基于PPR鞅置信序列的PAC模式估计
PAC Mode Estimation using PPR Martingale Confidence Sequences
摘要：
我们考虑的问题，正确识别的\textit{mode}的离散分布$\mathcal{P}$具有足够高的概率，通过观察一个序列的i.i.d.从$\mathcal{P}$中抽取样本。当$\mathcal{P}$具有大小为$K = 2$的支持集时，该问题简化为单个参数的估计。在注意到这种特殊情况下，解决了很好的先验后验比（PPR）鞅置信序列\citep{waudby-ramdas-ppr}，我们提出了一个推广模式估计，其中$\mathcal{P}$可能采取$K \geq 2$值。首先，我们表明，“一对一”的原则，从$K = 2$推广到$K \geq 2$类是更有效的“一对休息”的替代。然后，我们证明了我们得到的停止规则，表示为PPR-1v 1，是渐近最优的（作为错误概率采取$0$）。PPR-1v 1是无参数和计算量轻，即使在非渐近制度中，也比竞争对手产生更少的样本。我们在采样的两个实际应用中展示了它的收益：选举预测和区块链中智能合约的验证。
英文摘要：
We consider the problem of correctly identifying the \textit{mode} of a discrete distribution $\mathcal{P}$ with sufficiently high probability by observing a sequence of i.i.d. samples drawn from $\mathcal{P}$. This problem reduces to the estimation of a single parameter when $\mathcal{P}$ has a support set of size $K = 2$. After noting that this special case is tackled very well by prior-posterior-ratio (PPR) martingale confidence sequences \citep{waudby-ramdas-ppr}, we propose a generalisation to mode estimation, in which $\mathcal{P}$ may take $K \geq 2$ values. To begin, we show that the "one-versus-one" principle to generalise from $K = 2$ to $K \geq 2$ classes is more efficient than the "one-versus-rest" alternative. We then prove that our resulting stopping rule, denoted PPR-1v1, is asymptotically optimal (as the mistake probability is taken to $0$). PPR-1v1 is parameter-free and computationally light, and incurs significantly fewer samples than competitors even in the non-asymptotic regime. We demonstrate its gains in two practical applications of sampling: election forecasting and verification of smart contracts in blockchains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
