GaussianCopula

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GaussianCopula#

class liesel.distributions.GaussianCopula(*args, **kwargs)[source]#

Bases: TransformedDistribution

The bivariate Gaussian copula.

Parameters:

  • dependence (default: None) – The correlation parameter.

  • validate_args (default: False) – Python bool, default False. When True, distribution parameters are checked for validity despite possibly degrading runtime performance. When False, invalid inputs may silently render incorrect outputs.

  • allow_nan_stats (default: True) – Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When False, an exception is raised if one or more of the statistic’s batch members are undefined.

  • name (default: 'GaussianCopula') – Python str, name prefixed to Ops created by this class.

See also

liesel.model.PIT

A Liesel variable for the probability integral transformation.

Examples

This is an example for how to use this class with Liesel.

>>> import jax.numpy as jnp
>>> import liesel.model as lsl
>>> import tensorflow_probability.substrates.jax.bijectors as tfb
>>> import tensorflow_probability.substrates.jax.distributions as tfd
>>> from liesel.distributions import GaussianCopula

>>> correlation = lsl.Var.new_param(0.2, bijector=tfb.Tanh(), name="rho")
>>> correlation.bijected_var
Var(name="h(rho)")

>>> dist1 = lsl.Dist(tfd.Normal, loc=0.0, scale=1.0)
>>> x1 = lsl.Var.new_obs(jnp.array([-0.5, -0.1, -0.25]), dist1).update()
>>> dist2 = lsl.Dist(tfd.Normal, loc=0.0, scale=1.0)
>>> x2 = lsl.Var.new_obs(jnp.array([0.5, 0.1, 0.25]), dist2).update()

>>> x1_pit = lsl.PIT(x1, name="PIT(x1)").update()
>>> x2_pit = lsl.PIT(x2, name="PIT(x2)").update()
>>> x_dependence = lsl.Var.new_calc(
...     lambda *inputs: jnp.stack(inputs, axis=1),
...     x1_pit,
...     x2_pit,
...     dist=lsl.Dist(GaussianCopula, dependence=correlation),
...     name="x_dependence",
... ).update()

>>> (x1.log_prob + x2.log_prob + x_dependence.log_prob).sum().round(1)
Array(-5.9, dtype=float32)

Comparing to an ordinary multivariate normal:

>>> dist = tfd.MultivariateNormalFullCovariance(
...     loc=jnp.zeros(2), covariance_matrix=jnp.array([[1.0, 0.2], [0.2, 1.0]])
... )
>>> dist.log_prob(jnp.stack((x1.value, x2.value), axis=-1)).sum().round(1)
Array(-5.9, dtype=float32)

Methods

cross_entropy(other[, name])

Computes the (Shannon) cross entropy.

kl_divergence(other[, name])

Computes the Kullback--Leibler divergence.
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