基于1比特测量的参数模型中最快变化检测
Quickest Change Detection in Parametric Models With 1-Bit Measurements
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中文总结 AI 辅助
针对含未知参数的1比特量化观测的参数模型变化检测问题，提出AQuTeCUSUM算法，其通过在线估计参数并自适应选阈值最大化Kullback-Leibler散度，经理论证明渐近最优，并在高斯、泊松分布下验证性能。
中文摘要 AI 辅助
我们研究从1比特量化观测中进行最快变化检测，其中变化后分布为含未知参数的参数模型，且量化阈值与检测统计量共同选择。我们提出自适应量化阈值CUSUM（AQuTeCUSUM）算法，该算法在线估计变化后参数并自适应选择量化阈值以最大化诱导的Kullback-Leibler散度。在合适的正则性条件下，我们表征了AQuTe-CUSUM过程的平均运行长度和最坏情况平均检测延迟，证明当平均运行长度趋于无穷时，其在一阶意义下渐近最优。最后，我们针对高斯分布和泊松分布两种分布评估了AQuTe-CUSUM的性能。
英文摘要
We consider the quickest change detection from 1-bit quantized observations, where the post-change distribution is a parametric model with unknown parameters and the quantization thresholds are jointly chosen with the detection statistic. We propose an Adaptive-Quantization-Threshold CUSUM (AQuTeCUSUM) algorithm, which estimates the post-change parameter online and adaptively selects the quantization threshold to maximize the induced Kullback-Leibler divergence. Under suitable regularity conditions, we characterize the average run length and worst-case average detection delay of the AQuTe-CUSUM procedure, and show that it is asymptotically optimal in first-order as the average run length goes to infinity. Finally, we assess the performance of AQuTe-CUSUM for two distributions, namely the Gaussian and Poisson.
