GP.logP_hessianable_stored

GP.logP_hessianable_stored(p: Any, Y: Array, stored_values: Any) → Tuple[Any, Any]

Computes the log posterior and also returns any stored values from the decomposition of the covariance matrix.

Note

This function is slower for gradient calculations than GP.logP_stored but is more numerically stable for second-order derivative calculations as required when calculating the hessian. This function still only returns the log posterior so jax.hessian must be applied to return the hessian of the log posterior.

Parameters:

• p (PyTree) – Pytree of hyperparameters used to calculate the covariance matrix in addition to any mean function parameters which may be needed to calculate the mean function. Also input to the logPrior function for the calculation of the log priors.

• Y (JAXArray) – Observed data to fit, must be of shape (N_l, N_t).

• stored_values (PyTree) – Stored values from the decomposition of the covariance matrix. The specific values contained in this PyTree depend on the choice of Kernel object and are returned by Kernel.decomp_fn.

Returns:

A tuple where the first element is the value of the log posterior. The second element is a PyTree which contains stored values from the decomposition of the covariance matrix.

Return type:

(Scalar, PyTree)