tf.contrib.distributions.bijectors.Kumaraswamy

Class `Kumaraswamy`

Compute `Y = g(X) = (1 - (1 - X)**(1 / b))**(1 / a), X in [0, 1]`.

Inherits From: `Bijector`

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

``````Y ~ Kumaraswamy(a, b)
pdf(y; a, b, 0 <= y <= 1) = a * b * y ** (a - 1) * (1 - y**a) ** (b - 1)
``````

`__init__`

``````__init__(
concentration1=None,
concentration0=None,
validate_args=False,
name='kumaraswamy'
)
``````

Instantiates the `Kumaraswamy` bijector. (deprecated)

Args:

• `concentration1`: Python `float` scalar indicating the transform power, i.e., `Y = g(X) = (1 - (1 - X)**(1 / b))**(1 / a)` where `a` is `concentration1`.
• `concentration0`: Python `float` scalar indicating the transform power, i.e., `Y = g(X) = (1 - (1 - X)**(1 / b))**(1 / a)` where `b` is `concentration0`.
• `validate_args`: Python `bool` indicating whether arguments should be checked for correctness.
• `name`: Python `str` name given to ops managed by this object.

Properties

`concentration0`

The `b` in: `Y = g(X) = (1 - (1 - X)**(1 / b))**(1 / a)`.

`concentration1`

The `a` in: `Y = g(X) = (1 - (1 - X)**(1 / b))**(1 / a)`.

`dtype`

dtype of `Tensor`s transformable by this distribution.

`forward_min_event_ndims`

Returns the minimal number of dimensions bijector.forward operates on.

`graph_parents`

Returns this `Bijector`'s graph_parents as a Python list.

`inverse_min_event_ndims`

Returns the minimal number of dimensions bijector.inverse operates on.

`is_constant_jacobian`

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

Returns:

• `is_constant_jacobian`: Python `bool`.

`name`

Returns the string name of this `Bijector`.

`validate_args`

Returns True if Tensor arguments will be validated.

Methods

`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,
event_ndims,
name='forward_log_det_jacobian'
)
``````

Returns both the forward_log_det_jacobian.

Args:

• `x`: `Tensor`. The input to the "forward" Jacobian determinant evaluation.
• `event_ndims`: Number of dimensions in the probabilistic events being transformed. Must be greater than or equal to `self.forward_min_event_ndims`. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shape `x.shape.ndims - event_ndims` dimensions.
• `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,
event_ndims,
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 determinant evaluation.
• `event_ndims`: Number of dimensions in the probabilistic events being transformed. Must be greater than or equal to `self.inverse_min_event_ndims`. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shape `y.shape.ndims - event_ndims` dimensions.
• `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.