# tf.contrib.distributions.bijectors.Gumbel

## Class Gumbel

Inherits From: Bijector

Compute Y = g(X) = exp(-exp(-(X - loc) / scale)).

This bijector maps inputs from [-inf, inf] to [0, 1]. The inverse of the bijector applied to a uniform random variableX ~ U(0, 1) gives back a random variable with the Gumbel distribution:

Y ~ Gumbel(loc, scale)
pdf(y; loc, scale) = exp(
-( (y - loc) / scale + exp(- (y - loc) / scale) ) ) / scale


## Properties

### dtype

dtype of Tensors transformable by this distribution.

### event_ndims

Returns then number of event dimensions this bijector operates on.

### graph_parents

Returns this Bijector's graph_parents as a Python list.

### is_constant_jacobian

Returns true iff the Jacobian is not a function of x.

#### Returns:

• is_constant_jacobian: Python bool.

### loc

The loc in Y = g(X) = exp(-exp(-(X - loc) / scale)).

### name

Returns the string name of this Bijector.

### scale

This is scale in Y = g(X) = exp(-exp(-(X - loc) / scale)).

### validate_args

Returns True if Tensor arguments will be validated.

## Methods

### __init__

__init__(
loc=0.0,
scale=1.0,
event_ndims=0,
validate_args=False,
name='gumbel'
)


Instantiates the Gumbel bijector.

#### Args:

• loc: Float-like Tensor that is the same dtype and is broadcastable with scale. This is loc in Y = g(X) = exp(-exp(-(X - loc) / scale)).
• scale: Positive Float-like Tensor that is the same dtype and is broadcastable with loc. This is scale in Y = g(X) = exp(-exp(-(X - loc) / scale)).
• event_ndims: Python scalar indicating the number of dimensions associated with a particular draw from the distribution.
• validate_args: Python bool indicating whether arguments should be checked for correctness.
• name: Python str name given to ops managed by this object.

### forward

forward(
x,
name='forward'
)


Returns the forward Bijector evaluation, i.e., X = g(Y).

#### Args:

• x: Tensor. The input to the "forward" evaluation.
• name: The name to give this op.

#### Returns:

Tensor.

#### Raises:

• TypeError: if self.dtype is specified and x.dtype is not self.dtype.
• NotImplementedError: if _forward is not implemented.

### forward_event_shape

forward_event_shape(input_shape)


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

Same meaning as forward_event_shape_tensor. May be only partially defined.

#### Args:

• input_shape: TensorShape indicating event-portion shape passed into forward function.

#### Returns:

• forward_event_shape_tensor: TensorShape indicating event-portion shape after applying forward. Possibly unknown.

### forward_event_shape_tensor

forward_event_shape_tensor(
input_shape,
name='forward_event_shape_tensor'
)


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

#### Args:

• input_shape: Tensor, int32 vector indicating event-portion shape passed into forward function.
• name: name to give to the op

#### Returns:

• forward_event_shape_tensor: Tensor, int32 vector indicating event-portion shape after applying forward.

### forward_log_det_jacobian

forward_log_det_jacobian(
x,
name='forward_log_det_jacobian'
)


Returns both the forward_log_det_jacobian.

#### Args:

• x: Tensor. The input to the "forward" Jacobian evaluation.
• name: The name to give this op.

#### Returns:

Tensor, if this bijector is injective. If not injective this is not implemented.

#### Raises:

• TypeError: if self.dtype is specified and y.dtype is not self.dtype.
• NotImplementedError: if neither _forward_log_det_jacobian nor {_inverse, _inverse_log_det_jacobian} are implemented, or this is a non-injective bijector.

### inverse

inverse(
y,
name='inverse'
)


Returns the inverse Bijector evaluation, i.e., X = g^{-1}(Y).

#### Args:

• y: Tensor. The input to the "inverse" evaluation.
• name: The name to give this op.

#### Returns:

Tensor, if this bijector is injective. If not injective, returns the k-tuple containing the unique k points (x1, ..., xk) such that g(xi) = y.

#### Raises:

• TypeError: if self.dtype is specified and y.dtype is not self.dtype.
• NotImplementedError: if _inverse is not implemented.

### inverse_event_shape

inverse_event_shape(output_shape)


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

Same meaning as inverse_event_shape_tensor. May be only partially defined.

#### Args:

• output_shape: TensorShape indicating event-portion shape passed into inverse function.

#### Returns:

• inverse_event_shape_tensor: TensorShape indicating event-portion shape after applying inverse. Possibly unknown.

### inverse_event_shape_tensor

inverse_event_shape_tensor(
output_shape,
name='inverse_event_shape_tensor'
)


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

#### Args:

• output_shape: Tensor, int32 vector indicating event-portion shape passed into inverse function.
• name: name to give to the op

#### Returns:

• inverse_event_shape_tensor: Tensor, int32 vector indicating event-portion shape after applying inverse.

### inverse_log_det_jacobian

inverse_log_det_jacobian(
y,
name='inverse_log_det_jacobian'
)


Returns the (log o det o Jacobian o inverse)(y).

Mathematically, returns: log(det(dX/dY))(Y). (Recall that: X=g^{-1}(Y).)

Note that forward_log_det_jacobian is the negative of this function, evaluated at g^{-1}(y).

#### Args:

• y: Tensor. The input to the "inverse" Jacobian evaluation.
• name: The name to give this op.

#### Returns:

Tensor, if this bijector is injective. If not injective, returns the tuple of local log det Jacobians, log(det(Dg_i^{-1}(y))), where g_i is the restriction of g to the ith partition Di.

#### Raises:

• TypeError: if self.dtype is specified and y.dtype is not self.dtype.
• NotImplementedError: if _inverse_log_det_jacobian is not implemented.