During operation, the system obtains a training dataset during a training mode, wherein the training dataset includes counts of actions performed by users while operating applications in the computer system. Next, the system uses the training dataset to produce corresponding per-action datasets. The system then cleanses the training dataset based on counts of actions in the per-action datasets to produce a cleansed training dataset, and uses the cleansed training dataset to produce corresponding per-user datasets. Next, the system trains per-user models based on the per-user datasets to detect anomalous actions of users. The system then obtains a surveillance dataset during a surveillance mode, wherein the surveillance dataset includes counts of actions performed by users while operating applications in the computer system. Next, the system uses the trained per-user models to detect anomalous actions in the surveillance dataset. Finally, when an anomalous action is detected, the system triggers an alert.