Distributed Statistical Estimation of High-Dimensional and Nonparametric Distributions
Distributed Statistical Estimation of High-Dimensional and Nonparametric Distributions
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DOI：
10.1109/isit.2018.8437818
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
Yanjun Han;P. Mukherjee;Ayfer Özgür;T. Weissman
中科院分区：
文献类型：
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作者：
Yanjun Han;P. Mukherjee;Ayfer Özgür;T. Weissman
我们考虑在分布式网络中估计高维和非参数分布的问题，其中网络中的每个传感器从底层分布中观察一个独立的样本，并可以通过在公共黑板上最多写$k$位将其传递给中央处理器。我们得到了在$L$ 1loss下估计底层分布的最小、最大风险的匹配上界和下界。我们的结果表明，极大极小风险在k中呈指数下降。我们没有像文献中通常那样依赖于相反的强数据处理不等式，而是建立在通信约束的新表示上，这导致了对问题的严格描述。
We consider the problem of estimating high-dimensional and nonparametric distributions in distributed networks, where each sensor in the network observes an independent sample from the underlying distribution and can communicate it to a central processor by writing at most $k$ bits on a public blackboard. We obtain matching upper and lower bounds for the minimax risk of estimating the underlying distribution under $L$ 1loss. Our results reveal that the minimax risk reduces exponentially in k. Instead of relying on strong data processing inequalities for the converse as commonly done in the literature, we build on a new representation of the communication constraint, which leads to a tight characterization of the problem.