Mean estimation for entangled single-sample distributions
Mean estimation for entangled single-sample distributions
复制标题
纠缠单样本分布的均值估计
DOI：
10.1109/isit.2019.8849279
复制
发表时间：
2019
期刊：
影响因子：
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通讯作者：
Loh, Po-Ling
中科院分区：
文献类型：
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作者：
Pensia, Ankit;Jog, Varun;Loh, Po-Ling
我们考虑的问题估计的共同均值的单变量数据时，独立的样本是从不同的对称，单峰分布。这捕获了所有样本均为具有不同未知方差的高斯分布的设置。我们提出了一个估计，适应数据的异质性水平，实现近最优的i.i.d.设置和一些异构设置，其中"低噪声"点的分数小到log n n。我们的估计是一个混合的模态区间，短，从经典统计中值估计。比率取决于混合分布的百分位数，使得我们的估计甚至对具有无穷方差的分布也有用。
We consider the problem of estimating the common mean of univariate data, when independent samples are drawn from non-identical symmetric, unimodal distributions. This captures the setting where all samples are Gaussian with different unknown variances. We propose an estimator that adapts to the level of heterogeneity in the data, achieving near-optimality in both the i.i.d. setting and some heterogeneous settings, where the fraction of “low-noise" points is as small as log n n . Our estimator is a hybrid of the modal interval, shorth, and median estimators from classical statistics. The rates depend on the percentile of the mixture distribution, making our estimators useful even for distributions with infinite variance.
学习任意高斯的混合
DOI：
10.1145/380752.380808
发表时间：
2001
期刊：
The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
影响因子：
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作者：
Sanjeev Arora;R. Kannan
通讯作者：
R. Kannan