Nonparametric Detection of Geometric Structures Over Networks
Nonparametric Detection of Geometric Structures Over Networks
复制标题
通过网络进行几何结构的非参数检测
DOI：
10.1109/tsp.2017.2718977
复制
发表时间：
2017
影响因子：
5.4
通讯作者：
Poor, H. Vincent
中科院分区：
文献类型：
--
作者：
Zou, Shaofeng;Liang, Yingbin;Poor, H. Vincent
研究了网络中可能存在异常结构的非参数检测问题。对应于异常结构的节点（如果存在异常结构的话）接收由分布q生成的样本，该分布q不同于为其他节点生成样本的分布p。如果不存在异常结构，则所有节点接收由p生成的样本。假设分布p和q是任意的且未知的。我们的目标是设计统计上一致的测试，随着网络规模逐渐变大，误差收敛到零的概率。基于核的测试是基于最大平均差异提出的，它测量分布嵌入再生核Hilbert空间的平均值之间的距离。首先研究了线路网络中异常间隔的检测问题。为了保证所提出的测试是一致的，候选异常区间的最小和最大尺寸的充分条件的特点。它还表明，某些必要条件必须保持，以保证任何测试是普遍一致的。充分和必要条件的比较产生的建议的测试是顺序级最优和近最优的候选异常区间的最小和最大尺寸分别。推广到其他网络的结果进一步发展。数值结果证明了所提出的测试的性能。
Nonparametric detection of the possible existence of an anomalous structure over a network is investigated. Nodes corresponding to the anomalous structure (if one exists) receive samples generated by a distribution q, which is different from a distribution p generating samples for other nodes. If an anomalous structure does not exist, all nodes receive samples generated by p. It is assumed that the distributions p and q are arbitrary and unknown. The goal is to design statistically consistent tests with probability of errors converging to zero as the network size becomes asymptotically large. Kernel-based tests are proposed based on maximum mean discrepancy, which measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space. Detection of an anomalous interval over a line network is first studied. Sufficient conditions on minimum and maximum sizes of candidate anomalous intervals are characterized in order to guarantee that the proposed test is consistent. It is also shown that certain necessary conditions must hold in order to guarantee that any test is universally consistent. Comparison of sufficient and necessary conditions yields that the proposed test is order-level optimal and nearly optimal respectively in terms of minimum and maximum sizes of candidate anomalous intervals. Generalization of the results to other networks is further developed. Numerical results are provided to demonstrate the performance of the proposed tests.
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DOI：
10.1214/10-aos817
发表时间：
2009-08
期刊：
--
影响因子：
--
作者：
L. Addario-Berry;N. Broutin;L. Devroye;G. Lugosi
通讯作者：
L. Addario-Berry;N. Broutin;L. Devroye;G. Lugosi
DOI：
10.1080/01621459.2017.1286240
发表时间：
2018-01-01
影响因子：
3.7
作者：
Arias-Castro, Ery;Castro, Rui M.;Wang, Meng
通讯作者：
Wang, Meng
影响因子：
4.5
作者：
Arias-Castro, Ery;Candes, Emmanuel J.;Zeitouni, Ofer
通讯作者：
Zeitouni, Ofer
影响因子：
2.5
作者：
Arias-Castro, E;Donoho, DL;Huo, XM
通讯作者：
Huo, XM
用于线路网络异常检测的基于内核的非参数测试
DOI：
--
发表时间：
2014
期刊：
International Workshop on Machine Learning for Signal Processing
影响因子：
--
作者：
Shaofeng Zou;Yingbin Liang;H. Poor
通讯作者：
H. Poor