LatentPosterior

class gpjax.conditioning.LatentPosterior(prior, likelihood, latent, train_data)

Bases: Posterior

Approximately conditioned GP for non-Gaussian likelihoods.

Conditioning is on the model’s whitened latent vector rather than on the observations directly: the cached factor is the prior gram’s Cholesky, and the latent plays the role of the representer weights. The joint log-density (log_posterior_density) is the quantity MCMC or MAP optimisation targets.

Parameters:

• prior (Any)

• likelihood (Any)

• latent (Float[jaxlib._jax.Array, 'N 1'] | Float[ndarray, 'N 1'])

• train_data (Dataset)

property log_posterior_density: float | Float[jaxlib._jax.Array, ''] | Float[ndarray, '']

Unnormalised log-posterior density of the whitened latent model.

\(\log p(y \mid f(x)) + \log \mathcal{N}(w_x \mid 0, I)\) where \(f(x) = m(x) + L_x w_x\).