Optimal Boolean Locality-Sensitive Hashing

12/04/2018

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by   Tobias Christiani, et al.

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For 0 ≤β < α < 1 the distribution H over Boolean functions h {-1, 1}^d →{-1, 1} that minimizes the expression ρ_α, β = (1/_h ∼H (x, y) α-corr.[h(x) = h(y)])/(1/_h ∼H (x, y) β-corr.[h(x) = h(y)]) assigns nonzero probability only to members of the set of dictator functions h(x) = ± x_i.