Previous works on the CERT insider threat detection case have neglected graph and text features despite their relevance to describe user behavior. Additionally, existing systems heavily rely on feature engineering and audit data aggregation to detect malicious activities. This is time consuming, requires expert knowledge and prevents tracing back alerts to precise user actions. To address these issues we introduce ADSAGE to detect anomalies in audit log events modeled as graph edges. Our general method is the first to perform anomaly detection at edge level while supporting both edge sequences and attributes, which can be numeric, categorical or even text. We describe how ADSAGE can be used for fine-grained, event level insider threat detection in different audit logs from the CERT use case. Remarking that there is no standard benchmark for the CERT problem, we use a previously proposed evaluation setting based on realistic recall-based metrics. We evaluate ADSAGE on authentication, email traffic and web browsing logs from the CERT insider threat datasets, as well as on real-world authentication events. ADSAGE is effective to detect anomalies in authentications, modeled as user to computer interactions, and in email communications. Simple baselines give surprisingly strong results as well. We also report performance split by malicious scenarios present in the CERT datasets: interestingly, several detectors are complementary and could be combined to improve detection. Overall, our results show that graph features are informative to characterize malicious insider activities, and that detection at fine-grained level is possible.