Detection of correlated components in multivariate Gaussian models
Detection of correlated components in multivariate Gaussian models
复制标题
多元高斯模型中相关分量的检测
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
L. Lai
中科院分区：
文献类型：
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作者：
Jun Geng;Weiyu Xu;L. Lai
本文研究了p维高斯向量中相关分量的检测问题。在所考虑的设置中，s个未知分量与已知的协方差结构相关。因此，对于未知的一组相关分量存在等式可能的假设。在本文中，我们假设观测器能够观测到向量中任何分量的子集，而不是在每个时间索引处进行全向量观测。由于观察的灵活性，观察者有兴趣找到最佳的抽样策略，以最大限度地提高多假设检验问题的误差指数（每个样本）。结果表明，当这些s分量的相关性较弱时，观测器采用全矢量观测是最优的;当相关性较强时，采用全矢量观测的策略不再是最优的，最优采样策略与全矢量观测策略相比，检测误差指数至少增加了25%。
In this paper, the problem of detecting correlated components in a p-dimensional Gaussian vector is considered. In the setup considered, s unknown components are correlated with a known covariance structure. Hence, there are equation possible hypotheses for the unknown set of correlated components. Instead of taking a full-vector observation at each time index, in this paper we assume that the observer is capable of observing any subset of components in the vector. With this flexibility in taking observations, the observer is interested in finding the optimal sampling strategy to maximize the error exponent (per sample) of the multi-hypothesis testing problem. We show that, when the correlation of these s components is weak, it is optimal for the observer to take full-vector observations; when the correlation is strong, the strategy of taking full-vector observation is not optimal anymore, and the optimal sampling strategy increases the detection error exponent by 25% at least, compared with the full-vector observation strategy.