We characterize the exact rate--exponent tradeoff for new classes of one-way distributed hypothesis testing problems by demonstrating that a recent upper bound, derived via the auxiliary-receiver technique, coincides with known lower bounds. We achieve this by relaxing the upper bound on the type-II error exponent into a form that shares the same inner functional as Han's lower bound, differing only in the outer rate constraint. Furthermore, we prove that this upper bound is tight for testing against dependence and for the doubly symmetric binary source (DSBS) with crossover probabilities $\kappa_0$ under the null hypothesis and $\kappa_1$ under the alternative hypothesis, provided $0<\kappa_1<\kappa_0<\frac12$. The characterization of the exact error exponent for the DSBS source holds for every communication rate $R \geq 0$.
The characterisation shows that the two information costs can be quite different and identifies three parameter regimes, with optimal protocols based respectively on clean samples, a noisy binary symmetric channel, and an asymmetric $Z$-channel.
We investigate composite binary hypothesis testing in the finite sample regime under asymmetric error constraints. Using R\'enyi divergences, we derive explicit achievability and converse bounds for the optimal Type II error. When the Type I error is constrained to decay exponentially with sample size, the bounds ident...
The conjectured upper bound of k statistical queries on a universe of size T can be released under pure differential privacy with expected worst-coordinate error at the square-root rate suggested by known lower bounds is proved.
We study distributed hypothesis testing and establish the exact error exponent in single-letter form for new testing problems. In distributed hypothesis testing, a receiver decides between $\mathcal{H}_0:P_{XY}$ and $\mathcal{H}_1:Q_{XY}$ based on $Y^n$ and a rate-limited description of $X^n$. So far, such single-lette...
The pairwise independent correlation gap is the ratio of the maximum expected value of a set function under arbitrary dependence to that under pairwise independence, measuring the loss from this independence restriction. Under mutual independence, this gap is universally bounded by $e/(e-1)$ for monotone submodular fun...
This work generalizes the implicit representation framework of Gupta et al. (SODA 2010) by allowing the encoder to run in fixed-parameter tractable time, and provides representation-dependent lower bounds that hold even for larger $\epsilon$.
Pritish Kamath, Ravi Kumar, Pasin Manurangsi· 1 citation
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