path: root/tensorflow/g3doc/api_docs/python/functions_and_classes/shard0/tf.contrib.distributions.RelaxedOneHotCategorical.md

RelaxedOneHotCategorical distribution with temperature and logits.

The RelaxedOneHotCategorical is a distribution over random probability
vectors, vectors of positive real values that sum to one, which continuously
approximates a OneHotCategorical. The degree of approximation is controlled by
a temperature: as the temperaturegoes to 0 the RelaxedOneHotCategorical
becomes discrete with a distribution described by the `logits` or `probs`
parameters, as the temperature goes to infinity the RelaxedOneHotCategorical
becomes the constant distribution that is identically the constant vector of
(1/event_size, ..., 1/event_size).

The RelaxedOneHotCategorical distribution was concurrently introduced as the
Gumbel-Softmax (Jang et al., 2016) and Concrete (Maddison et al., 2016)
distributions for use as a reparameterized continuous approximation to the
`Categorical` one-hot distribution. If you use this distribution, please cite
both papers.

#### Examples

Creates a continuous distribution, which approximates a 3-class one-hot
categorical distiribution. The 2nd class is the most likely to be the
largest component in samples drawn from this distribution.

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

Creates a continuous distribution, which approximates a 3-class one-hot
categorical distiribution. The 2nd class is the most likely to be the
largest component in samples drawn from this distribution.

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

Creates a continuous distribution, which approximates a 3-class one-hot
categorical distiribution. Because the temperature is very low, samples from
this distribution are almost discrete, with one component almost 1 and the
others nearly 0. The 2nd class is the most likely to be the largest component
in samples drawn from this distribution.

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

Creates a continuous distribution, which approximates a 3-class one-hot
categorical distiribution. Because the temperature is very high, samples from
this distribution are usually close to the (1/3, 1/3, 1/3) vector. The 2nd
class is still the most likely to be the largest component
in samples drawn from this distribution.

```python
temperature = 10
logits = [-2, 2, 0]
dist = RelaxedOneHotCategorical(temperature, logits=logits)
```

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

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

#### `tf.contrib.distributions.RelaxedOneHotCategorical.__init__(temperature, logits=None, probs=None, dtype=tf.float32, validate_args=False, allow_nan_stats=True, name='RelaxedOneHotCategorical')` {#RelaxedOneHotCategorical.__init__}

Initialize RelaxedOneHotCategorical using class log-probabilities.

##### Args:


*  <b>`temperature`</b>: An 0-D `Tensor`, representing the temperature
    of a set of RelaxedOneHotCategorical distributions. The temperature
    should be positive.
*  <b>`logits`</b>: An N-D `Tensor`, `N >= 1`, representing the log probabilities
    of a set of RelaxedOneHotCategorical distributions. The first
    `N - 1` dimensions index into a batch of independent distributions and
    the last dimension represents a vector of logits for each class. Only
    one of `logits` or `probs` should be passed in.
*  <b>`probs`</b>: An N-D `Tensor`, `N >= 1`, representing the probabilities
    of a set of RelaxedOneHotCategorical distributions. The first `N - 1`
    dimensions index into a batch of independent distributions and the last
    dimension represents a vector of probabilities for each class. Only one
    of `logits` or `probs` should be passed in.
*  <b>`dtype`</b>: The type of the event samples (default: int32).
*  <b>`validate_args`</b>: Unused in this distribution.
*  <b>`allow_nan_stats`</b>: Python `bool`, default `True`. If `False`, raise an
    exception if a statistic (e.g. mean/mode/etc...) is undefined for any
    batch member. If `True`, batch members with valid parameters leading to
    undefined statistics will return NaN for this statistic.
*  <b>`name`</b>: A name for this distribution (optional).


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#### `tf.contrib.distributions.RelaxedOneHotCategorical.allow_nan_stats` {#RelaxedOneHotCategorical.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.

##### Returns:


*  <b>`allow_nan_stats`</b>: Python `bool`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.batch_shape` {#RelaxedOneHotCategorical.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.

##### Returns:


*  <b>`batch_shape`</b>: `TensorShape`, possibly unknown.


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#### `tf.contrib.distributions.RelaxedOneHotCategorical.batch_shape_tensor(name='batch_shape_tensor')` {#RelaxedOneHotCategorical.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.

##### Args:


*  <b>`name`</b>: name to give to the op

##### Returns:


*  <b>`batch_shape`</b>: `Tensor`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.bijector` {#RelaxedOneHotCategorical.bijector}

Function transforming x => y.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.cdf(value, name='cdf')` {#RelaxedOneHotCategorical.cdf}

Cumulative distribution function.

Given random variable `X`, the cumulative distribution function `cdf` is:

```
cdf(x) := P[X <= x]
```

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`cdf`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.


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#### `tf.contrib.distributions.RelaxedOneHotCategorical.copy(**override_parameters_kwargs)` {#RelaxedOneHotCategorical.copy}

Creates a deep copy of the distribution.

Note: the copy distribution may continue to depend on the original
intialization arguments.

##### Args:


*  <b>`**override_parameters_kwargs`</b>: String/value dictionary of initialization
    arguments to override with new values.

##### Returns:


*  <b>`distribution`</b>: A new instance of `type(self)` intitialized from the union
    of self.parameters and override_parameters_kwargs, i.e.,
    `dict(self.parameters, **override_parameters_kwargs)`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.covariance(name='covariance')` {#RelaxedOneHotCategorical.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,

```none
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.,

```none
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.

##### Args:


*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`covariance`</b>: Floating-point `Tensor` with shape `[B1, ..., Bn, k', k']`
    where the first `n` dimensions are batch coordinates and
    `k' = reduce_prod(self.event_shape)`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.distribution` {#RelaxedOneHotCategorical.distribution}

Base distribution, p(x).


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.dtype` {#RelaxedOneHotCategorical.dtype}

The `DType` of `Tensor`s handled by this `Distribution`.


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#### `tf.contrib.distributions.RelaxedOneHotCategorical.entropy(name='entropy')` {#RelaxedOneHotCategorical.entropy}

Shannon entropy in nats.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.event_shape` {#RelaxedOneHotCategorical.event_shape}

Shape of a single sample from a single batch as a `TensorShape`.

May be partially defined or unknown.

##### Returns:


*  <b>`event_shape`</b>: `TensorShape`, possibly unknown.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.event_shape_tensor(name='event_shape_tensor')` {#RelaxedOneHotCategorical.event_shape_tensor}

Shape of a single sample from a single batch as a 1-D int32 `Tensor`.

##### Args:


*  <b>`name`</b>: name to give to the op

##### Returns:


*  <b>`event_shape`</b>: `Tensor`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.is_continuous` {#RelaxedOneHotCategorical.is_continuous}




- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.is_scalar_batch(name='is_scalar_batch')` {#RelaxedOneHotCategorical.is_scalar_batch}

Indicates that `batch_shape == []`.

##### Args:


*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`is_scalar_batch`</b>: `bool` scalar `Tensor`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.is_scalar_event(name='is_scalar_event')` {#RelaxedOneHotCategorical.is_scalar_event}

Indicates that `event_shape == []`.

##### Args:


*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`is_scalar_event`</b>: `bool` scalar `Tensor`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.log_cdf(value, name='log_cdf')` {#RelaxedOneHotCategorical.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`.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`logcdf`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.log_prob(value, name='log_prob')` {#RelaxedOneHotCategorical.log_prob}

Log probability density/mass function (depending on `is_continuous`).

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`log_prob`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.log_survival_function(value, name='log_survival_function')` {#RelaxedOneHotCategorical.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`.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.

##### Returns:

  `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type
    `self.dtype`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.mean(name='mean')` {#RelaxedOneHotCategorical.mean}

Mean.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.mode(name='mode')` {#RelaxedOneHotCategorical.mode}

Mode.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.name` {#RelaxedOneHotCategorical.name}

Name prepended to all ops created by this `Distribution`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.param_shapes(cls, sample_shape, name='DistributionParamShapes')` {#RelaxedOneHotCategorical.param_shapes}

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`.

##### Args:


*  <b>`sample_shape`</b>: `Tensor` or python list/tuple. Desired shape of a call to
    `sample()`.
*  <b>`name`</b>: name to prepend ops with.

##### Returns:

  `dict` of parameter name to `Tensor` shapes.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.param_static_shapes(cls, sample_shape)` {#RelaxedOneHotCategorical.param_static_shapes}

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.

##### Args:


*  <b>`sample_shape`</b>: `TensorShape` or python list/tuple. Desired shape of a call
    to `sample()`.

##### Returns:

  `dict` of parameter name to `TensorShape`.

##### Raises:


*  <b>`ValueError`</b>: if `sample_shape` is a `TensorShape` and is not fully defined.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.parameters` {#RelaxedOneHotCategorical.parameters}

Dictionary of parameters used to instantiate this `Distribution`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.prob(value, name='prob')` {#RelaxedOneHotCategorical.prob}

Probability density/mass function (depending on `is_continuous`).

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`prob`</b>: a `Tensor` of shape `sample_shape(x) + self.batch_shape` with
    values of type `self.dtype`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.reparameterization_type` {#RelaxedOneHotCategorical.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`.

##### Returns:

  An instance of `ReparameterizationType`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.sample(sample_shape=(), seed=None, name='sample')` {#RelaxedOneHotCategorical.sample}

Generate samples of the specified shape.

Note that a call to `sample()` without arguments will generate a single
sample.

##### Args:


*  <b>`sample_shape`</b>: 0D or 1D `int32` `Tensor`. Shape of the generated samples.
*  <b>`seed`</b>: Python integer seed for RNG
*  <b>`name`</b>: name to give to the op.

##### Returns:


*  <b>`samples`</b>: a `Tensor` with prepended dimensions `sample_shape`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.stddev(name='stddev')` {#RelaxedOneHotCategorical.stddev}

Standard deviation.

Standard deviation is defined as,

```none
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`.

##### Args:


*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`stddev`</b>: Floating-point `Tensor` with shape identical to
    `batch_shape + event_shape`, i.e., the same shape as `self.mean()`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.survival_function(value, name='survival_function')` {#RelaxedOneHotCategorical.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).
```

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.

##### Returns:

  `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type
    `self.dtype`.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.validate_args` {#RelaxedOneHotCategorical.validate_args}

Python `bool` indicating possibly expensive checks are enabled.


- - -

#### `tf.contrib.distributions.RelaxedOneHotCategorical.variance(name='variance')` {#RelaxedOneHotCategorical.variance}

Variance.

Variance is defined as,

```none
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`.

##### Args:


*  <b>`name`</b>: The name to give this op.

##### Returns:


*  <b>`variance`</b>: Floating-point `Tensor` with shape identical to
    `batch_shape + event_shape`, i.e., the same shape as `self.mean()`.