A clear trade-off emerges from the comparison of eq. 14 and eq. 16, between (a) drawing from precomputed distributions with constant scaling and subsequently discarded excitations, and (b) from ad hoc constrained probability distributions with linear scaling and no discarded excitations. We will refer to unconstrained sampling (p(I), . . .) as fast-weighted (eq. 14), and to constrained sampling (p(I)| I∈|D i , . . .) as fully-weighted sampling (eq. 16).