StudentT

class gpjax.likelihoods.StudentT(degrees_of_freedom=4.0, scale=1.0, integrator=<gpjax.integrators.GHQuadratureIntegrator object>)

Bases: AbstractLikelihood

Student’s t likelihood object for robust regression.

Replaces the Gaussian likelihood’s light-tailed noise model with a heavy-tailed Student’s t distribution, so that outlying observations pull the posterior mean less strongly (Jylanki, Vanhatalo & Vehtari, 2011). Since the Student’s t distribution is not conjugate to a Gaussian prior, the expected log likelihood has no closed form and is instead computed by Gauss-Hermite quadrature via GHQuadratureIntegrator.

Parameters:

• degrees_of_freedom (Any)

• scale (Any)

• integrator (AbstractIntegrator)

link_function(f)

The link function of the Student’s t likelihood.

Parameters:

f (Float[Array, "..."]) – Function values.

Returns:

The likelihood function.

Return type:

npd.StudentT

predict(dist)

Evaluate the pointwise predictive distribution.

Evaluate the pointwise predictive distribution, given a Gaussian process posterior and likelihood parameters. As with Poisson, the Student’s t distribution is not conjugate to a Gaussian latent, so this evaluates the link function at the posterior mean rather than marginalising the latent uncertainty.

Parameters:

dist (tp.Union[npd.MultivariateNormal, GaussianDistribution]) – The Gaussian process posterior, evaluated at a finite set of test points.

Returns:

The pointwise predictive distribution.

Return type:

npd.StudentT