`RelaxedBernoulli`

Inherits From: `RandomVariable`

RelaxedBernoulli distribution with temperature and logits parameters.

The RelaxedBernoulli is a distribution over the unit interval (0,1), which continuously approximates a Bernoulli. The degree of approximation is controlled by a temperature: as the temperaturegoes to 0 the RelaxedBernoulli becomes discrete with a distribution described by the `logits`

or `probs`

parameters, as the temperature goes to infinity the RelaxedBernoulli becomes the constant distribution that is identically 0.5.

The RelaxedBernoulli distribution is a reparameterized continuous distribution that is the binary special case of the RelaxedOneHotCategorical distribution (Maddison et al., 2016; Jang et al., 2016). For details on the binary special case see the appendix of Maddison et al. (2016) where it is referred to as BinConcrete. If you use this distribution, please cite both papers.

Some care needs to be taken for loss functions that depend on the log-probability of RelaxedBernoullis, because computing log-probabilities of the RelaxedBernoulli can suffer from underflow issues. In many case loss functions such as these are invariant under invertible transformations of the random variables. The KL divergence, found in the variational autoencoder loss, is an example. Because RelaxedBernoullis are sampled by a Logistic random variable followed by a `tf.sigmoid`

op, one solution is to treat the Logistic as the random variable and `tf.sigmoid`

as downstream. The KL divergences of two Logistics, which are always followed by a `tf.sigmoid`

op, is equivalent to evaluating KL divergences of RelaxedBernoulli samples. See Maddison et al., 2016 for more details where this distribution is called the BinConcrete.

An alternative approach is to evaluate Bernoulli log probability or KL directly on relaxed samples, as done in Jang et al., 2016. In this case, guarantees on the loss are usually violated. For instance, using a Bernoulli KL in a relaxed ELBO is no longer a lower bound on the log marginal probability of the observation. Thus care and early stopping are important.

Creates three continuous distributions, which approximate 3 Bernoullis with probabilities (0.1, 0.5, 0.4). Samples from these distributions will be in the unit interval (0,1).

```
temperature = 0.5
p = [0.1, 0.5, 0.4]
dist = RelaxedBernoulli(temperature, probs=p)
```

Creates three continuous distributions, which approximate 3 Bernoullis with logits (-2, 2, 0). Samples from these distributions will be in the unit interval (0,1).

```
temperature = 0.5
logits = [-2, 2, 0]
dist = RelaxedBernoulli(temperature, logits=logits)
```

Creates three continuous distributions, whose sigmoid approximate 3 Bernoullis with logits (-2, 2, 0).

```
temperature = 0.5
logits = [-2, 2, 0]
dist = Logistic(logits/temperature, 1./temperature)
samples = dist.sample()
sigmoid_samples = tf.sigmoid(samples)
# sigmoid_samples has the same distribution as samples from
# RelaxedBernoulli(temperature, logits=logits)
```

Creates three continuous distributions, which approximate 3 Bernoullis with logits (-2, 2, 0). Samples from these distributions will be in the unit interval (0,1). Because the temperature is very low, samples from these distributions are almost discrete, usually taking values very close to 0 or 1.

```
temperature = 1e-5
logits = [-2, 2, 0]
dist = RelaxedBernoulli(temperature, logits=logits)
```

Creates three continuous distributions, which approximate 3 Bernoullis with logits (-2, 2, 0). Samples from these distributions will be in the unit interval (0,1). Because the temperature is very high, samples from these distributions are usually close to the (0.5, 0.5, 0.5) vector.

```
temperature = 100
logits = [-2, 2, 0]
dist = RelaxedBernoulli(temperature, logits=logits)
```

Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables. 2016.

Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with Gumbel-Softmax. 2016.

`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.

: Python`allow_nan_stats`

`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.

`bijector`

Function transforming x => y.

`distribution`

Base distribution, p(x).

`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.

`logits`

Log-odds of `1`

.

`name`

Name prepended to all ops created by this `Distribution`

.

`parameters`

Dictionary of parameters used to instantiate this `Distribution`

.

`probs`

Probability of `1`

.

`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.

`shape`

Shape of random variable.

`temperature`

Distribution parameter for the location.

`validate_args`

Python `bool`

indicating possibly expensive checks are enabled.

**init**

```
__init__(
*args,
**kwargs
)
```

Construct RelaxedBernoulli distributions.

: An 0-D`temperature`

`Tensor`

, representing the temperature of a set of RelaxedBernoulli distributions. The temperature should be positive.: An N-D`logits`

`Tensor`

representing the log-odds of a positive event. Each entry in the`Tensor`

parametrizes an independent RelaxedBernoulli distribution where the probability of an event is sigmoid(logits). Only one of`logits`

or`probs`

should be passed in.: An N-D`probs`

`Tensor`

representing the probability of a positive event. Each entry in the`Tensor`

parameterizes an independent Bernoulli distribution. Only one of`logits`

or`probs`

should be passed in.: Python`validate_args`

`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.: Python`allow_nan_stats`

`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.: Python`name`

`str`

name prefixed to Ops created by this class.

: If both`ValueError`

`probs`

and`logits`

are passed, or if neither.

**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]
```

: A`x`

`Tensor`

or`SparseTensor`

of type`float32`

,`float64`

,`int32`

,`int64`

,`complex64`

or`complex128`

.: A name for the operation (optional).`name`

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

: A`x`

`Tensor`

. Must be one of the following types:`half`

,`bfloat16`

,`float32`

,`float64`

,`uint8`

,`int8`

,`int16`

,`int32`

,`int64`

,`complex64`

,`complex128`

,`string`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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

: A`x`

`Tensor`

of type`bool`

.: A`y`

`Tensor`

of type`bool`

.: A name for the operation (optional).`name`

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.: A name for the operation (optional).`name`

`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.: A name for the operation (optional).`name`

`x / y`

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

: If the inputs are complex.`TypeError`

**ge**

```
__ge__(
a,
*args
)
```

Returns the truth value of (x >= y) element-wise.

*NOTE*: `GreaterEqual`

supports broadcasting. More about broadcasting here

: A`x`

`Tensor`

. Must be one of the following types:`float32`

,`float64`

,`int32`

,`uint8`

,`int16`

,`int8`

,`int64`

,`bfloat16`

,`uint16`

,`half`

,`uint32`

,`uint64`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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.

: An ops.Tensor object.`tensor`

: The arguments to Tensor.__getitem__.`slice_spec`

: In the case of variable slice assignment, the Variable object to slice (i.e. tensor is the read-only view of this variable).`var`

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

: If a slice range is negative size.`ValueError`

: If the slice indices aren’t int, slice, or Ellipsis.`TypeError`

**gt**

```
__gt__(
a,
*args
)
```

Returns the truth value of (x > y) element-wise.

*NOTE*: `Greater`

supports broadcasting. More about broadcasting here

: A`x`

`Tensor`

. Must be one of the following types:`float32`

,`float64`

,`int32`

,`uint8`

,`int16`

,`int8`

,`int64`

,`bfloat16`

,`uint16`

,`half`

,`uint32`

,`uint64`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

A `Tensor`

of type `bool`

.

**invert**

```
__invert__(
a,
*args
)
```

Returns the truth value of NOT x element-wise.

: A`x`

`Tensor`

of type`bool`

.: A name for the operation (optional).`name`

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

: A`x`

`Tensor`

. Must be one of the following types:`float32`

,`float64`

,`int32`

,`uint8`

,`int16`

,`int8`

,`int64`

,`bfloat16`

,`uint16`

,`half`

,`uint32`

,`uint64`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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

: A`x`

`Tensor`

. Must be one of the following types:`float32`

,`float64`

,`int32`

,`uint8`

,`int16`

,`int8`

,`int64`

,`bfloat16`

,`uint16`

,`half`

,`uint32`

,`uint64`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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`

.: If`transpose_a`

`True`

,`a`

is transposed before multiplication.: If`transpose_b`

`True`

,`b`

is transposed before multiplication.: If`adjoint_a`

`True`

,`a`

is conjugated and transposed before multiplication.: If`adjoint_b`

`True`

,`b`

is conjugated and transposed before multiplication.: If`a_is_sparse`

`True`

,`a`

is treated as a sparse matrix.: If`b_is_sparse`

`True`

,`b`

is treated as a sparse matrix.: Name for the operation (optional).`name`

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.

: This is matrix product, not element-wise product.`Note`

: If transpose_a and adjoint_a, or transpose_b and adjoint_b are both set to True.`ValueError`

**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

: A`x`

`Tensor`

. Must be one of the following types:`int32`

,`int64`

,`bfloat16`

,`float32`

,`float64`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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., \(y = -x\).

: A`x`

`Tensor`

. Must be one of the following types:`half`

,`bfloat16`

,`float32`

,`float64`

,`int32`

,`int64`

,`complex64`

,`complex128`

.: A name for the operation (optional).`name`

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

: A`x`

`Tensor`

of type`bool`

.: A`y`

`Tensor`

of type`bool`

.: A name for the operation (optional).`name`

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]]
```

: A`x`

`Tensor`

of type`float32`

,`float64`

,`int32`

,`int64`

,`complex64`

, or`complex128`

.: A`y`

`Tensor`

of type`float32`

,`float64`

,`int32`

,`int64`

,`complex64`

, or`complex128`

.: A name for the operation (optional).`name`

A `Tensor`

.

**radd**

```
__radd__(
a,
*args
)
```

Returns x + y element-wise.

*NOTE*: `Add`

supports broadcasting. `AddN`

does not. More about broadcasting here

: A`x`

`Tensor`

. Must be one of the following types:`half`

,`bfloat16`

,`float32`

,`float64`

,`uint8`

,`int8`

,`int16`

,`int32`

,`int64`

,`complex64`

,`complex128`

,`string`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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

: A`x`

`Tensor`

of type`bool`

.: A`y`

`Tensor`

of type`bool`

.: A name for the operation (optional).`name`

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.: A name for the operation (optional).`name`

`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.: A name for the operation (optional).`name`

`x / y`

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

: If the inputs are complex.`TypeError`

**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`

.: If`transpose_a`

`True`

,`a`

is transposed before multiplication.: If`transpose_b`

`True`

,`b`

is transposed before multiplication.: If`adjoint_a`

`True`

,`a`

is conjugated and transposed before multiplication.: If`adjoint_b`

`True`

,`b`

is conjugated and transposed before multiplication.: If`a_is_sparse`

`True`

,`a`

is treated as a sparse matrix.: If`b_is_sparse`

`True`

,`b`

is treated as a sparse matrix.: Name for the operation (optional).`name`

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.

: This is matrix product, not element-wise product.`Note`

: If transpose_a and adjoint_a, or transpose_b and adjoint_b are both set to True.`ValueError`

**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

: A`x`

`Tensor`

. Must be one of the following types:`int32`

,`int64`

,`bfloat16`

,`float32`

,`float64`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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

: A`x`

`Tensor`

of type`bool`

.: A`y`

`Tensor`

of type`bool`

.: A name for the operation (optional).`name`

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]]
```

: A`x`

`Tensor`

of type`float32`

,`float64`

,`int32`

,`int64`

,`complex64`

, or`complex128`

.: A`y`

`Tensor`

of type`float32`

,`float64`

,`int32`

,`int64`

,`complex64`

, or`complex128`

.: A name for the operation (optional).`name`

A `Tensor`

.

**rsub**

```
__rsub__(
a,
*args
)
```

Returns x - y element-wise.

*NOTE*: `Subtract`

supports broadcasting. More about broadcasting here

: A`x`

`Tensor`

. Must be one of the following types:`half`

,`bfloat16`

,`float32`

,`float64`

,`uint8`

,`int8`

,`uint16`

,`int16`

,`int32`

,`int64`

,`complex64`

,`complex128`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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

: A`x`

`Tensor`

. Must be one of the following types:`half`

,`bfloat16`

,`float32`

,`float64`

,`uint8`

,`int8`

,`uint16`

,`int16`

,`int32`

,`int64`

,`complex64`

,`complex128`

.: A`y`

`Tensor`

. Must have the same type as`x`

.: A name for the operation (optional).`name`

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 to give to the op`name`

:`batch_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`

.: Python`name`

`str`

prepended to names of ops created by this function.

: a`cdf`

`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.

: A new instance of`distribution`

`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.

: Python`name`

`str`

prepended to names of ops created by this function.

: Floating-point`covariance`

`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.: Python`name`

`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.

: tf.BaseSession. The`session`

`tf.Session`

to use to evaluate this random variable. If none, the default session is used.: dict. A dictionary that maps`feed_dict`

`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 to give to the op`name`

:`event_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 == []`

.

: Python`name`

`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 == []`

.

: Python`name`

`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.: Python`name`

`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`

.: Python`name`

`str`

prepended to names of ops created by this function.

: a`logcdf`

`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`

.: Python`name`

`str`

prepended to names of ops created by this function.

: a`log_prob`

`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`

.: Python`name`

`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 to prepend ops with.`name`

`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`

.

: if`ValueError`

`sample_shape`

is a`TensorShape`

and is not fully defined.

`prob`

```
prob(
value,
name='prob'
)
```

Probability density/mass function.

:`value`

`float`

or`double`

`Tensor`

.: Python`name`

`str`

prepended to names of ops created by this function.

: a`prob`

`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`

.: Python`name`

`str`

prepended to names of ops created by this function.

: a`quantile`

`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.

: 0D or 1D`sample_shape`

`int32`

`Tensor`

. Shape of the generated samples.: Python integer seed for RNG`seed`

: name to give to the op.`name`

: a`samples`

`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`

.

: Python`name`

`str`

prepended to names of ops created by this function.

: Floating-point`stddev`

`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`

.: Python`name`

`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`

.

: Python`name`

`str`

prepended to names of ops created by this function.

: Floating-point`variance`

`Tensor`

with shape identical to`batch_shape + event_shape`

, i.e., the same shape as`self.mean()`

.

**array_priority**