(note- if we rename the variance field we'll have to update this)

More of a general question at other maintainers (@vdutor @markvdw @awav) & anyone else ...: what should the name of this field be? In code we often abbreviate the variance to "var", but also it sometimes represents the covariance... or maybe that should be a different type? MeanAndVariance and MeanAndCov (and return a different one depending on full_cov etc)?

i like the idea of the two types. Haven't thought about it in detail

do you always know for sure if you've got the cov or var?

If you pass in full_cov=False and full_output_cov=False, you get the marginals back. If one of full_cov or full_output_cov is True, you get the covariance over inputs or outputs, respectively. If both are True, you should get the N P x N P covariance matrix (though this combination isn't actually implemented in several cases, I believe). So the output type is solely determined by the full_cov and full_output_cov arguments.

btw you can use typing.overload and typing.Literal to give more information than just MeanAndVariance | MeanAndCov, if you wanted to do that

I've created a small example, which should work as wanted:

But I' not comfortable with the if-else statement :/

from typing import Literal, NamedTuple, overload

class MeanAndVariance(NamedTuple):
    mean: int
    variance: int

class MeanAndCovariance(NamedTuple):
    mean: int
    covariance: int

@overload
def predict_f(auto_cov: Literal[False]) -> MeanAndVariance:
    ...

@overload
def predict_f(auto_cov: Literal[True]) -> MeanAndCovariance:
    ...

def predict_f(auto_cov: bool = False) -> (MeanAndVariance | MeanAndCovariance):
    # calculations
    return  MeanAndCovariance(1, 2) if auto_cov else MeanAndVariance(1, 2)

I don't think there's a good way around the if-else, and I think it's better to be explicit than the ambiguity of having to remember whether it's a [N, Q] or [Q, N, N] tensor ...:) I'd be happy with this.

As it pointed out, typing.Literal is only available from Python 3.8 and up :/

@antonykamp the typing_extensions module provides backports for older versions of Python, it does seem to include Literal. :)

I added this pattern with overload and Tuple to the abstract method predict_f in gpflow/models/models.py. Should the overloads of predict_f be marked as abstract too? In any case I see no chance to test the Ellipsis operator of each overloaded funciton :/

Also, I wanted to ask if the parameters of the model constructor should be listed in the parametrization?