Nowadays, sensor networks are being used to monitor increasingly complex physical systems, necessitating advanced signal analysis capabilities as well as the ability to handle large amounts of network data. For the first time, we present a methodology to enable advanced decision support on a low-power sensor node through the direct use of compressively-sensed signals in a supervised-learning framework; such signals provide a highly efficient means of representing data in the network, and their direct use overcomes the need for energy-intensive signal reconstruction. Sensor networks for advanced patient monitoring are representative of the complexities involved. We demonstrate our technique on a patient-specific seizure detection algorithm based on electroencephalograph (EEG) sensing. Using data from 21 patients in the CHB-MIT database, our approach demonstrates an overall detection sensitivity, latency, and false alarm rate of 94.70%, 5.83 seconds, and 0.199 per hour, respectively, while achieving data compression by a factor of 10x. This compares well with the state-of-the-art baseline detector with corresponding results being 96.02%, 4.59 seconds, and 0.145 per hour, respectively.