论文标题
有效实施高精度的最大可能性最大可能性
On the Efficient Implementation of High Accuracy Optimality of Profile Maximum Likelihood
论文作者
论文摘要
我们提供了一种有效的统一插件方法，用于估计给定$ n $独立样本的分布的对称属性。我们的估计器基于配置文件最大含量（PML），是当估计误差$ε\ gg n^{ - 1/3} $时估算各种对称属性的最佳样品。该结果在以前的最佳准确度阈值的$ε\ gg n^{ - 1/4} $可通过多项式时间可计算的基于PML的通用估计器[acsss21，acss20]实现。我们的估计器达到了通用对称属性估计的理论限制，因为[HAN21]表明，当$ 1 $ -LIPSCHITZ属性时，广泛的通用估计器（包含许多知名方法）不能是最佳样品。
We provide an efficient unified plug-in approach for estimating symmetric properties of distributions given $n$ independent samples. Our estimator is based on profile-maximum-likelihood (PML) and is sample optimal for estimating various symmetric properties when the estimation error $ε\gg n^{-1/3}$. This result improves upon the previous best accuracy threshold of $ε\gg n^{-1/4}$ achievable by polynomial time computable PML-based universal estimators [ACSS21, ACSS20]. Our estimator reaches a theoretical limit for universal symmetric property estimation as [Han21] shows that a broad class of universal estimators (containing many well known approaches including ours) cannot be sample optimal for every $1$-Lipschitz property when $ε\ll n^{-1/3}$.
