Global testing against sparse alternatives under Ising models
Global testing against sparse alternatives under Ising models
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DOI：
10.1214/17-aos1612
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
R. Mukherjee;S. Mukherjee;Ming Yuan
中科院分区：
文献类型：
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作者：
R. Mukherjee;S. Mukherjee;Ming Yuan
本文研究了相关性对稀疏信号检测的影响。特别是，我们专注于针对依辛模型的二元结果均值的稀疏替代方法的全局测试，并建立信号的强度和稀疏度之间的相互作用如何决定其在各种依赖概念下的可检测性。在居里-魏斯模型下，我们观察到“热力学”相变的影响，依赖性的深刻影响得到了最好的说明。特别是，临界状态表现出一种微妙的“依赖的祝福”现象，在临界状态下，人们可以检测到比其他情况弱得多的信号。此外，我们开发了一个广泛适用于解释相关性的测试程序，并证明了它在相当一般的正则性条件下是渐近极小极大最优的。
In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence. The profound impact of dependence is best illustrated under the Curie-Weiss model where we observe the effect of a "thermodynamic" phase transition. In particular, the critical state exhibits a subtle "blessing of dependence" phenomenon in that one can detect much weaker signals at criticality than otherwise. Furthermore, we develop a testing procedure that is broadly applicable to account for dependence and show that it is asymptotically minimax optimal under fairly general regularity conditions.