Positive-feature proposals are sampleable mixtures: feature c ∝ φ_c(q)·S_c then key ∝ ψ_c(j) gives P(j) = ⟨φ(q),ψ(j)⟩ / Σ_j' ⟨φ(q),ψ(j')⟩

For all $\htmlData{mx=1}{r, n \in \htmlData{mx=0}{\mathbb{N}}}$, $\htmlData{mx=5}{\varphi : \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{r}} \mathrel{\htmlData{mx=4}{\to}} \htmlData{mx=3}{\mathbb{R}}}$, $\htmlData{mx=9}{\psi : \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{r}} \mathrel{\htmlData{mx=8}{\to}} \htmlData{mx=5}{\htmlData{mx=3}{\operatorname{Fin}}\,\htmlData{mx=4}{n}} \mathrel{\htmlData{mx=7}{\to}} \htmlData{mx=6}{\mathbb{R}}}$ and $\htmlData{mx=3}{j \in \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{n}}}$, if $\htmlData{mx=4}{\forall c,\ 0 \mathrel{\htmlData{mx=3}{<}} \htmlData{mx=2}{\htmlData{mx=0}{\varphi}(\htmlData{mx=1}{c})}}$, $\htmlData{mx=5}{\forall c, i,\ 0 \mathrel{\htmlData{mx=4}{<}} \htmlData{mx=3}{\htmlData{mx=0}{\psi}(\htmlData{mx=1}{c}, \htmlData{mx=2}{i})}}$, $0 \mathrel{\htmlData{mx=1}{<}} \htmlData{mx=0}{n}$ and $0 \mathrel{\htmlData{mx=1}{<}} \htmlData{mx=0}{r}$, then