tfp.substrates.numpy.bijectors.GeneralizedExtremeValueCDF

Compute the GeneralizedExtremeValue CDF.

Inherits From: AutoCompositeTensorBijector, Bijector

View aliases

Main aliases

tfp.experimental.substrates.numpy.bijectors.GeneralizedExtremeValueCDF

tfp.substrates.numpy.bijectors.GeneralizedExtremeValueCDF(
    loc=0.0,
    scale=1.0,
    concentration=0,
    validate_args=False,
    name='generalizedextremevalue_cdf'
)

Compute Y = g(X) = exp(-t(X)),

where t(x) is defined to be: *(1 + conc * (x - loc) / scale) ) ** (-1 / conc) when conc != 0; *exp(-(x - loc) / scale) when conc = 0.

This bijector maps inputs from the domain to [0, 1], where the domain is

[loc - scale/conc, inf) when conc > 0;
(-inf, loc - scale/conc] when conc < 0;
(-inf, inf) when conc = 0;

The inverse of the bijector applied to a uniform random variable X ~ U(0, 1) gives back a random variable with the Generalized extreme value distribution:

When concentration -> +-inf, the probability mass concentrates near loc.

Y ~ GeneralizedExtremeValueCDF(loc, scale, conc)
pdf(y; loc, scale, conc) = t(y; loc, scale, conc) ** (1 + conc) * exp(
- t(y; loc, scale, conc) ) / scale
where t(x) =
  * (1 + conc * (x - loc) / scale) ) ** (-1 / conc) when conc != 0;
  * exp(-(x - loc) / scale) when conc = 0.

Args
`loc`	Float-like `Tensor` that is the same dtype and is broadcastable with `scale` and `concentration`.
`scale`	Positive Float-like `Tensor` that is the same dtype and is broadcastable with `loc` and `concentration`.
`concentration`	Nonzero float-like `Tensor` that is the same dtype and is broadcastable with `loc` and `scale`.
`validate_args`	Python `bool` indicating whether arguments should be checked for correctness.
`name`	Python `str` name given to ops managed by this object.

Attributes
`concentration`	The concentration parameter in the Generalized Extreme Value CDF.
`dtype`
`forward_min_event_ndims`	Returns the minimal number of dimensions bijector.forward operates on. Multipart bijectors return structured `ndims`, which indicates the expected structure of their inputs. Some multipart bijectors, notably Composites, may return structures of `None`.
`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. Multipart bijectors return structured `event_ndims`, which indicates the expected structure of their outputs. Some multipart bijectors, notably Composites, may return structures of `None`.
`is_constant_jacobian`	Returns true iff the Jacobian matrix is not a function of x. Note: Jacobian matrix is either constant for both forward and inverse or neither.
`loc`	The location parameter in the Generalized Extreme Value CDF.
`name`	Returns the string name of this `Bijector`.
`parameters`	Dictionary of parameters used to instantiate this `Bijector`.
`scale`	The scale parameter in the Generalized Extreme Value CDF.
`trainable_variables`
`validate_args`	Returns True if Tensor arguments will be validated.
`variables`

Methods

`copy`

View source

copy(
    **override_parameters_kwargs
)

Creates a copy of the bijector.

Args
`**override_parameters_kwargs`	String/value dictionary of initialization arguments to override with new values.

Returns
`bijector`	A new instance of `type(self)` initialized from the union of self.parameters and override_parameters_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`.

`experimental_batch_shape`

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experimental_batch_shape(
    x_event_ndims=None, y_event_ndims=None
)

Returns the batch shape of this bijector for inputs of the given rank.

The batch shape of a bijector decribes the set of distinct transformations it represents on events of a given size. For example: the bijector tfb.Scale([1., 2.]) has batch shape [2] for scalar events (event_ndims = 0), because applying it to a scalar event produces two scalar outputs, the result of two different scaling transformations. The same bijector has batch shape [] for vector events, because applying it to a vector produces (via elementwise multiplication) a single vector output.

Bijectors that operate independently on multiple state parts, such as tfb.JointMap, must broadcast to a coherent batch shape. Some events may not be valid: for example, the bijector tfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])]) does not produce a valid batch shape when event_ndims = [0, 0], since the batch shapes of the two parts are inconsistent. The same bijector does define valid batch shapes of [], [2], and [3] if event_ndims is [1, 1], [0, 1], or [1, 0], respectively.

Since transforming a single event produces a scalar log-det-Jacobian, the batch shape of a bijector with non-constant Jacobian is expected to equal the shape of forward_log_det_jacobian(x, event_ndims=x_event_ndims) or inverse_log_det_jacobian(y, event_ndims=y_event_ndims), for x or y of the specified ndims.

Args
`x_event_ndims`	Optional Python `int` (structure) number of dimensions in a probabilistic event passed to `forward`; this must be greater than or equal to `self.forward_min_event_ndims`. If `None`, defaults to `self.forward_min_event_ndims`. Mutually exclusive with `y_event_ndims`. Default value: `None`.
`y_event_ndims`	Optional Python `int` (structure) number of dimensions in a probabilistic event passed to `inverse`; this must be greater than or equal to `self.inverse_min_event_ndims`. Mutually exclusive with `x_event_ndims`. Default value: `None`.

Returns
`batch_shape`	`TensorShape` batch shape of this bijector for a value with the given event rank. May be unknown or partially defined.

`experimental_batch_shape_tensor`

View source

experimental_batch_shape_tensor(
    x_event_ndims=None, y_event_ndims=None
)

Returns the batch shape of this bijector for inputs of the given rank.

Args
`x_event_ndims`	Optional Python `int` (structure) number of dimensions in a probabilistic event passed to `forward`; this must be greater than or equal to `self.forward_min_event_ndims`. If `None`, defaults to `self.forward_min_event_ndims`. Mutually exclusive with `y_event_ndims`. Default value: `None`.
`y_event_ndims`	Optional Python `int` (structure) number of dimensions in a probabilistic event passed to `inverse`; this must be greater than or equal to `self.inverse_min_event_ndims`. Mutually exclusive with `x_event_ndims`. Default value: `None`.

Returns
`batch_shape_tensor`	integer `Tensor` batch shape of this bijector for a value with the given event rank.

`experimental_compute_density_correction`

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experimental_compute_density_correction(
    x, tangent_space, backward_compat=False, **kwargs
)

Density correction for this transformation wrt the tangent space, at x.

Subclasses of Bijector may call the most specific applicable method of TangentSpace, based on whether the transformation is dimension-preserving, coordinate-wise, a projection, or something more general. The backward-compatible assumption is that the transformation is dimension-preserving (goes from R^n to R^n).

Args
`x`	`Tensor` (structure). The point at which to calculate the density.
`tangent_space`	`TangentSpace` or one of its subclasses. The tangent to the support manifold at `x`.
`backward_compat`	`bool` specifying whether to assume that the Bijector is dimension-preserving.
`**kwargs`	Optional keyword arguments forwarded to tangent space methods.

Returns
`density_correction`	`Tensor` representing the density correction---in log space---under the transformation that this Bijector denotes.

Raises
TypeError if `backward_compat` is False but no method of `TangentSpace` has been called explicitly.

`forward`

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forward(
    x, name='forward', **kwargs
)

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

Args
`x`	`Tensor` (structure). The input to the 'forward' evaluation.
`name`	The name to give this op.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`Tensor` (structure).

Raises
`TypeError`	if `self.dtype` is specified and `x.dtype` is not `self.dtype`.
`NotImplementedError`	if `_forward` is not implemented.

`forward_dtype`

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forward_dtype(
    dtype=UNSPECIFIED, name='forward_dtype', **kwargs
)

Returns the dtype returned by forward for the provided input.

`forward_event_ndims`

View source

forward_event_ndims(
    event_ndims, **kwargs
)

Returns the number of event dimensions produced by forward.

Args
`event_ndims`	Structure of Python and/or Tensor `int`s, and/or `None` values. The structure should match that of `self.forward_min_event_ndims`, and all non-`None` values must be greater than or equal to the corresponding value in `self.forward_min_event_ndims`.
`**kwargs`	Optional keyword arguments forwarded to nested bijectors.

Returns

forward_event_ndims Structure of integers and/or None values matching self.inverse_min_event_ndims. These are computed using 'prefer static' semantics: if any inputs are None, some or all of the outputs may be None, indicating that the output dimension could not be inferred (conversely, if all inputs are non-None, all outputs will be non-None). If all input event_ndims are Python ints, all of the (non-None) outputs will be Python ints; otherwise, some or all of the outputs may be Tensor ints.

Returns
`forward_event_ndims`	Structure of integers and/or `None` values matching `self.inverse_min_event_ndims`. These are computed using 'prefer static' semantics: if any inputs are `None`, some or all of the outputs may be `None`, indicating that the output dimension could not be inferred (conversely, if all inputs are non-`None`, all outputs will be non-`None`). If all input `event_ndims` are Python `int`s, all of the (non-`None`) outputs will be Python `int`s; otherwise, some or all of the outputs may be `Tensor` `int`s.

`forward_event_shape`

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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` (structure) indicating event-portion shape passed into `forward` function.

Returns
`forward_event_shape_tensor`	`TensorShape` (structure) indicating event-portion shape after applying `forward`. Possibly unknown.

`forward_event_shape_tensor`

View source

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 (structure) indicating event-portion shape passed into `forward` function.
`name`	name to give to the op

Returns
`forward_event_shape_tensor`	`Tensor`, `int32` vector (structure) indicating event-portion shape after applying `forward`.

`forward_log_det_jacobian`

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forward_log_det_jacobian(
    x, event_ndims=None, name='forward_log_det_jacobian', **kwargs
)

Returns both the forward_log_det_jacobian.

Args
`x`	`Tensor` (structure). The input to the 'forward' Jacobian determinant evaluation.
`event_ndims`	Optional number of dimensions in the probabilistic events being transformed; this must be greater than or equal to `self.forward_min_event_ndims`. If `event_ndims` is specified, the log Jacobian determinant is summed to produce a scalar log-determinant for each event. Otherwise (if `event_ndims` is `None`), no reduction is performed. Multipart bijectors require structured event_ndims, such that the batch rank `rank(y[i]) - event_ndims[i]` is the same for all elements `i` of the structured input. In most cases (with the exception of `tfb.JointMap`) they further require that `event_ndims[i] - self.inverse_min_event_ndims[i]` is the same for all elements `i` of the structured input. Default value: `None` (equivalent to `self.forward_min_event_ndims`).
`name`	The name to give this op.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`Tensor` (structure), if this bijector is injective. If not injective this is not implemented.

Raises
`TypeError`	if `y`'s dtype is incompatible with the expected output dtype.
`NotImplementedError`	if neither `_forward_log_det_jacobian` nor {`_inverse`, `_inverse_log_det_jacobian`} are implemented, or this is a non-injective bijector.
`ValueError`	if the value of `event_ndims` is not valid for this bijector.

`inverse`

View source

inverse(
    y, name='inverse', **kwargs
)

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

Args
`y`	`Tensor` (structure). The input to the 'inverse' evaluation.
`name`	The name to give this op.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`Tensor` (structure), 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 `y`'s structured dtype is incompatible with the expected output dtype.
`NotImplementedError`	if `_inverse` is not implemented.

`inverse_dtype`

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inverse_dtype(
    dtype=UNSPECIFIED, name='inverse_dtype', **kwargs
)

Returns the dtype returned by inverse for the provided input.

`inverse_event_ndims`

View source

inverse_event_ndims(
    event_ndims, **kwargs
)

Returns the number of event dimensions produced by inverse.

Args
`event_ndims`	Structure of Python and/or Tensor `int`s, and/or `None` values. The structure should match that of `self.inverse_min_event_ndims`, and all non-`None` values must be greater than or equal to the corresponding value in `self.inverse_min_event_ndims`.
`**kwargs`	Optional keyword arguments forwarded to nested bijectors.

Returns

inverse_event_ndims Structure of integers and/or None values matching self.forward_min_event_ndims. These are computed using 'prefer static' semantics: if any inputs are None, some or all of the outputs may be None, indicating that the output dimension could not be inferred (conversely, if all inputs are non-None, all outputs will be non-None). If all input event_ndims are Python ints, all of the (non-None) outputs will be Python ints; otherwise, some or all of the outputs may be Tensor ints.

Returns
`inverse_event_ndims`	Structure of integers and/or `None` values matching `self.forward_min_event_ndims`. These are computed using 'prefer static' semantics: if any inputs are `None`, some or all of the outputs may be `None`, indicating that the output dimension could not be inferred (conversely, if all inputs are non-`None`, all outputs will be non-`None`). If all input `event_ndims` are Python `int`s, all of the (non-`None`) outputs will be Python `int`s; otherwise, some or all of the outputs may be `Tensor` `int`s.

`inverse_event_shape`

View source

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` (structure) indicating event-portion shape passed into `inverse` function.

Returns
`inverse_event_shape_tensor`	`TensorShape` (structure) indicating event-portion shape after applying `inverse`. Possibly unknown.

`inverse_event_shape_tensor`

View source

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 (structure) indicating event-portion shape passed into `inverse` function.
`name`	name to give to the op

Returns
`inverse_event_shape_tensor`	`Tensor`, `int32` vector (structure) indicating event-portion shape after applying `inverse`.

`inverse_log_det_jacobian`

View source

inverse_log_det_jacobian(
    y, event_ndims=None, name='inverse_log_det_jacobian', **kwargs
)

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` (structure). The input to the 'inverse' Jacobian determinant evaluation.
`event_ndims`	Optional number of dimensions in the probabilistic events being transformed; this must be greater than or equal to `self.inverse_min_event_ndims`. If `event_ndims` is specified, the log Jacobian determinant is summed to produce a scalar log-determinant for each event. Otherwise (if `event_ndims` is `None`), no reduction is performed. Multipart bijectors require structured event_ndims, such that the batch rank `rank(y[i]) - event_ndims[i]` is the same for all elements `i` of the structured input. In most cases (with the exception of `tfb.JointMap`) they further require that `event_ndims[i] - self.inverse_min_event_ndims[i]` is the same for all elements `i` of the structured input. Default value: `None` (equivalent to `self.inverse_min_event_ndims`).
`name`	The name to give this op.
`**kwargs`	Named arguments forwarded to subclass implementation.

Returns
`ildj`	`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 `x`'s dtype is incompatible with the expected inverse-dtype.
`NotImplementedError`	if `_inverse_log_det_jacobian` is not implemented.
`ValueError`	if the value of `event_ndims` is not valid for this bijector.

`parameter_properties`

View source

@classmethod
parameter_properties(
    dtype=tf.float32
)

Returns a dict mapping constructor arg names to property annotations.

This dict should include an entry for each of the bijector's Tensor-valued constructor arguments.

Args
`dtype`	Optional float `dtype` to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., `tfb.Softplus.low`) must be instantiated with the same dtype as the values to be transformed.

Returns
`parameter_properties`	A `str ->`tfp.python.internal.parameter_properties.ParameterProperties`dict mapping constructor argument names to`ParameterProperties` instances.

`call`

View source

__call__(
    value, name=None, **kwargs
)

Applies or composes the Bijector, depending on input type.

This is a convenience function which applies the Bijector instance in three different ways, depending on the input:

If the input is a tfd.Distribution instance, return tfd.TransformedDistribution(distribution=input, bijector=self).
If the input is a tfb.Bijector instance, return tfb.Chain([self, input]).
Otherwise, return self.forward(input)

Args
`value`	A `tfd.Distribution`, `tfb.Bijector`, or a (structure of) `Tensor`.
`name`	Python `str` name given to ops created by this function.
`**kwargs`	Additional keyword arguments passed into the created `tfd.TransformedDistribution`, `tfb.Bijector`, or `self.forward`.

Returns
`composition`	A `tfd.TransformedDistribution` if the input was a `tfd.Distribution`, a `tfb.Chain` if the input was a `tfb.Bijector`, or a (structure of) `Tensor` computed by `self.forward`.

Examples

sigmoid = tfb.Reciprocal()(
    tfb.Shift(shift=1.)(
      tfb.Exp()(
        tfb.Scale(scale=-1.))))
# ==> `tfb.Chain([
#         tfb.Reciprocal(),
#         tfb.Shift(shift=1.),
#         tfb.Exp(),
#         tfb.Scale(scale=-1.),
#      ])`  # ie, `tfb.Sigmoid()`

log_normal = tfb.Exp()(tfd.Normal(0, 1))
# ==> `tfd.TransformedDistribution(tfd.Normal(0, 1), tfb.Exp())`

tfb.Exp()([-1., 0., 1.])
# ==> tf.exp([-1., 0., 1.])

`eq`

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__eq__(
    other
)

Return self==value.

`getitem`

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__getitem__(
    slices
)

`iter`

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__iter__()

tfp.substrates.numpy.bijectors.GeneralizedExtremeValueCDFStay organized with collections Save and categorize content based on your preferences.

View aliases

Args

Attributes

Methods

copy

experimental_batch_shape

experimental_batch_shape_tensor

experimental_compute_density_correction

forward

forward_dtype

forward_event_ndims

forward_event_shape

forward_event_shape_tensor

forward_log_det_jacobian

inverse

inverse_dtype

inverse_event_ndims

inverse_event_shape

inverse_event_shape_tensor

inverse_log_det_jacobian

parameter_properties

__call__

Examples

__eq__

__getitem__

__iter__

tfp.substrates.numpy.bijectors.GeneralizedExtremeValueCDF

`copy`

`experimental_batch_shape`

`experimental_batch_shape_tensor`

`experimental_compute_density_correction`

`forward`

`forward_dtype`

`forward_event_ndims`

`forward_event_shape`

`forward_event_shape_tensor`

`forward_log_det_jacobian`

`inverse`

`inverse_dtype`

`inverse_event_ndims`

`inverse_event_shape`

`inverse_event_shape_tensor`

`inverse_log_det_jacobian`

`parameter_properties`

`call`

`eq`

`getitem`

`iter`