Data Compression for Simultaneous/Sequential Inference Tasks in Sensor Networks

Sensor networks typically perform multiple inference tasks and compression is often used to aid in the sharing of data. Compression degrades the inference accuracy and should be optimized for the tasks at hand. Unfortunately, simultaneous optimization for multiple tasks is not generally possible - typically a fundamental trade-off exists that has not been previously explored. A particularly relevant and interesting scenario occurs with a task-driven sequence of inferences. This paper develops a framework for data-optimized data compression for the case of multiple inferences. In particular, the Fisher information matrix (FIM) is used to derive a suitable scalar distortion measure for multiple estimation tasks, while the Chernoff distance is used for decision tasks. Theoretical results are presented that support the use of this particular scalar FIM-based distortion. The method is demonstrated with application to the sequential problem of first detecting a common intercepted signal among sensors and then once detected progressing to the location of the source