# ed.RandomVariable

## Class RandomVariable

### Aliases:

• Class ed.RandomVariable
• Class ed.models.RandomVariable

Defined in edward/models/random_variable.py.

Base class for random variables.

A random variable is an object parameterized by tensors. It is equipped with methods such as the log-density, mean, and sample.

It also wraps a tensor, where the tensor corresponds to a sample from the random variable. This enables operations on the TensorFlow graph, allowing random variables to be used in conjunction with other TensorFlow ops.

The random variable’s shape is given by

sample_shape + batch_shape + event_shape,

where sample_shape is an optional argument representing the dimensions of samples drawn from the distribution (default is a scalar); batch_shape is the number of independent random variables (determined by the shape of its parameters); and event_shape is the shape of one draw from the distribution (e.g., Normal has a scalar event_shape; Dirichlet has a vector event_shape).

#### Notes

RandomVariable assumes use in a multiple inheritance setting. The child class must first inherit RandomVariable, then second inherit a class in tf.contrib.distributions. With Python’s method resolution order, this implies the following during initialization (using distributions.Bernoulli as an example):

1. Start the __init__() of the child class, which passes all *args, **kwargs to RandomVariable.
2. This in turn passes all *args, **kwargs to distributions.Bernoulli, completing the __init__() of distributions.Bernoulli.
3. Complete the __init__() of RandomVariable, which calls self.sample(), relying on the method from distributions.Bernoulli.
4. Complete the __init__() of the child class.

Methods from both RandomVariable and distributions.Bernoulli populate the namespace of the child class. Methods from RandomVariable will take higher priority if there are conflicts.

#### Examples

p = tf.constant(0.5)
x = Bernoulli(p)

z1 = tf.constant([[1.0, -0.8], [0.3, -1.0]])
z2 = tf.constant([[0.9, 0.2], [2.0, -0.1]])
x = Bernoulli(logits=tf.matmul(z1, z2))

mu = Normal(tf.constant(0.0), tf.constant(1.0))
x = Normal(mu, tf.constant(1.0))

## Properties

### sample_shape

Sample shape of random variable.

### shape

Shape of random variable.

## Methods

### init

__init__(
*args,
**kwargs
)

Create a new random variable.

#### Args:

• sample_shape: tf.TensorShape. Shape of samples to draw from the random variable.
• value: tf.Tensor. Fixed tensor to associate with random variable. Must have shape sample_shape + batch_shape + event_shape.
• collections: list. Optional list of graph collections (lists). The random variable is added to these collections. Defaults to [ed.random_variables()].

### 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]

#### Args:

• x: A Tensor or SparseTensor of type float32, float64, int32, int64, complex64 or complex128.
• name: A name for the operation (optional).

#### Returns:

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

#### Args:

• 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).

#### Returns:

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

#### Args:

• x: A Tensor of type bool.
• y: A Tensor of type bool.
• name: A name for the operation (optional).

#### Returns:

A Tensor of type bool.

### bool

__bool__()

### div

__div__(
a,
*args
)

Divide two values using Python 2 semantics. Used for Tensor.__div__.

#### Args:

• x: Tensor numerator of real numeric type.
• y: Tensor denominator of real numeric type.
• name: A name for the operation (optional).

#### Returns:

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.

#### Args:

• x: Tensor numerator of real numeric type.
• y: Tensor denominator of real numeric type.
• name: A name for the operation (optional).

#### Returns:

x / y rounded down (except possibly towards zero for negative integers).

#### Raises:

• 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

#### Args:

• x: A Tensor. Must be one of the following types: float32, float64, int32, int64, uint8, int16, int8, uint16, half, uint32, uint64, bfloat16.
• y: A Tensor. Must have the same type as x.
• name: A name for the operation (optional).

#### Returns:

A Tensor of type bool.

### getitem

__getitem__(
a,
*args
)

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 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]]

# 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.

#### Args:

• 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).

#### Returns:

The appropriate slice of “tensor”, based on “slice_spec”.

#### Raises:

• 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

#### Args:

• x: A Tensor. Must be one of the following types: float32, float64, int32, int64, uint8, int16, int8, uint16, half, uint32, uint64, bfloat16.
• y: A Tensor. Must have the same type as x.
• name: A name for the operation (optional).

#### Returns:

A Tensor of type bool.

### invert

__invert__(
a,
*args
)

Returns the truth value of NOT x element-wise.

#### Args:

• x: A Tensor of type bool.
• name: A name for the operation (optional).

#### Returns:

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

#### Args:

• x: A Tensor. Must be one of the following types: float32, float64, int32, int64, uint8, int16, int8, uint16, half, uint32, uint64, bfloat16.
• y: A Tensor. Must have the same type as x.
• name: A name for the operation (optional).

#### Returns:

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

#### Args:

• x: A Tensor. Must be one of the following types: float32, float64, int32, int64, uint8, int16, int8, uint16, half, uint32, uint64, bfloat16.
• y: A Tensor. Must have the same type as x.
• name: A name for the operation (optional).

#### Returns:

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.]])

#### Args:

• 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).

#### Returns:

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.

#### Raises:

• 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

#### Args:

• 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).

#### Returns:

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., $$y = -x$$.

#### Args:

• 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).

#### Returns:

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

#### Args:

• x: A Tensor of type bool.
• y: A Tensor of type bool.
• name: A name for the operation (optional).

#### Returns:

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]]

#### Args:

• 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).

#### Returns:

A Tensor.

### radd

__radd__(
a,
*args
)

Returns x + y element-wise.

NOTE: Add supports broadcasting. AddN does not. More about broadcasting here

#### Args:

• 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).

#### Returns:

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

#### Args:

• x: A Tensor of type bool.
• y: A Tensor of type bool.
• name: A name for the operation (optional).

#### Returns:

A Tensor of type bool.

### rdiv

__rdiv__(
a,
*args
)

Divide two values using Python 2 semantics. Used for Tensor.__div__.

#### Args:

• x: Tensor numerator of real numeric type.
• y: Tensor denominator of real numeric type.
• name: A name for the operation (optional).

#### Returns:

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.

#### Args:

• x: Tensor numerator of real numeric type.
• y: Tensor denominator of real numeric type.
• name: A name for the operation (optional).

#### Returns:

x / y rounded down (except possibly towards zero for negative integers).

#### Raises:

• 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.]])

#### Args:

• 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).

#### Returns:

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.

#### Raises:

• 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

#### Args:

• 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).

#### Returns:

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

#### Args:

• x: A Tensor of type bool.
• y: A Tensor of type bool.
• name: A name for the operation (optional).

#### Returns:

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]]

#### Args:

• 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).

#### Returns:

A Tensor.

### rsub

__rsub__(
a,
*args
)

Returns x - y element-wise.

NOTE: Subtract supports broadcasting. More about broadcasting here

#### Args:

• 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).

#### Returns:

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

#### Args:

• 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).

#### Returns:

A Tensor. Has the same type as x.

### truediv

__truediv__(
a,
*args
)

### xor

__xor__(
a,
*args
)

x ^ y = (x | y) & ~(x & y).

### 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.

#### Args:

• 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.

#### Examples

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())

### 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.

### value

value()

Get tensor that the random variable corresponds to.