_random_ops.random_gamma(
shape, alpha_broadcast, seed=seed1, seed2=seed2) / beta)
