Entropy Equivalence Testing
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given samples from two unknown distributions $p,q$ and a parameter $\varepsilon \in(0,1/2]$, between $p=q$ and $|H(p)-H(q)| \geq \varepsilon$ (where $H$ denotes the Shannon entropy). We provide a time- and sample-efficient algorithm for this task, showing that the optimal sample complexity for this task can be significantly lower than that of closeness testing. As an application, we leverage this result to provide the first non-trivial testing algorithm for (st...
| Authors | Clément L. Canonne, Yash Pote, Jonathan Scarlett et al. |
|---|---|
| Primary category | cs.DS |
| Published | 22 May 2026 |
| Last updated at source | 14 July 2026 |
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