CollapsedVariationalGaussian

class gpjax.variational_families.CollapsedVariationalGaussian(posterior, inducing_inputs, jitter=1e-06)

Bases: AbstractVariationalGaussian[GL]

Collapsed variational Gaussian.

Collapsed variational Gaussian family of probability distributions. The key reference is Titsias, (2009) - Variational Learning of Inducing Variables in Sparse Gaussian Processes.

The bound is collapsed: the variational parameters are solved for analytically, which requires a Gaussian likelihood and a pass over the full dataset. Lift either restriction and you need the uncollapsed bound of VariationalGaussian instead.

See also

Sparse Gaussian Process Regression works through the sparse regression setting this family is designed for.

Parameters:

• posterior (AbstractPosterior)

• inducing_inputs (Any)

• jitter (float)

predict(test_inputs, train_data)

Compute the predictive distribution of the GP at the test inputs.

Parameters:

• test_inputs (Float[Array, "N D"]) – The test inputs \(t\) at which to make predictions.

• train_data (Dataset) – The training data that was used to fit the GP.

Returns:

The predictive distribution of the collapsed

variational Gaussian process at the test inputs \(t\).

Return type:

GaussianDistribution