Quantization for Communication-Efficient Change-Point Detection Over Networks

Change-Point Detection (CPD) has been researched for a long time in statistical signal processing, and has been widely used in many applications such as monitoring and anomaly detection. When detecting over networks, existing algorithms require sensors to exchange information via transmitting full-precision variables, which requires large bandwidth and consumes a large amount of energy. To address these problems, we explore the idea of quantizing data with low precision without deteriorating the detection performance. Specifically, considering the strong autocorrelation of the transmitted sequence in time domain and the accumulation of quantization error due to the autocorrelation, we design a scheme that combines the differential quantization technique and the error feedback technique. Based on this scheme, we propose a communication-efficient decentralized CPD algorithm named Quantized CUSUM (Q-CUSUM), which only requires small bandwidth and has low energy consumption. We theoretically analyze two commonly-used detection criteria, namely Average Run Length (ARL) and Expected Detection Delay (EDD), and compute their theoretical bounds. It is proved that the detection performance is robust to the quantization error. The proposed quantization scheme can be easily extended to the partial-communication case, where at each time only a subset of sensor pairs are allowed to exchange information. Experiments are implemented on both synthetic and real-world datasets. The results indicate that the proposed quantization scheme can effectively reduce the communication cost without deteriorating the detection performance.