Predictive mean calculation confusion

[InfProbSciX]

I do not understand the calculation that happens on this line:

            L = self._cholesky_factor(induc_induc_covar)
        interp_term = L.inv_matmul(induc_data_covar.type(_linalg_dtype_cholesky.value())).to(full_inputs.dtype)

        # Compute the mean of q(f)
        # k_XZ K_ZZ^{-1/2} (m - K_ZZ^{-1/2} \mu_Z) + \mu_X
        predictive_mean = (interp_term.transpose(-1, -2) @ inducing_values.unsqueeze(-1)).squeeze(-1) + test_mean

Shouldn't the predictive mean be k_XZ * k_ZZ^{-1} * inducing_values + \mu_X?
interp_term seems to calculate k_XZ K_ZZ^{-1/2}, inducing_values are variational_distribution.loc, so it seems like the computation happening here is just k_XZ * k_ZZ^{>> -1/2 <<} * inducing_values + \mu_X (isn't there a factor of K_ZZ^{-1/2} missing?)

[InfProbSciX]

Looks like the same question as #1761.

[wjmaddox]

Oops, yes it is. This is due to whitening in the variational strategy, see the more explained version there.