Spatio-temporal event data are becoming increasingly commonplace in a wide variety of applications, such as electronic transaction records, social network data, and crime incident reports. How to efficiently detect anomalies in these dynamic systems using these streaming event data? This work proposes a novel anomaly detection framework for such event data combining the Long Short-Term Memory (LSTM) and marked spatio-temporal point processes. The detection procedure can be computed in an online and distributed fashion via feeding the streaming data through an LSTM and a neural network-based discriminator. This work studies the falsealarm- rate and detection delay using theory and simulation and shows that it can achieve weak signal detection by aggregating local statistics over time and networks. Finally, we demonstrate the good performance using real-world data sets.