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tf.compat.v1.distributions.Categorical

Categorical distribution.

Inherits From: Distribution

tf.compat.v1.distributions.Categorical(
    logits=None, probs=None, dtype=tf.dtypes.int32, validate_args=False,
    allow_nan_stats=True, name='Categorical'
)

The Categorical distribution is parameterized by either probabilities or log-probabilities of a set of K classes. It is defined over the integers {0, 1, ..., K}.

The Categorical distribution is closely related to the OneHotCategorical and Multinomial distributions. The Categorical distribution can be intuited as generating samples according to argmax{ OneHotCategorical(probs) } itself being identical to argmax{ Multinomial(probs, total_count=1) }.

Mathematical Details

The probability mass function (pmf) is,

pmf(k; pi) = prod_j pi_j**[k == j]

Pitfalls

The number of classes, K, must not exceed:

the largest integer representable by self.dtype, i.e., 2**(mantissa_bits+1) (IEEE 754),
the maximum Tensor index, i.e., 2**31-1.

In other words,

K <= min(2**31-1, {
  tf.float16: 2**11,
  tf.float32: 2**24,
  tf.float64: 2**53 }[param.dtype])

Note: This condition is validated only when self.validate_args = True.

Examples

Creates a 3-class distribution with the 2nd class being most likely.

dist = Categorical(probs=[0.1, 0.5, 0.4])
n = 1e4
empirical_prob = tf.cast(
    tf.histogram_fixed_width(
      dist.sample(int(n)),
      [0., 2],
      nbins=3),
    dtype=tf.float32) / n
# ==> array([ 0.1005,  0.5037,  0.3958], dtype=float32)

Creates a 3-class distribution with the 2nd class being most likely. Parameterized by logits rather than probabilities.

dist = Categorical(logits=np.log([0.1, 0.5, 0.4])
n = 1e4
empirical_prob = tf.cast(
    tf.histogram_fixed_width(
      dist.sample(int(n)),
      [0., 2],
      nbins=3),
    dtype=tf.float32) / n
# ==> array([0.1045,  0.5047, 0.3908], dtype=float32)

Creates a 3-class distribution with the 3rd class being most likely. The distribution functions can be evaluated on counts.

# counts is a scalar.
p = [0.1, 0.4, 0.5]
dist = Categorical(probs=p)
dist.prob(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.prob(counts)  # Shape [2]

# p will be broadcast to shape [3, 5, 7, 3] to match counts.
counts = [[...]] # Shape [5, 7, 3]
dist.prob(counts)  # Shape [5, 7, 3]

Args
`logits`	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 `probs` should be passed in.
`probs`	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 `probs` should be passed in.
`dtype`	The type of the event samples (default: int32).
`validate_args`	Python `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.
`allow_nan_stats`	Python `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.
`name`	Python `str` name prefixed to Ops created by this class.

Attributes
`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.
`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.
`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_size`	Scalar `int32` tensor: the number of classes.
`logits`	Vector of coordinatewise logits.
`name`	Name prepended to all ops created by this `Distribution`.
`parameters`	Dictionary of parameters used to instantiate this `Distribution`.
`probs`	Vector of coordinatewise probabilities.
`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`.
`validate_args`	Python `bool` indicating possibly expensive checks are enabled.

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.

Args
`other`	`tfp.distributions.Distribution` instance.
`name`	Python `str` prepended to names of ops created by this function.

Args
`sample_shape`	`Tensor` or python list/tuple. Desired shape of a call to `sample()`.
`name`	name to prepend ops with.

Args
`sample_shape`	0D or 1D `int32` `Tensor`. Shape of the generated samples.
`seed`	Python integer seed for RNG
`name`	name to give to the op.

tf.compat.v1.distributions.Categorical

Mathematical Details

Pitfalls

Examples

Methods

batch_shape_tensor

cdf

copy

covariance

cross_entropy

entropy

event_shape_tensor

is_scalar_batch

is_scalar_event

kl_divergence

log_cdf

log_prob

log_survival_function

mean

mode

param_shapes

param_static_shapes

prob

quantile

sample

stddev

survival_function

variance

`batch_shape_tensor`

`cdf`

`copy`

`covariance`

`cross_entropy`

`entropy`

`event_shape_tensor`

`is_scalar_batch`

`is_scalar_event`

`kl_divergence`

`log_cdf`

`log_prob`

`log_survival_function`

`mean`

`mode`

`param_shapes`

`param_static_shapes`

`prob`

`quantile`

`sample`

`stddev`

`survival_function`

`variance`