updated models.gpr docstring
Doc update. Resolves
* updated models.gpr docstring
* Elaboration.
@@ -33,12 +33,20 @@ class GPR(GPModel, InternalDataTrainingLossMixin):
This is a vanilla implementation of GP regression with a Gaussian
likelihood. Multiple columns of Y are treated independently.
- The log likelihood of this model is sometimes referred to as the 'log
- marginal likelihood', and is given by
+ The log likelihood of this model is given by
.. math::
- \log p(\mathbf y \,|\, \mathbf f) =
- \mathcal N(\mathbf{y} \,|\, 0, \mathbf{K} + \sigma_n \mathbf{I})
+ \log p(Y \,|\, \mathbf f) =
+ \mathcal N(Y \,|\, 0, \sigma_n^2 \mathbf{I})
+
+ To train the model, we maximise the log _marginal_ likelihood
+ w.r.t. the likelihood variance and kernel hyperparameters theta.
+ The marginal likelihood is found by integrating the likelihood
+ over the prior, and has the form
+
+ .. math::
+ \log p(Y \,|\, \sigma_n, \theta) =
+ \mathcal N(Y \,|\, 0, \mathbf{K} + \sigma_n^2 \mathbf{I})
"""
def __init__(
