Event stream is an important data format in real life. The events are usually expected to follow some regular patterns over time. However, the patterns could be contaminated by unexpected absences or occurrences of events. In this paper, we adopt the temporal point process framework for learning event stream and we provide a simple-but-effective method to deal with both commission and omission event outliers.In particular, we introduce a novel weight function to dynamically adjust the importance of each observed event so that the final estimator could offer multiple statistical merits. We compare the proposed method with the vanilla one in the classification problems, where event streams can be clustered into different groups. Both theoretical and numerical results confirm the effectiveness of our new approach. To our knowledge, our method is the first one to provably handle both commission and omission outliers simultaneously.