LaplaceWithSoftplusScale
Inherits From: RandomVariable
Laplace with softplus applied to scale
.
allow_nan_stats
Python bool
describing behavior when a stat is undefined.
Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution’s pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student’s T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.
allow_nan_stats
: Python bool
.batch_shape
Shape of a single sample from a single event index as a TensorShape
.
May be partially defined or unknown.
The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
batch_shape
: TensorShape
, possibly unknown.dtype
The DType
of Tensor
s handled by this Distribution
.
event_shape
Shape of a single sample from a single batch as a TensorShape
.
May be partially defined or unknown.
event_shape
: TensorShape
, possibly unknown.loc
Distribution parameter for the location.
name
Name prepended to all ops created by this Distribution
.
parameters
Dictionary of parameters used to instantiate this Distribution
.
reparameterization_type
Describes how samples from the distribution are reparameterized.
Currently this is one of the static instances distributions.FULLY_REPARAMETERIZED
or distributions.NOT_REPARAMETERIZED
.
An instance of ReparameterizationType
.
sample_shape
Sample shape of random variable.
scale
Distribution parameter for scale.
shape
Shape of random variable.
validate_args
Python bool
indicating possibly expensive checks are enabled.
init
__init__(
*args,
**kwargs
)
abs
__abs__(
a,
*args
)
Computes the absolute value of a tensor.
Given a tensor x
of complex numbers, this operation returns a tensor of type float32
or float64
that is the absolute value of each element in x
. All elements in x
must be complex numbers of the form \(a + bj\). The absolute value is computed as \( \). For example:
x = tf.constant([[-2.25 + 4.75j], [-3.25 + 5.75j]])
tf.abs(x) # [5.25594902, 6.60492229]
x
: A Tensor
or SparseTensor
of type float32
, float64
, int32
, int64
, complex64
or complex128
.name
: A name for the operation (optional).A Tensor
or SparseTensor
the same size and type as x
with absolute values. Note, for complex64
or complex128
input, the returned Tensor
will be of type float32
or float64
, respectively.
add
__add__(
a,
*args
)
Returns x + y element-wise.
NOTE: Add
supports broadcasting. AddN
does not. More about broadcasting here
x
: A Tensor
. Must be one of the following types: half
, bfloat16
, float32
, float64
, uint8
, int8
, int16
, int32
, int64
, complex64
, complex128
, string
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
. Has the same type as x
.
and
__and__(
a,
*args
)
Returns the truth value of x AND y element-wise.
NOTE: LogicalAnd
supports broadcasting. More about broadcasting here
x
: A Tensor
of type bool
.y
: A Tensor
of type bool
.name
: A name for the operation (optional).A Tensor
of type bool
.
bool
__bool__()
div
__div__(
a,
*args
)
Divide two values using Python 2 semantics. Used for Tensor.__div__.
x
: Tensor
numerator of real numeric type.y
: Tensor
denominator of real numeric type.name
: A name for the operation (optional).x / y
returns the quotient of x and y.
eq
__eq__(other)
floordiv
__floordiv__(
a,
*args
)
Divides x / y
elementwise, rounding toward the most negative integer.
The same as tf.div(x,y)
for integers, but uses tf.floor(tf.div(x,y))
for floating point arguments so that the result is always an integer (though possibly an integer represented as floating point). This op is generated by x // y
floor division in Python 3 and in Python 2.7 with from __future__ import division
.
Note that for efficiency, floordiv
uses C semantics for negative numbers (unlike Python and Numpy).
x
and y
must have the same type, and the result will have the same type as well.
x
: Tensor
numerator of real numeric type.y
: Tensor
denominator of real numeric type.name
: A name for the operation (optional).x / y
rounded down (except possibly towards zero for negative integers).
TypeError
: If the inputs are complex.ge
__ge__(
a,
*args
)
Returns the truth value of (x >= y) element-wise.
NOTE: GreaterEqual
supports broadcasting. More about broadcasting here
x
: A Tensor
. Must be one of the following types: float32
, float64
, int32
, uint8
, int16
, int8
, int64
, bfloat16
, uint16
, half
, uint32
, uint64
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
of type bool
.
getitem
__getitem__(
a,
*args
)
Overload for Tensor.__getitem__.
This operation extracts the specified region from the tensor. The notation is similar to NumPy with the restriction that currently only support basic indexing. That means that using a non-scalar tensor as input is not currently allowed.
Some useful examples:
# strip leading and trailing 2 elements
foo = tf.constant([1,2,3,4,5,6])
print(foo[2:-2].eval()) # => [3,4]
# skip every row and reverse every column
foo = tf.constant([[1,2,3], [4,5,6], [7,8,9]])
print(foo[::2,::-1].eval()) # => [[3,2,1], [9,8,7]]
# Use scalar tensors as indices on both dimensions
print(foo[tf.constant(0), tf.constant(2)].eval()) # => 3
# Insert another dimension
foo = tf.constant([[1,2,3], [4,5,6], [7,8,9]])
print(foo[tf.newaxis, :, :].eval()) # => [[[1,2,3], [4,5,6], [7,8,9]]]
print(foo[:, tf.newaxis, :].eval()) # => [[[1,2,3]], [[4,5,6]], [[7,8,9]]]
print(foo[:, :, tf.newaxis].eval()) # => [[[1],[2],[3]], [[4],[5],[6]],
[[7],[8],[9]]]
# Ellipses (3 equivalent operations)
foo = tf.constant([[1,2,3], [4,5,6], [7,8,9]])
print(foo[tf.newaxis, :, :].eval()) # => [[[1,2,3], [4,5,6], [7,8,9]]]
print(foo[tf.newaxis, ...].eval()) # => [[[1,2,3], [4,5,6], [7,8,9]]]
print(foo[tf.newaxis].eval()) # => [[[1,2,3], [4,5,6], [7,8,9]]]
Notes: - tf.newaxis
is None
as in NumPy. - An implicit ellipsis is placed at the end of the slice_spec
- NumPy advanced indexing is currently not supported.
tensor
: An ops.Tensor object.slice_spec
: The arguments to Tensor.__getitem__.var
: In the case of variable slice assignment, the Variable object to slice (i.e. tensor is the read-only view of this variable).The appropriate slice of “tensor”, based on “slice_spec”.
ValueError
: If a slice range is negative size.TypeError
: If the slice indices aren’t int, slice, or Ellipsis.gt
__gt__(
a,
*args
)
Returns the truth value of (x > y) element-wise.
NOTE: Greater
supports broadcasting. More about broadcasting here
x
: A Tensor
. Must be one of the following types: float32
, float64
, int32
, uint8
, int16
, int8
, int64
, bfloat16
, uint16
, half
, uint32
, uint64
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
of type bool
.
invert
__invert__(
a,
*args
)
Returns the truth value of NOT x element-wise.
x
: A Tensor
of type bool
.name
: A name for the operation (optional).A Tensor
of type bool
.
iter
__iter__()
le
__le__(
a,
*args
)
Returns the truth value of (x <= y) element-wise.
NOTE: LessEqual
supports broadcasting. More about broadcasting here
x
: A Tensor
. Must be one of the following types: float32
, float64
, int32
, uint8
, int16
, int8
, int64
, bfloat16
, uint16
, half
, uint32
, uint64
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
of type bool
.
lt
__lt__(
a,
*args
)
Returns the truth value of (x < y) element-wise.
NOTE: Less
supports broadcasting. More about broadcasting here
x
: A Tensor
. Must be one of the following types: float32
, float64
, int32
, uint8
, int16
, int8
, int64
, bfloat16
, uint16
, half
, uint32
, uint64
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
of type bool
.
matmul
__matmul__(
a,
*args
)
Multiplies matrix a
by matrix b
, producing a
* b
.
The inputs must, following any transpositions, be tensors of rank >= 2 where the inner 2 dimensions specify valid matrix multiplication arguments, and any further outer dimensions match.
Both matrices must be of the same type. The supported types are: float16
, float32
, float64
, int32
, complex64
, complex128
.
Either matrix can be transposed or adjointed (conjugated and transposed) on the fly by setting one of the corresponding flag to True
. These are False
by default.
If one or both of the matrices contain a lot of zeros, a more efficient multiplication algorithm can be used by setting the corresponding a_is_sparse
or b_is_sparse
flag to True
. These are False
by default. This optimization is only available for plain matrices (rank-2 tensors) with datatypes bfloat16
or float32
.
For example:
# 2-D tensor `a`
# [[1, 2, 3],
# [4, 5, 6]]
a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3])
# 2-D tensor `b`
# [[ 7, 8],
# [ 9, 10],
# [11, 12]]
b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2])
# `a` * `b`
# [[ 58, 64],
# [139, 154]]
c = tf.matmul(a, b)
# 3-D tensor `a`
# [[[ 1, 2, 3],
# [ 4, 5, 6]],
# [[ 7, 8, 9],
# [10, 11, 12]]]
a = tf.constant(np.arange(1, 13, dtype=np.int32),
shape=[2, 2, 3])
# 3-D tensor `b`
# [[[13, 14],
# [15, 16],
# [17, 18]],
# [[19, 20],
# [21, 22],
# [23, 24]]]
b = tf.constant(np.arange(13, 25, dtype=np.int32),
shape=[2, 3, 2])
# `a` * `b`
# [[[ 94, 100],
# [229, 244]],
# [[508, 532],
# [697, 730]]]
c = tf.matmul(a, b)
# Since python >= 3.5 the @ operator is supported (see PEP 465).
# In TensorFlow, it simply calls the `tf.matmul()` function, so the
# following lines are equivalent:
d = a @ b @ [[10.], [11.]]
d = tf.matmul(tf.matmul(a, b), [[10.], [11.]])
a
: Tensor
of type float16
, float32
, float64
, int32
, complex64
, complex128
and rank > 1.b
: Tensor
with same type and rank as a
.transpose_a
: If True
, a
is transposed before multiplication.transpose_b
: If True
, b
is transposed before multiplication.adjoint_a
: If True
, a
is conjugated and transposed before multiplication.adjoint_b
: If True
, b
is conjugated and transposed before multiplication.a_is_sparse
: If True
, a
is treated as a sparse matrix.b_is_sparse
: If True
, b
is treated as a sparse matrix.name
: Name for the operation (optional).A Tensor
of the same type as a
and b
where each inner-most matrix is the product of the corresponding matrices in a
and b
, e.g. if all transpose or adjoint attributes are False
:
output
[…, i, j] = sum_k (a
[…, i, k] * b
[…, k, j]), for all indices i, j.
Note
: This is matrix product, not element-wise product.ValueError
: If transpose_a and adjoint_a, or transpose_b and adjoint_b are both set to True.mod
__mod__(
a,
*args
)
Returns element-wise remainder of division. When x < 0
xor y < 0
is
true, this follows Python semantics in that the result here is consistent with a flooring divide. E.g. floor(x / y) * y + mod(x, y) = x
.
NOTE: FloorMod
supports broadcasting. More about broadcasting here
x
: A Tensor
. Must be one of the following types: int32
, int64
, bfloat16
, float32
, float64
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
. Has the same type as x
.
mul
__mul__(
a,
*args
)
Dispatches cwise mul for “Dense*Dense" and “Dense*Sparse“.
neg
__neg__(
a,
*args
)
Computes numerical negative value element-wise.
I.e., \(y = -x\).
x
: A Tensor
. Must be one of the following types: half
, bfloat16
, float32
, float64
, int32
, int64
, complex64
, complex128
.name
: A name for the operation (optional).A Tensor
. Has the same type as x
.
nonzero
__nonzero__()
or
__or__(
a,
*args
)
Returns the truth value of x OR y element-wise.
NOTE: LogicalOr
supports broadcasting. More about broadcasting here
x
: A Tensor
of type bool
.y
: A Tensor
of type bool
.name
: A name for the operation (optional).A Tensor
of type bool
.
pow
__pow__(
a,
*args
)
Computes the power of one value to another.
Given a tensor x
and a tensor y
, this operation computes \(x^y\) for corresponding elements in x
and y
. For example:
x = tf.constant([[2, 2], [3, 3]])
y = tf.constant([[8, 16], [2, 3]])
tf.pow(x, y) # [[256, 65536], [9, 27]]
x
: A Tensor
of type float32
, float64
, int32
, int64
, complex64
, or complex128
.y
: A Tensor
of type float32
, float64
, int32
, int64
, complex64
, or complex128
.name
: A name for the operation (optional).A Tensor
.
radd
__radd__(
a,
*args
)
Returns x + y element-wise.
NOTE: Add
supports broadcasting. AddN
does not. More about broadcasting here
x
: A Tensor
. Must be one of the following types: half
, bfloat16
, float32
, float64
, uint8
, int8
, int16
, int32
, int64
, complex64
, complex128
, string
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
. Has the same type as x
.
rand
__rand__(
a,
*args
)
Returns the truth value of x AND y element-wise.
NOTE: LogicalAnd
supports broadcasting. More about broadcasting here
x
: A Tensor
of type bool
.y
: A Tensor
of type bool
.name
: A name for the operation (optional).A Tensor
of type bool
.
rdiv
__rdiv__(
a,
*args
)
Divide two values using Python 2 semantics. Used for Tensor.__div__.
x
: Tensor
numerator of real numeric type.y
: Tensor
denominator of real numeric type.name
: A name for the operation (optional).x / y
returns the quotient of x and y.
rfloordiv
__rfloordiv__(
a,
*args
)
Divides x / y
elementwise, rounding toward the most negative integer.
The same as tf.div(x,y)
for integers, but uses tf.floor(tf.div(x,y))
for floating point arguments so that the result is always an integer (though possibly an integer represented as floating point). This op is generated by x // y
floor division in Python 3 and in Python 2.7 with from __future__ import division
.
Note that for efficiency, floordiv
uses C semantics for negative numbers (unlike Python and Numpy).
x
and y
must have the same type, and the result will have the same type as well.
x
: Tensor
numerator of real numeric type.y
: Tensor
denominator of real numeric type.name
: A name for the operation (optional).x / y
rounded down (except possibly towards zero for negative integers).
TypeError
: If the inputs are complex.rmatmul
__rmatmul__(
a,
*args
)
Multiplies matrix a
by matrix b
, producing a
* b
.
The inputs must, following any transpositions, be tensors of rank >= 2 where the inner 2 dimensions specify valid matrix multiplication arguments, and any further outer dimensions match.
Both matrices must be of the same type. The supported types are: float16
, float32
, float64
, int32
, complex64
, complex128
.
Either matrix can be transposed or adjointed (conjugated and transposed) on the fly by setting one of the corresponding flag to True
. These are False
by default.
If one or both of the matrices contain a lot of zeros, a more efficient multiplication algorithm can be used by setting the corresponding a_is_sparse
or b_is_sparse
flag to True
. These are False
by default. This optimization is only available for plain matrices (rank-2 tensors) with datatypes bfloat16
or float32
.
For example:
# 2-D tensor `a`
# [[1, 2, 3],
# [4, 5, 6]]
a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3])
# 2-D tensor `b`
# [[ 7, 8],
# [ 9, 10],
# [11, 12]]
b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2])
# `a` * `b`
# [[ 58, 64],
# [139, 154]]
c = tf.matmul(a, b)
# 3-D tensor `a`
# [[[ 1, 2, 3],
# [ 4, 5, 6]],
# [[ 7, 8, 9],
# [10, 11, 12]]]
a = tf.constant(np.arange(1, 13, dtype=np.int32),
shape=[2, 2, 3])
# 3-D tensor `b`
# [[[13, 14],
# [15, 16],
# [17, 18]],
# [[19, 20],
# [21, 22],
# [23, 24]]]
b = tf.constant(np.arange(13, 25, dtype=np.int32),
shape=[2, 3, 2])
# `a` * `b`
# [[[ 94, 100],
# [229, 244]],
# [[508, 532],
# [697, 730]]]
c = tf.matmul(a, b)
# Since python >= 3.5 the @ operator is supported (see PEP 465).
# In TensorFlow, it simply calls the `tf.matmul()` function, so the
# following lines are equivalent:
d = a @ b @ [[10.], [11.]]
d = tf.matmul(tf.matmul(a, b), [[10.], [11.]])
a
: Tensor
of type float16
, float32
, float64
, int32
, complex64
, complex128
and rank > 1.b
: Tensor
with same type and rank as a
.transpose_a
: If True
, a
is transposed before multiplication.transpose_b
: If True
, b
is transposed before multiplication.adjoint_a
: If True
, a
is conjugated and transposed before multiplication.adjoint_b
: If True
, b
is conjugated and transposed before multiplication.a_is_sparse
: If True
, a
is treated as a sparse matrix.b_is_sparse
: If True
, b
is treated as a sparse matrix.name
: Name for the operation (optional).A Tensor
of the same type as a
and b
where each inner-most matrix is the product of the corresponding matrices in a
and b
, e.g. if all transpose or adjoint attributes are False
:
output
[…, i, j] = sum_k (a
[…, i, k] * b
[…, k, j]), for all indices i, j.
Note
: This is matrix product, not element-wise product.ValueError
: If transpose_a and adjoint_a, or transpose_b and adjoint_b are both set to True.rmod
__rmod__(
a,
*args
)
Returns element-wise remainder of division. When x < 0
xor y < 0
is
true, this follows Python semantics in that the result here is consistent with a flooring divide. E.g. floor(x / y) * y + mod(x, y) = x
.
NOTE: FloorMod
supports broadcasting. More about broadcasting here
x
: A Tensor
. Must be one of the following types: int32
, int64
, bfloat16
, float32
, float64
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
. Has the same type as x
.
rmul
__rmul__(
a,
*args
)
Dispatches cwise mul for “Dense*Dense" and “Dense*Sparse“.
ror
__ror__(
a,
*args
)
Returns the truth value of x OR y element-wise.
NOTE: LogicalOr
supports broadcasting. More about broadcasting here
x
: A Tensor
of type bool
.y
: A Tensor
of type bool
.name
: A name for the operation (optional).A Tensor
of type bool
.
rpow
__rpow__(
a,
*args
)
Computes the power of one value to another.
Given a tensor x
and a tensor y
, this operation computes \(x^y\) for corresponding elements in x
and y
. For example:
x = tf.constant([[2, 2], [3, 3]])
y = tf.constant([[8, 16], [2, 3]])
tf.pow(x, y) # [[256, 65536], [9, 27]]
x
: A Tensor
of type float32
, float64
, int32
, int64
, complex64
, or complex128
.y
: A Tensor
of type float32
, float64
, int32
, int64
, complex64
, or complex128
.name
: A name for the operation (optional).A Tensor
.
rsub
__rsub__(
a,
*args
)
Returns x - y element-wise.
NOTE: Subtract
supports broadcasting. More about broadcasting here
x
: A Tensor
. Must be one of the following types: half
, bfloat16
, float32
, float64
, uint8
, int8
, uint16
, int16
, int32
, int64
, complex64
, complex128
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
. Has the same type as x
.
rtruediv
__rtruediv__(
a,
*args
)
rxor
__rxor__(
a,
*args
)
x ^ y = (x | y) & ~(x & y).
sub
__sub__(
a,
*args
)
Returns x - y element-wise.
NOTE: Subtract
supports broadcasting. More about broadcasting here
x
: A Tensor
. Must be one of the following types: half
, bfloat16
, float32
, float64
, uint8
, int8
, uint16
, int16
, int32
, int64
, complex64
, complex128
.y
: A Tensor
. Must have the same type as x
.name
: A name for the operation (optional).A Tensor
. Has the same type as x
.
truediv
__truediv__(
a,
*args
)
xor
__xor__(
a,
*args
)
x ^ y = (x | y) & ~(x & y).
batch_shape_tensor
batch_shape_tensor(name='batch_shape_tensor')
Shape of a single sample from a single event index as a 1-D Tensor
.
The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
name
: name to give to the opbatch_shape
: Tensor
.cdf
cdf(
value,
name='cdf'
)
Cumulative distribution function.
Given random variable X
, the cumulative distribution function cdf
is:
cdf(x) := P[X <= x]
value
: float
or double
Tensor
.name
: Python str
prepended to names of ops created by this function.cdf
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.copy
copy(**override_parameters_kwargs)
Creates a deep copy of the distribution.
Note: the copy distribution may continue to depend on the original initialization arguments.
**override_parameters_kwargs: String/value dictionary of initialization arguments to override with new values.
distribution
: A new instance of type(self)
initialized from the union of self.parameters and override_parameters_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs)
.covariance
covariance(name='covariance')
Covariance.
Covariance is (possibly) defined only for non-scalar-event distributions.
For example, for a length-k
, vector-valued distribution, it is calculated as,
Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
where Cov
is a (batch of) k x k
matrix, 0 <= (i, j) < k
, and E
denotes expectation.
Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance
shall return a (batch of) matrices under some vectorization of the events, i.e.,
Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
where Cov
is a (batch of) k' x k'
matrices, 0 <= (i, j) < k' = reduce_prod(event_shape)
, and Vec
is some function mapping indices of this distribution’s event dimensions to indices of a length-k'
vector.
name
: Python str
prepended to names of ops created by this function.covariance
: Floating-point Tensor
with shape [B1, ..., Bn, k', k']
where the first n
dimensions are batch coordinates and k' = reduce_prod(self.event_shape)
.cross_entropy
cross_entropy(
other,
name='cross_entropy'
)
Computes the (Shannon) cross entropy.
Denote this distribution (self
) by P
and the other
distribution by Q
. Assuming P, Q
are absolutely continuous with respect to one another and permit densities p(x) dr(x)
and q(x) dr(x)
, (Shanon) cross entropy is defined as:
H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
where F
denotes the support of the random variable X ~ P
.
other
: tf.distributions.Distribution
instance.name
: Python str
prepended to names of ops created by this function.cross_entropy
: self.dtype
Tensor
with shape [B1, ..., Bn]
representing n
different calculations of (Shanon) cross entropy.entropy
entropy(name='entropy')
Shannon entropy in nats.
eval
eval(
session=None,
feed_dict=None
)
In a session, computes and returns the value of this random variable.
This is not a graph construction method, it does not add ops to the graph.
This convenience method requires a session where the graph containing this variable has been launched. If no session is passed, the default session is used.
session
: tf.BaseSession. The tf.Session
to use to evaluate this random variable. If none, the default session is used.feed_dict
: dict. A dictionary that maps tf.Tensor
objects to feed values. See tf.Session.run()
for a description of the valid feed values.x = Normal(0.0, 1.0)
with tf.Session() as sess:
# Usage passing the session explicitly.
print(x.eval(sess))
# Usage with the default session. The 'with' block
# above makes 'sess' the default session.
print(x.eval())
event_shape_tensor
event_shape_tensor(name='event_shape_tensor')
Shape of a single sample from a single batch as a 1-D int32 Tensor
.
name
: name to give to the opevent_shape
: Tensor
.get_ancestors
get_ancestors(collection=None)
Get ancestor random variables.
get_blanket
get_blanket(collection=None)
Get the random variable’s Markov blanket.
get_children
get_children(collection=None)
Get child random variables.
get_descendants
get_descendants(collection=None)
Get descendant random variables.
get_parents
get_parents(collection=None)
Get parent random variables.
get_shape
get_shape()
Get shape of random variable.
get_siblings
get_siblings(collection=None)
Get sibling random variables.
get_variables
get_variables(collection=None)
Get TensorFlow variables that the random variable depends on.
is_scalar_batch
is_scalar_batch(name='is_scalar_batch')
Indicates that batch_shape == []
.
name
: Python str
prepended to names of ops created by this function.is_scalar_batch
: bool
scalar Tensor
.is_scalar_event
is_scalar_event(name='is_scalar_event')
Indicates that event_shape == []
.
name
: Python str
prepended to names of ops created by this function.is_scalar_event
: bool
scalar Tensor
.kl_divergence
kl_divergence(
other,
name='kl_divergence'
)
Computes the Kullback–Leibler divergence.
Denote this distribution (self
) by p
and the other
distribution by q
. Assuming p, q
are absolutely continuous with respect to reference measure r
, the KL divergence is defined as:
KL[p, q] = E_p[log(p(X)/q(X))]
= -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
= H[p, q] - H[p]
where F
denotes the support of the random variable X ~ p
, H[., .]
denotes (Shanon) cross entropy, and H[.]
denotes (Shanon) entropy.
other
: tf.distributions.Distribution
instance.name
: Python str
prepended to names of ops created by this function.kl_divergence
: self.dtype
Tensor
with shape [B1, ..., Bn]
representing n
different calculations of the Kullback-Leibler divergence.log_cdf
log_cdf(
value,
name='log_cdf'
)
Log cumulative distribution function.
Given random variable X
, the cumulative distribution function cdf
is:
log_cdf(x) := Log[ P[X <= x] ]
Often, a numerical approximation can be used for log_cdf(x)
that yields a more accurate answer than simply taking the logarithm of the cdf
when x << -1
.
value
: float
or double
Tensor
.name
: Python str
prepended to names of ops created by this function.logcdf
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.log_prob
log_prob(
value,
name='log_prob'
)
Log probability density/mass function.
value
: float
or double
Tensor
.name
: Python str
prepended to names of ops created by this function.log_prob
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.log_survival_function
log_survival_function(
value,
name='log_survival_function'
)
Log survival function.
Given random variable X
, the survival function is defined:
log_survival_function(x) = Log[ P[X > x] ]
= Log[ 1 - P[X <= x] ]
= Log[ 1 - cdf(x) ]
Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x)
when x >> 1
.
value
: float
or double
Tensor
.name
: Python str
prepended to names of ops created by this function.Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.
mean
mean(name='mean')
Mean.
mode
mode(name='mode')
Mode.
param_shapes
param_shapes(
cls,
sample_shape,
name='DistributionParamShapes'
)
Shapes of parameters given the desired shape of a call to sample()
.
This is a class method that describes what key/value arguments are required to instantiate the given Distribution
so that a particular shape is returned for that instance’s call to sample()
.
Subclasses should override class method _param_shapes
.
sample_shape
: Tensor
or python list/tuple. Desired shape of a call to sample()
.name
: name to prepend ops with.dict
of parameter name to Tensor
shapes.
param_static_shapes
param_static_shapes(
cls,
sample_shape
)
param_shapes with static (i.e. TensorShape
) shapes.
This is a class method that describes what key/value arguments are required to instantiate the given Distribution
so that a particular shape is returned for that instance’s call to sample()
. Assumes that the sample’s shape is known statically.
Subclasses should override class method _param_shapes
to return constant-valued tensors when constant values are fed.
sample_shape
: TensorShape
or python list/tuple. Desired shape of a call to sample()
.dict
of parameter name to TensorShape
.
ValueError
: if sample_shape
is a TensorShape
and is not fully defined.prob
prob(
value,
name='prob'
)
Probability density/mass function.
value
: float
or double
Tensor
.name
: Python str
prepended to names of ops created by this function.prob
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.quantile
quantile(
value,
name='quantile'
)
Quantile function. Aka “inverse cdf” or “percent point function”.
Given random variable X
and p in [0, 1]
, the quantile
is:
quantile(p) := x such that P[X <= x] == p
value
: float
or double
Tensor
.name
: Python str
prepended to names of ops created by this function.quantile
: a Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.sample
sample(
sample_shape=(),
seed=None,
name='sample'
)
Generate samples of the specified shape.
Note that a call to sample()
without arguments will generate a single sample.
sample_shape
: 0D or 1D int32
Tensor
. Shape of the generated samples.seed
: Python integer seed for RNGname
: name to give to the op.samples
: a Tensor
with prepended dimensions sample_shape
.stddev
stddev(name='stddev')
Standard deviation.
Standard deviation is defined as,
stddev = E[(X - E[X])**2]**0.5
where X
is the random variable associated with this distribution, E
denotes expectation, and stddev.shape = batch_shape + event_shape
.
name
: Python str
prepended to names of ops created by this function.stddev
: Floating-point Tensor
with shape identical to batch_shape + event_shape
, i.e., the same shape as self.mean()
.survival_function
survival_function(
value,
name='survival_function'
)
Survival function.
Given random variable X
, the survival function is defined:
survival_function(x) = P[X > x]
= 1 - P[X <= x]
= 1 - cdf(x).
value
: float
or double
Tensor
.name
: Python str
prepended to names of ops created by this function.Tensor
of shape sample_shape(x) + self.batch_shape
with values of type self.dtype
.
value
value()
Get tensor that the random variable corresponds to.
variance
variance(name='variance')
Variance.
Variance is defined as,
Var = E[(X - E[X])**2]
where X
is the random variable associated with this distribution, E
denotes expectation, and Var.shape = batch_shape + event_shape
.
name
: Python str
prepended to names of ops created by this function.variance
: Floating-point Tensor
with shape identical to batch_shape + event_shape
, i.e., the same shape as self.mean()
.array_priority