We define the discriminant to be ∆H = 1 + 2γ + γ2 log 1 − 1 γ 2 − 8γ 1 + γ + γ2 log 1 − 1 γ which is non-negative

Moreover, G′(α) = 2α − 1 − γ2 log 1 − 1 γ − γ2 γ − α, multiplying by ( γ − α) > 0 (recall that α < γ) shows G′(α) has the same sign as the quadratic H(α) := (γ − α)G′(α) = (2α − 1)(γ − α) − γ2(γ − α) log 1 − 1 γ − γ2 = −2α2 + 1 + 2γ + · 2017

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The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketches

cs.LG · 2025-05-30 · conditional · novelty 6.0

Gaussian sketching with additive Gaussian noise satisfies a closed-form Rényi differential privacy bound that is tighter than prior analyses and improves private linear and logistic regression.

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The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketches cs.LG · 2025-05-30 · conditional · none · ref 11
Gaussian sketching with additive Gaussian noise satisfies a closed-form Rényi differential privacy bound that is tighter than prior analyses and improves private linear and logistic regression.

We define the discriminant to be ∆H = 1 + 2γ + γ2 log 1 − 1 γ 2 − 8γ 1 + γ + γ2 log 1 − 1 γ which is non-negative

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