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January 20, 20260 citationsOpen Access

Binary Worst-Case Theorem for Jensen-Shannon Chain-Rule Ratio

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ASAlex B. Shvets

Key Points

  • This research aims to determine the maximum of the Jensen-Shannon chain-rule ratio for binary alphabets.
  • Utilized Jensen-Shannon information measures to derive the chain-rule ratio.
  • Applied Dinkelbach linearization for analytic proofs.
  • Reduced convex envelopes to study two-point martingales.
  • The supremum of the chain-rule ratio is found to be approximately 1.4903.
  • An explicit KKT system provides a characterization of the sharp constant.
  • The maximum is approached in a nested rare-event limit as ε approaches 0.

Abstract

The supremum of the Jensen-Shannon chain-rule ratio R = IJS (X;Y, Z) / IJS (X;Y) + IJS (X;Z|Y) is achieved on binary alphabets: C* = sup R = 1. 4903. . . with |X|=|Y|=|Z|=2. Proof via Dinkelbach linearization and double concave envelope reduction to two-point martingales. The sharp constant satisfies an explicit KKT system and is approached but not attained — only in a nested rare-event limit ε→0.

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Cite This Study

Alex B. Shvets (2026) studied this question.

synapsesocial.com/papers/696f1a9f9e64f732b51eeeb7https://doi.org/10.5281/zenodo.18292419
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