Replacing the conditional GP prior inside sparse variational inference with a Gaussian sharing its mean but using diagonal, analytically optimal variance corrections yields a strictly tighter evidence lower bound at unchanged O(NM^2) cost.
14 By maximizing wrt v we obtain v∗ = 1 +tr(Kff−Qff) N σ2 −1 , and by substituting this back into the bound we obtain Artemev et al
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New Bounds for Sparse Variational Gaussian Processes
Replacing the conditional GP prior inside sparse variational inference with a Gaussian sharing its mean but using diagonal, analytically optimal variance corrections yields a strictly tighter evidence lower bound at unchanged O(NM^2) cost.