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February 11, 20260 citationsOpen Access

Universal Asymptotics for Jensen–Shannon Divergence in the Shuffle Model

ASAlex Shvets

Key Points

  • The research aims to establish universal asymptotic results for Jensen–Shannon divergence in a shuffle model.
  • Derivation of asymptotic expansions for JSD with fixed local randomizers.
  • Statistical analysis using Berry–Esseen bounds.
  • Comparison of explicit (ε,δ) curves against FMT amplification bounds.
  • Established a universal expansion for JSD incorporating χ² and higher order terms.
  • Demonstrated μ-GDP equivalence yielding tighter bounds than previous models.

Abstract

Two asymptotic results for the shuffle model with a fixed finite-output local randomizer and canonical binary neighboring datasets. (1) A universal expansion JSD = χ²/(8n) − μ₃/(16n²) + 7χ⁴/(64n²) + O(n⁻³). (2) Asymptotic μ-GDP equivalence with μ = √(χ²/n) via Berry–Esseen bounds under both hypotheses, yielding an explicit (ε,δ) curve 6–9× tighter than the FMT amplification bound.

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Cite This Study

Alex Shvets (2026) studied this question.

synapsesocial.com/papers/698c1c22267fb587c655e4a5https://doi.org/10.5281/zenodo.18530707
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