Now we want to show that for all ε ∈ R≥0 and p(i) ∈ [0, 1], δDT g,D′T g(ε) ≥ δD′T g,DT g(ε)

Plugging the above expression of δD′T g,DT g(ε) in Proposition 9, we have δD′T g,DT g(ε) = erf   s −ε − 1 2 ln 1 − p(i) p(i)   − exp ε + 1 2 ln 1 − p(i) p1 − p(i) · erf   s

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The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learning

cs.CR · 2023-09-03 · unverdicted · novelty 7.0

NDIS lemma computes closed-form hockey-stick divergence δ(ε) between arbitrary multivariate Gaussians and is applied to obtain tighter privacy for random projection.

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The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learning cs.CR · 2023-09-03 · unverdicted · none · ref 65
NDIS lemma computes closed-form hockey-stick divergence δ(ε) between arbitrary multivariate Gaussians and is applied to obtain tighter privacy for random projection.

Now we want to show that for all ε ∈ R≥0 and p(i) ∈ [0, 1], δDT g,D′T g(ε) ≥ δD′T g,DT g(ε)

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