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Asymmetric Likelihood-Free Hypothesis Testing

Gunjan Kumar, Yash Pote, Jonathan Scarlett · 2026 · arXiv

DOI: 10.48550/arXiv.2610.29798 · open-access PDF

Japanese

確率フリーの仮説テスト(LFHT)では、未知の2つの分布から $P、Q$ を $[n]$ で $\mathrm{d_{TV}}(P,Q)\geq\varepsilon$、および第3の分布から $D\in\{P,Q\}$ を採取すると、目標は $D=P$ または $D=Q$ を識別することです。我々は、サンプル予算 $s_P$ と $s_Q$ for $P$ と $Q$ が異なる場合、非対称の確率フリーの仮説テストを研究し、実行可能な3倍の $(s_P,P,Q,S_D)を論理的要因に特徴づける。我々は、

Machine translation (Meta M2M100); the English original follows.

Abstract

In likelihood-free hypothesis testing (LFHT), given samples from two unknown distributions $P,Q$ on $[n]$ with $\mathrm{d_{TV}}(P,Q)\geq\varepsilon$, and from a third distribution $D\in\{P,Q\}$, the goal is to identify whether $D=P$ or $D=Q$. We study asymmetric likelihood-free hypothesis testing, where the sample budgets $s_P$ and $s_Q$ for $P$ and $Q$ may differ, and characterize the feasible triples $(s_P,s_Q,s_D)$ up to logarithmic factors. We establish that unequal reference budgets can give a polynomial saving. For instance, for constant separation, $n$ samples from $P$ and $n^{3/4}$ fro

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