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tfp.experimental.tangent_spaces.AxisAlignedSpace

Tangent space of M for a distribution with axis-aligned subspace support.

Inherits From: TangentSpace

This subclass covers cases where the support of the distribution is on an axis-aligned subspace, such as lower-triangular matrices. In this special case we can represent the standard basis of the subspace with a mask. The subclass is designed to support axis-aligned injections like the FillTriangular Bijector.

axis_mask Tensor. A bit-mask defining the live dimensions of the space.

Methods

transform_coordinatewise

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Same as transform_dimension_preserving, for a coordinatewise f.

Default falls back to transform_dimension_preserving, which may be overridden in subclasses.

Args
x same as in transform_dimension_preserving.
f same as in transform_dimension_preserving.

Returns
density A Tensor representing the density correction of f at x
space A TangentSpace representing the tangent to fM at f(x)

Raises
NotImplementedError if the TangentSpace subclass does not implement transform_dimension_preserving.

transform_dimension_preserving

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Same as transform_general, assuming f goes from R^n to R^n.

Default falls back to transform_general, which may be overridden in subclasses.

Args
x same as in transform_general.
f same as in transform_general.

Returns
density A Tensor representing the density correction of f at x
space A TangentSpace representing the tangent to fM at f(x)

Raises
NotImplementedError if the TangentSpace subclass does not implement transform_general.

transform_general

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Returns the density correction corresponding to f at x.

Also returns a new TangentSpace representing the tangent to fM at f(x).

Args
x Tensor (structure). The point at which to calculate the density.
f Bijector or one of its subclasses. The transformation that requires a density correction based on this tangent space.

Returns
density A Tensor representing the density correction of f at x
space A TangentSpace representing the tangent to fM at f(x)

Raises
NotImplementedError if the TangentSpace subclass does not implement this method.

transform_projection

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Same as transform_general, with f a projection on some coordinates.

Default falls back to transform_general, which may be overridden in subclasses.

Args
x same as in transform_general.
f same as in transform_general.

Returns
density A Tensor representing the density correction of f at x
space A TangentSpace representing the tangent to fM at f(x)

Raises
NotImplementedError if the TangentSpace subclass does not implement transform_general.