It is shown that cells with low average distortion cover constant measure, that each such cell has exponentially small measure, and that Gaussian-profile isoperimetry forces total boundary Ω( p k ) .
A fully non-adaptive protocol whose query list is fixed before any bit is observed and whose sample complexity matches the adaptive one-bit minimax rate in every moment regime.
It is shown that the classical Bayesian bootstrap closes this gap in U-calibration, which asks one online probability fore-caster to have low regret for every bounded proper loss, including losses unknown when the forecasts are made.
Together, these results give a substitution map for privacy accounting: when Poisson-based computations remain sound for structured participation, where they fail, and what sound alternatives cost in deployment.
Entropy estimation from short samples recurs in symmetric cryptography, where the reference distribution is uniform by design and no single estimator in the considered classical comparison set minimizes mean squared error (MSE) across the full range of ratios n/k. We introduce the adaptive sample-conditional entropy di...
Probability estimation over large alphabets under log loss is a well-studied problem, with celebrated methods such as the Good-Turing estimator. We introduce and study a new Bayesian estimator with four notable properties. First, its construction is exceptionally simple: multiply independent uniform draws from the prob...
Meir Feder, Yaniv Fogel, Rüdiger L. Urbanke· 0 citations
This study extends the computational and information-theoretic analysis of Bernard and Letac's method for uniform random sampling among $m$ outcomes by presenting five algorithms with formal correctness guarantees and comprehensive complexity analyses.
Claude Gravel· 0 citations
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