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# tfp.experimental.substrates.numpy.experimental.inference_gym.targets.IllConditionedGaussian

Creates a random ill-conditioned Gaussian.

Inherits From: `BayesianModel`

``````tfp.experimental.substrates.numpy.experimental.inference_gym.targets.IllConditionedGaussian(
ndims=100, gamma_shape_parameter=0.5, max_eigvalue=None, seed=10,
name='ill_conditioned_gaussian', pretty_name='Ill-Conditioned Gaussian'
)
``````

The covariance matrix has eigenvalues sampled from the inverse Gamma distribution with the specified shape, and then rotated by a random orthogonal matrix.

Note that this function produces reproducible targets, i.e. the constructor `seed` argument always needs to be non-`None`.

#### Args:

• `ndims`: Python `int`. Dimensionality of the Gaussian.
• `gamma_shape_parameter`: Python `float`. The shape parameter of the inverse Gamma distribution. Anything below 2 is likely to yield poorly conditioned covariance matrices.
• `max_eigvalue`: Python `float`. If set, will normalize the eigenvalues such that the maximum is this value.
• `seed`: Seed to use when generating the eigenvalues and the random orthogonal matrix.
• `name`: Python `str` name prefixed to Ops created by this class.
• `pretty_name`: A Python `str`. The pretty name of this model.

#### Attributes:

• `covariance_eigenvalues`
• `default_event_space_bijector`: Bijector mapping the reals (R**n) to the event space of this model.
• `dtype`: The `DType` of `Tensor`s handled by this model.
• `event_shape`: Shape of a single sample from as a `TensorShape`.

May be partially defined or unknown.

• `name`: Python `str` name prefixed to Ops created by this class.

• `sample_transformations`: A dictionary of names to `SampleTransformation`s.

## Child Classes

`class SampleTransformation`

## Methods

### `evidence`

View source

``````evidence(
name='evidence'
)
``````

The evidence that the joint model is conditioned on.

### `joint_distribution`

View source

``````joint_distribution(
name='joint_distribution'
)
``````

The joint distribution before any conditioning.

### `sample`

View source

``````sample(
sample_shape=(), seed=None, name='sample'
)
``````

Generate samples of the specified shape from the target distribution.

The returned samples are exact (and independent) samples from the target distribution of this model.

Note that a call to `sample()` without arguments will generate a single sample.

#### Args:

• `sample_shape`: 0D or 1D `int32` `Tensor`. Shape of the generated samples.
• `seed`: Python integer or `tfp.util.SeedStream` instance, for seeding PRNG.
• `name`: Name to give to the prefix the generated ops.

#### Returns:

• `samples`: a `Tensor` with prepended dimensions `sample_shape`.

### `unnormalized_log_prob`

View source

``````unnormalized_log_prob(
value, name='unnormalized_log_prob'
)
``````

The un-normalized log density of evaluated at a point.

This corresponds to the target distribution associated with the model, often its posterior.

#### Args:

• `value`: A (nest of) `Tensor` to evaluate the log density at.
• `name`: Python `str` name prefixed to Ops created by this method.

#### Returns:

• `unnormalized_log_prob`: A floating point `Tensor`.