Minimax Robust Decentralized Hypothesis Testing for Parallel Sensor Networks
Minimax Robust Decentralized Hypothesis Testing for Parallel Sensor Networks
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DOI：
10.1109/tit.2020.3028451
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发表时间：
2021-01-01
影响因子：
2.5
通讯作者：
Guel, Goekhan
中科院分区：
文献类型：
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作者：
Guel, Goekhan
研究了并行接入传感器网络的分散检测问题，其中传感器统计量不完全已知，并假设其服从属于已知不确定性类的分布函数。结果表明，对于基于Kullback-Leibler （KL）散度建立的不确定性类的确定性决策规则，不存在极大极小鲁棒性检验。对于kl -散度以及其他一些不确定性类，如α -散度，联合随机有界性，这是证明极大极小鲁棒性的基本规则，不成立。这就提出了一个自然的问题，如果不确定性类不具有此属性，是否可以给出最小化鲁棒分散检测问题的解决方案。这个问题的答案已经被证明是肯定的，这导致了对现有工作的概括。此外，对于Huber的扩展不确定性类，为了保证极大极小鲁棒性，传感器处的量化函数不需要是单调的。讨论了将该理论推广到极大极小和内曼-皮尔逊公式、重复观察、不完善的报告渠道和不同的网络拓扑结构的可能性。给出了考虑截断似然比检验和截尾似然比检验的仿真实例。
Decentralized detection is studied for parallel-access sensor networks, where sensor statistics are not known completely and are assumed to follow distribution functions which belong to known uncertainty classes. It is shown that there exist no minimax robust tests over the deterministic decision rules for the uncertainty classes built with respect to the Kullback-Leibler (KL)-divergence. For the KL-divergence as well as for some other uncertainty classes, such as the alpha-divergences, the joint stochastic boundedness property, which is the fundamental rule to prove minimax robustness, fails to hold. This raises a natural question whether a solution to minimax robust decentralized detection problem can be given if the uncertainty classes do not own this property. An answer to this question has been shown to be positive, which leads to a generalization of an existing work. Moreover, it is shown that for Huber's extended uncertainty classes quantization functions at the sensors are not required to be monotone in order to claim minimax robustness. A possible generalization of the theory to minimax- and Neyman-Pearson formulations, repeated observations, imperfect reporting channels and different network topologies have been discussed. Simulation examples are provided considering clipped- and censored likelihood ratio tests.