Then for any fixedε >0, δ ≤ ε, min A is (ε, δ)-DP max p∈P E x∼S(n,p) [dist(p, A(x))] ≥ 1 2 kX i=1 wi · τi · f (Pi) (17) Proof

For each i ∈ [k], there existsτi ≥ 0, ¯pi ∈ Pi, such that for any fixedpj ∈ Pj, j̸= i, it holds that Z min pi∈Pi dS(n, Pk j=1 wjpj) dS(n, wi ¯pi + P j̸=i wjpj) ! dS(n, wi ¯pi +

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Instance-Optimality for Private KL Distribution Estimation

stat.ML · 2025-05-29 · conditional · novelty 7.0

New private and non-private estimators achieve per-instance KL error within constant factors of the best possible error over a new additive local neighborhood.

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Instance-Optimality for Private KL Distribution Estimation stat.ML · 2025-05-29 · conditional · none · ref 2
New private and non-private estimators achieve per-instance KL error within constant factors of the best possible error over a new additive local neighborhood.

Then for any fixedε >0, δ ≤ ε, min A is (ε, δ)-DP max p∈P E x∼S(n,p) [dist(p, A(x))] ≥ 1 2 kX i=1 wi · τi · f (Pi) (17) Proof

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