What question did this study set out to answer?

This research aims to explore the asymptotic behavior of Jensen–Shannon leakage in subsampled Gaussian sum release.

January 14, 20260 citationsOpen Access

Two-Term Asymptotic Expansion of Jensen–Shannon Leakage for Subsampled Gaussian Sum Release

ASAlex B. ShvetsUniversity of Illinois Urbana-Champaign

Key Points

This research aims to explore the asymptotic behavior of Jensen–Shannon leakage in subsampled Gaussian sum release.
Analytical approach focusing on subsampling at rate q among n users.
Used a Gaussian mixture model with noise variance sigma^2 to derive results.
Proved the relationship involving JSD, SNR, and n.
Established that JSD(P0,P1) follows a specific asymptotic form as n increases.
The remainder term shows a uniform behavior across certain parameters.
Numerical quadrature confirmed the theoretical asymptotic behavior.

Abstract

We consider subsampling at rate q among n users and a Gaussian sum-release with noise variance sigma². For neighboring datasets D0= (0,. . . , 0) and D1= (mu, 0,. . . , 0), letting SNR=mu²/sigma², we prove JSD (P0, P1) = (q*SNR) / (8n) + ( (4-12q+7q²) /64) * (SNR²/n²) + O (n^-3). The remainder is uniform for q in eps, 1 (any fixed eps>0) and bounded SNR. The proof combines an exact mixture representation, a local Edgeworth expansion, uniform sixth-derivative control, and a parity argument. Numerical quadrature of the exact binomial–Gaussian mixture corroborates the uniform n^-3 behavior.

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