50d005f92a6c5c9646db4b761da676ba-Supplemental-Conference.pdf

Failure case 2: Augerino depends on the used parameterisation of invariance. The full GGN approximation in Eq. 5 is inO(NP2C) for computingN matrix-products. The diagonalGGNapproximation would be inO(NPC)and computation of the log-determinant onlyO(P). Computing the log-determinant can be done efficiently inO(D3 +G3)by decomposing the Kronecker factors (Immer et al., 2021a). The last two terms dependent onS come up due to the aggregation ofaugmentation samples inour approximation, that is,the expectations overaandg in the second line of Eq. 15.