tensorflow/contrib/distributions/python/ops/vector_laplace_diag.py - platform/external/tensorflow - Git at Google

 # Copyright 2017 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.
 # ==============================================================================
 """Distribution of a vectorized Laplace, with uncorrelated components."""

 from __future__ import absolute_import
 from __future__ import division
 from __future__ import print_function

 from tensorflow.contrib.distributions.python.ops import distribution_util
 from tensorflow.contrib.distributions.python.ops import vector_laplace_linear_operator as vector_laplace_linop
 from tensorflow.python.framework import ops
 from tensorflow.python.util import deprecation


 __all__ = [
     "VectorLaplaceDiag",
 ]


 class VectorLaplaceDiag(
     vector_laplace_linop.VectorLaplaceLinearOperator):
   """The vectorization of the Laplace distribution on `R^k`.

   The vector laplace distribution is defined over `R^k`, and parameterized by
   a (batch of) length-`k` `loc` vector (the means) and a (batch of) `k x k`
   `scale` matrix:  `covariance = 2 * scale @ scale.T`, where `@` denotes
   matrix-multiplication.

   #### Mathematical Details

   The probability density function (pdf) is,

   ```none
   pdf(x; loc, scale) = exp(-||y||_1) / Z,
   y = inv(scale) @ (x - loc),
   Z = 2**k |det(scale)|,
   ```

   where:

   * `loc` is a vector in `R^k`,
   * `scale` is a linear operator in `R^{k x k}`, `cov = scale @ scale.T`,
   * `Z` denotes the normalization constant, and,
   * `||y||_1` denotes the `l1` norm of `y`, `sum_i |y_i|.

   A (non-batch) `scale` matrix is:

   ```none
   scale = diag(scale_diag + scale_identity_multiplier * ones(k))
   ```

   where:

   * `scale_diag.shape = [k]`, and,
   * `scale_identity_multiplier.shape = []`.

   Additional leading dimensions (if any) will index batches.

   If both `scale_diag` and `scale_identity_multiplier` are `None`, then
   `scale` is the Identity matrix.

   The VectorLaplace distribution is a member of the [location-scale
   family](https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be
   constructed as,

   ```none
   X = (X_1, ..., X_k), each X_i ~ Laplace(loc=0, scale=1)
   Y = (Y_1, ...,Y_k) = scale @ X + loc
   ```

   #### About `VectorLaplace` and `Vector` distributions in TensorFlow.

   The `VectorLaplace` is a non-standard distribution that has useful properties.

   The marginals `Y_1, ..., Y_k` are *not* Laplace random variables, due to
   the fact that the sum of Laplace random variables is not Laplace.

   Instead, `Y` is a vector whose components are linear combinations of Laplace
   random variables.  Thus, `Y` lives in the vector space generated by `vectors`
   of Laplace distributions.  This allows the user to decide the mean and
   covariance (by setting `loc` and `scale`), while preserving some properties of
   the Laplace distribution.  In particular, the tails of `Y_i` will be (up to
   polynomial factors) exponentially decaying.

   To see this last statement, note that the pdf of `Y_i` is the convolution of
   the pdf of `k` independent Laplace random variables.  One can then show by
   induction that distributions with exponential (up to polynomial factors) tails
   are closed under convolution.

   #### Examples

   ```python
   tfd = tf.contrib.distributions

   # Initialize a single 2-variate VectorLaplace.
   vla = tfd.VectorLaplaceDiag(
       loc=[1., -1],
       scale_diag=[1, 2.])

   vla.mean().eval()
   # ==> [1., -1]

   vla.stddev().eval()
   # ==> [1., 2] * sqrt(2)

   # Evaluate this on an observation in `R^2`, returning a scalar.
   vla.prob([-1., 0]).eval()  # shape: []

   # Initialize a 3-batch, 2-variate scaled-identity VectorLaplace.
   vla = tfd.VectorLaplaceDiag(
       loc=[1., -1],
       scale_identity_multiplier=[1, 2., 3])

   vla.mean().eval()  # shape: [3, 2]
   # ==> [[1., -1]
   #      [1, -1],
   #      [1, -1]]

   vla.stddev().eval()  # shape: [3, 2]
   # ==> sqrt(2) * [[1., 1],
   #                [2, 2],
   #                [3, 3]]

   # Evaluate this on an observation in `R^2`, returning a length-3 vector.
   vla.prob([-1., 0]).eval()  # shape: [3]

   # Initialize a 2-batch of 3-variate VectorLaplace's.
   vla = tfd.VectorLaplaceDiag(
       loc=[[1., 2, 3],
            [11, 22, 33]]           # shape: [2, 3]
       scale_diag=[[1., 2, 3],
                   [0.5, 1, 1.5]])  # shape: [2, 3]

   # Evaluate this on a two observations, each in `R^3`, returning a length-2
   # vector.
   x = [[-1., 0, 1],
        [-11, 0, 11.]]   # shape: [2, 3].
   vla.prob(x).eval()    # shape: [2]
   ```

   """

   @deprecation.deprecated(
       "2018-10-01",
       "The TensorFlow Distributions library has moved to "
       "TensorFlow Probability "
       "(https://github.com/tensorflow/probability). You "
       "should update all references to use `tfp.distributions` "
       "instead of `tf.contrib.distributions`.",
       warn_once=True)
   def __init__(self,
                loc=None,
                scale_diag=None,
                scale_identity_multiplier=None,
                validate_args=False,
                allow_nan_stats=True,
                name="VectorLaplaceDiag"):
     """Construct Vector Laplace distribution on `R^k`.

     The `batch_shape` is the broadcast shape between `loc` and `scale`
     arguments.

     The `event_shape` is given by last dimension of the matrix implied by
     `scale`. The last dimension of `loc` (if provided) must broadcast with this.

     Recall that `covariance = 2 * scale @ scale.T`.

     ```none
     scale = diag(scale_diag + scale_identity_multiplier * ones(k))
     ```

     where:

     * `scale_diag.shape = [k]`, and,
     * `scale_identity_multiplier.shape = []`.

     Additional leading dimensions (if any) will index batches.

     If both `scale_diag` and `scale_identity_multiplier` are `None`, then
     `scale` is the Identity matrix.

     Args:
       loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
         implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
         `b >= 0` and `k` is the event size.
       scale_diag: Non-zero, floating-point `Tensor` representing a diagonal
         matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
         and characterizes `b`-batches of `k x k` diagonal matrices added to
         `scale`. When both `scale_identity_multiplier` and `scale_diag` are
         `None` then `scale` is the `Identity`.
       scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
         a scaled-identity-matrix added to `scale`. May have shape
         `[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scaled
         `k x k` identity matrices added to `scale`. When both
         `scale_identity_multiplier` and `scale_diag` are `None` then `scale` is
         the `Identity`.
       validate_args: Python `bool`, default `False`. When `True` distribution
         parameters are checked for validity despite possibly degrading runtime
         performance. When `False` invalid inputs may silently render incorrect
         outputs.
       allow_nan_stats: Python `bool`, default `True`. When `True`,
         statistics (e.g., mean, mode, variance) use the value "`NaN`" to
         indicate the result is undefined. When `False`, an exception is raised
         if one or more of the statistic's batch members are undefined.
       name: Python `str` name prefixed to Ops created by this class.

     Raises:
       ValueError: if at most `scale_identity_multiplier` is specified.
     """
     parameters = dict(locals())
     with ops.name_scope(name):
       with ops.name_scope("init", values=[
           loc, scale_diag, scale_identity_multiplier]):
         # No need to validate_args while making diag_scale.  The returned
         # LinearOperatorDiag has an assert_non_singular method that is called by
         # the Bijector.
         scale = distribution_util.make_diag_scale(
             loc=loc,
             scale_diag=scale_diag,
             scale_identity_multiplier=scale_identity_multiplier,
             validate_args=False,
             assert_positive=False)
     super(VectorLaplaceDiag, self).__init__(
         loc=loc,
         scale=scale,
         validate_args=validate_args,
         allow_nan_stats=allow_nan_stats,
         name=name)
     self._parameters = parameters
	# Copyright 2017 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.
	# ==============================================================================
	"""Distribution of a vectorized Laplace, with uncorrelated components."""

	from __future__ import absolute_import
	from __future__ import division
	from __future__ import print_function

	from tensorflow.contrib.distributions.python.ops import distribution_util
	from tensorflow.contrib.distributions.python.ops import vector_laplace_linear_operator as vector_laplace_linop
	from tensorflow.python.framework import ops
	from tensorflow.python.util import deprecation


	__all__ = [
	"VectorLaplaceDiag",
	]


	class VectorLaplaceDiag(
	vector_laplace_linop.VectorLaplaceLinearOperator):
	"""The vectorization of the Laplace distribution on `R^k`.

	The vector laplace distribution is defined over `R^k`, and parameterized by
	a (batch of) length-`k` `loc` vector (the means) and a (batch of) `k x k`
	`scale` matrix: `covariance = 2 * scale @ scale.T`, where `@` denotes
	matrix-multiplication.

	#### Mathematical Details

	The probability density function (pdf) is,

	```none
	pdf(x; loc, scale) = exp(-\|\|y\|\|_1) / Z,
	y = inv(scale) @ (x - loc),
	Z = 2**k \|det(scale)\|,
	```

	where:

	* `loc` is a vector in `R^k`,
	* `scale` is a linear operator in `R^{k x k}`, `cov = scale @ scale.T`,
	* `Z` denotes the normalization constant, and,
	* `\|\|y\|\|_1` denotes the `l1` norm of `y`, `sum_i \|y_i\|.

	A (non-batch) `scale` matrix is:

	```none
	scale = diag(scale_diag + scale_identity_multiplier * ones(k))
	```

	where:

	* `scale_diag.shape = [k]`, and,
	* `scale_identity_multiplier.shape = []`.

	Additional leading dimensions (if any) will index batches.

	If both `scale_diag` and `scale_identity_multiplier` are `None`, then
	`scale` is the Identity matrix.

	The VectorLaplace distribution is a member of the [location-scale
	family](https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be
	constructed as,

	```none
	X = (X_1, ..., X_k), each X_i ~ Laplace(loc=0, scale=1)
	Y = (Y_1, ...,Y_k) = scale @ X + loc
	```

	#### About `VectorLaplace` and `Vector` distributions in TensorFlow.

	The `VectorLaplace` is a non-standard distribution that has useful properties.

	The marginals `Y_1, ..., Y_k` are not Laplace random variables, due to
	the fact that the sum of Laplace random variables is not Laplace.

	Instead, `Y` is a vector whose components are linear combinations of Laplace
	random variables. Thus, `Y` lives in the vector space generated by `vectors`
	of Laplace distributions. This allows the user to decide the mean and
	covariance (by setting `loc` and `scale`), while preserving some properties of
	the Laplace distribution. In particular, the tails of `Y_i` will be (up to
	polynomial factors) exponentially decaying.

	To see this last statement, note that the pdf of `Y_i` is the convolution of
	the pdf of `k` independent Laplace random variables. One can then show by
	induction that distributions with exponential (up to polynomial factors) tails
	are closed under convolution.

	#### Examples

	```python
	tfd = tf.contrib.distributions

	# Initialize a single 2-variate VectorLaplace.
	vla = tfd.VectorLaplaceDiag(
	loc=[1., -1],
	scale_diag=[1, 2.])

	vla.mean().eval()
	# ==> [1., -1]

	vla.stddev().eval()
	# ==> [1., 2] * sqrt(2)

	# Evaluate this on an observation in `R^2`, returning a scalar.
	vla.prob([-1., 0]).eval() # shape: []

	# Initialize a 3-batch, 2-variate scaled-identity VectorLaplace.
	vla = tfd.VectorLaplaceDiag(
	loc=[1., -1],
	scale_identity_multiplier=[1, 2., 3])

	vla.mean().eval() # shape: [3, 2]
	# ==> [[1., -1]
	# [1, -1],
	# [1, -1]]

	vla.stddev().eval() # shape: [3, 2]
	# ==> sqrt(2) * [[1., 1],
	# [2, 2],
	# [3, 3]]

	# Evaluate this on an observation in `R^2`, returning a length-3 vector.
	vla.prob([-1., 0]).eval() # shape: [3]

	# Initialize a 2-batch of 3-variate VectorLaplace's.
	vla = tfd.VectorLaplaceDiag(
	loc=[[1., 2, 3],
	[11, 22, 33]] # shape: [2, 3]
	scale_diag=[[1., 2, 3],
	[0.5, 1, 1.5]]) # shape: [2, 3]

	# Evaluate this on a two observations, each in `R^3`, returning a length-2
	# vector.
	x = [[-1., 0, 1],
	[-11, 0, 11.]] # shape: [2, 3].
	vla.prob(x).eval() # shape: [2]
	```

	"""

	@deprecation.deprecated(
	"2018-10-01",
	"The TensorFlow Distributions library has moved to "
	"TensorFlow Probability "
	"(https://github.com/tensorflow/probability). You "
	"should update all references to use `tfp.distributions` "
	"instead of `tf.contrib.distributions`.",
	warn_once=True)
	def __init__(self,
	loc=None,
	scale_diag=None,
	scale_identity_multiplier=None,
	validate_args=False,
	allow_nan_stats=True,
	name="VectorLaplaceDiag"):
	"""Construct Vector Laplace distribution on `R^k`.

	The `batch_shape` is the broadcast shape between `loc` and `scale`
	arguments.

	The `event_shape` is given by last dimension of the matrix implied by
	`scale`. The last dimension of `loc` (if provided) must broadcast with this.

	Recall that `covariance = 2 * scale @ scale.T`.

	```none
	scale = diag(scale_diag + scale_identity_multiplier * ones(k))
	```

	where:

	* `scale_diag.shape = [k]`, and,
	* `scale_identity_multiplier.shape = []`.

	Additional leading dimensions (if any) will index batches.

	If both `scale_diag` and `scale_identity_multiplier` are `None`, then
	`scale` is the Identity matrix.

	Args:
	loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
	implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
	`b >= 0` and `k` is the event size.
	scale_diag: Non-zero, floating-point `Tensor` representing a diagonal
	matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
	and characterizes `b`-batches of `k x k` diagonal matrices added to
	`scale`. When both `scale_identity_multiplier` and `scale_diag` are
	`None` then `scale` is the `Identity`.
	scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
	a scaled-identity-matrix added to `scale`. May have shape
	`[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scaled
	`k x k` identity matrices added to `scale`. When both
	`scale_identity_multiplier` and `scale_diag` are `None` then `scale` is
	the `Identity`.
	validate_args: Python `bool`, default `False`. When `True` distribution
	parameters are checked for validity despite possibly degrading runtime
	performance. When `False` invalid inputs may silently render incorrect
	outputs.
	allow_nan_stats: Python `bool`, default `True`. When `True`,
	statistics (e.g., mean, mode, variance) use the value "`NaN`" to
	indicate the result is undefined. When `False`, an exception is raised
	if one or more of the statistic's batch members are undefined.
	name: Python `str` name prefixed to Ops created by this class.

	Raises:
	ValueError: if at most `scale_identity_multiplier` is specified.
	"""
	parameters = dict(locals())
	with ops.name_scope(name):
	with ops.name_scope("init", values=[
	loc, scale_diag, scale_identity_multiplier]):
	# No need to validate_args while making diag_scale. The returned
	# LinearOperatorDiag has an assert_non_singular method that is called by
	# the Bijector.
	scale = distribution_util.make_diag_scale(
	loc=loc,
	scale_diag=scale_diag,
	scale_identity_multiplier=scale_identity_multiplier,
	validate_args=False,
	assert_positive=False)
	super(VectorLaplaceDiag, self).__init__(
	loc=loc,
	scale=scale,
	validate_args=validate_args,
	allow_nan_stats=allow_nan_stats,
	name=name)
	self._parameters = parameters