path: root/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.distributions.Categorical.md

Categorical distribution.

The categorical distribution is parameterized by the log-probabilities
of a set of classes.

#### Examples

Creates a 3-class distiribution, with the 2nd class, the most likely to be
drawn from.

```python
p = [0.1, 0.5, 0.4]
dist = Categorical(p=p)
```

Creates a 3-class distiribution, with the 2nd class the most likely to be
drawn from, using logits.

```python
logits = [-50, 400, 40]
dist = Categorical(logits=logits)
```

Creates a 3-class distribution, with the 3rd class is most likely to be drawn.
The distribution functions can be evaluated on counts.

```python
# counts is a scalar.
p = [0.1, 0.4, 0.5]
dist = Categorical(p=p)
dist.pmf(0)  # Shape []

# p will be broadcast to [[0.1, 0.4, 0.5], [0.1, 0.4, 0.5]] to match counts.
counts = [1, 0]
dist.pmf(counts)  # Shape [2]

# p will be broadcast to shape [3, 5, 7, 3] to match counts.
counts = [[...]] # Shape [5, 7, 3]
dist.pmf(counts)  # Shape [5, 7, 3]
```
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#### `tf.contrib.distributions.Categorical.__init__(logits=None, p=None, dtype=tf.int32, validate_args=False, allow_nan_stats=True, name='Categorical')` {#Categorical.__init__}

Initialize Categorical distributions using class log-probabilities.

##### Args:


*  <b>`logits`</b>: An N-D `Tensor`, `N >= 1`, representing the log probabilities
      of a set of Categorical 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
      `p` should be passed in.
*  <b>`p`</b>: An N-D `Tensor`, `N >= 1`, representing the probabilities
      of a set of Categorical 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 `p` 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>: `Boolean`, 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.Categorical.allow_nan_stats` {#Categorical.allow_nan_stats}

Python boolean 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 boolean.


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#### `tf.contrib.distributions.Categorical.batch_shape(name='batch_shape')` {#Categorical.batch_shape}

Shape of a single sample from a single event index as a 1-D `Tensor`.

The product of the dimensions of the `batch_shape` is the number of
independent distributions of this kind the instance represents.

##### Args:


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

##### Returns:


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


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#### `tf.contrib.distributions.Categorical.cdf(value, name='cdf', **condition_kwargs)` {#Categorical.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.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### 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.Categorical.dtype` {#Categorical.dtype}

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


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

Shannon entropy in nats.


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#### `tf.contrib.distributions.Categorical.event_shape(name='event_shape')` {#Categorical.event_shape}

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`.


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#### `tf.contrib.distributions.Categorical.get_batch_shape()` {#Categorical.get_batch_shape}

Shape of a single sample from a single event index as a `TensorShape`.

Same meaning as `batch_shape`. May be only partially defined.

##### Returns:


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


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#### `tf.contrib.distributions.Categorical.get_event_shape()` {#Categorical.get_event_shape}

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

Same meaning as `event_shape`. May be only partially defined.

##### Returns:


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


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




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#### `tf.contrib.distributions.Categorical.is_reparameterized` {#Categorical.is_reparameterized}




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#### `tf.contrib.distributions.Categorical.log_cdf(value, name='log_cdf', **condition_kwargs)` {#Categorical.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.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


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


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#### `tf.contrib.distributions.Categorical.log_pdf(value, name='log_pdf', **condition_kwargs)` {#Categorical.log_pdf}

Log probability density function.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


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

##### Raises:


*  <b>`TypeError`</b>: if not `is_continuous`.


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#### `tf.contrib.distributions.Categorical.log_pmf(value, name='log_pmf', **condition_kwargs)` {#Categorical.log_pmf}

Log probability mass function.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


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

##### Raises:


*  <b>`TypeError`</b>: if `is_continuous`.


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#### `tf.contrib.distributions.Categorical.log_prob(value, name='log_prob', **condition_kwargs)` {#Categorical.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.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


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


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#### `tf.contrib.distributions.Categorical.log_survival_function(value, name='log_survival_function', **condition_kwargs)` {#Categorical.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.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:

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


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#### `tf.contrib.distributions.Categorical.logits` {#Categorical.logits}

Vector of coordinatewise logits.


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

Mean.


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

Mode.


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

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


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#### `tf.contrib.distributions.Categorical.num_classes` {#Categorical.num_classes}

Scalar `int32` tensor: the number of classes.


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#### `tf.contrib.distributions.Categorical.p` {#Categorical.p}

Vector of probabilities summing to one.

Each element is the probability of drawing that coordinate.


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

Shapes of parameters given the desired shape of a call to `sample()`.

Subclasses should override static 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.


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

param_shapes with static (i.e. TensorShape) shapes.

##### 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.


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

Dictionary of parameters used by this `Distribution`.


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#### `tf.contrib.distributions.Categorical.pdf(value, name='pdf', **condition_kwargs)` {#Categorical.pdf}

Probability density function.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


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

##### Raises:


*  <b>`TypeError`</b>: if not `is_continuous`.


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#### `tf.contrib.distributions.Categorical.pmf(value, name='pmf', **condition_kwargs)` {#Categorical.pmf}

Probability mass function.

##### Args:


*  <b>`value`</b>: `float` or `double` `Tensor`.
*  <b>`name`</b>: The name to give this op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


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

##### Raises:


*  <b>`TypeError`</b>: if `is_continuous`.


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#### `tf.contrib.distributions.Categorical.prob(value, name='prob', **condition_kwargs)` {#Categorical.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.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


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


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#### `tf.contrib.distributions.Categorical.sample(sample_shape=(), seed=None, name='sample', **condition_kwargs)` {#Categorical.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.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


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


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#### `tf.contrib.distributions.Categorical.sample_n(n, seed=None, name='sample_n', **condition_kwargs)` {#Categorical.sample_n}

Generate `n` samples.

##### Args:


*  <b>`n`</b>: `Scalar` `Tensor` of type `int32` or `int64`, the number of
    observations to sample.
*  <b>`seed`</b>: Python integer seed for RNG
*  <b>`name`</b>: name to give to the op.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:


*  <b>`samples`</b>: a `Tensor` with a prepended dimension (n,).

##### Raises:


*  <b>`TypeError`</b>: if `n` is not an integer type.


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#### `tf.contrib.distributions.Categorical.std(name='std')` {#Categorical.std}

Standard deviation.


- - -

#### `tf.contrib.distributions.Categorical.survival_function(value, name='survival_function', **condition_kwargs)` {#Categorical.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.
*  <b>`**condition_kwargs`</b>: Named arguments forwarded to subclass implementation.

##### Returns:

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


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

Python boolean indicated possibly expensive checks are enabled.


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

Variance.