Testing Distributions Against Bounded Distinguishers
Motivated by the challenge of testing distributions over high-dimensional or continuous domains, we study distribution testing with respect to bounded classes of distinguishers. A representative task is to use samples from an unknown distribution $P$ over a very large domain to decide between two cases: $P = P_{\mathsf{ref}}$ for a fixed reference distribution $P_{\mathsf{ref}}$, or there exists a distinguisher $f$ in a bounded class $\mathcal{F}$ which witnesses the separation $|\mathbf{E}_P[f] - \mathbf{E}_{P_{\mathsf{ref}}}[f]| > ε$. This is the task of identity testing with respect to fooling distance, a name inspired by the conceptual connection with pseudorandomness. (Formally, our ...
| Authors | Mark Bun, Rathin Desai, Renato Ferreira Pinto |
|---|---|
| Primary category | cs.DS |
| Published | 17 July 2026 |
| Last updated at source | 17 July 2026 |
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