Conformal Anomaly Detection in Event Sequences

Anomaly detection in continuous-time event sequences is a crucial task in safety-critical applications. While existing methods primarily focus on developing a superior test statistic, they fail to provide guarantees regarding the false positive rate (FPR), which undermines their reliability in practical deployments. In this paper, we propose CADES (Conformal Anomaly Detection in Event Sequences), a novel test procedure based on conformal inference for the studied task with finite-sample FPR control. Specifically, by using the time-rescaling theorem, we design two powerful non-conformity scores tailored to event sequences, which exhibit complementary sensitivities to different abnormal patterns. CADES combines these scores with Bonferroni correction to leverage their respective strengths and addresses non-identifiability issues of existing methods. Theoretically, we prove the validity of CADES and further provide strong guarantees on calibration-conditional FPR control. Experimental results on synthetic and real-world datasets, covering various types of anomalies, demonstrate that CADES outperforms state-of-the-art methods while maintaining FPR control. Conformal Anomaly Detection in Event Sequences non-identifiability issues (Zhang et al., 2024b), producing similar values for two markedly distinct sequences. This significantly reduces their detection power, motivating us to design a more expressive non-conformity score. Due to the variable length of event sequences and the intricate dependencies between events, the design of this score is both essential and non-trivial. To this end, we introduce CADES (Conformal Anomaly Detection in Event Sequences), a novel method based on conformal inference for detecting anomalous event sequences. Specifically, we design two powerful non-conformity scores tailored to event sequences using the time-rescaling theorem (Brown et al., 2002) . These scores are complementary in their sensitivity to different abnormal patterns and address the limitations mentioned above of existing test statistics. Unlike standard conformal inference methods, which rely on one-sided p-values and a single non-conformity score, CADES utilizes two-sided p-values and applies the Bonferroni correction (Shaffer, 1995) to combine both scores. This is because two-sided p-values are crucial, as we show that both small and large values of the proposed scores can indicate OOD sequences. Moreover, by combining both scores, CADES fully exploits the strengths of each, enabling more accurate anomaly detection. Theoretically, we prove the validity of CADES and provide guarantees on calibrationconditional FPR, which are stronger than marginal FPR guarantees averaged over all possible calibration sets. We summarize our contributions as follows: • We establish the connection between conformal inference and anomaly detection in event sequences. Building upon this, we propose CADES, a novel test procedure that combines two proposed scores with Bonferroni correction to perform hypothesis testing, offering a statistically sound anomaly detection method. • We design two new powerful non-conformity scores tailored to continuous-time event sequences. We demonstrate that these scores complement each other in terms of sensitivity to different anomalies and address nonidentifiability issues of existing test statistics. • We prove the validity of the p-values used in CADES. This guarantees controlling the marginal FPR at a prespecified level. We further provide theoretical guarantees on calibration-conditional FPR, which are stronger than marginal FPR guarantees. • We conduct extensive experiments on synthetic and realworld datasets, covering various types of anomalies, to validate the effectiveness of CADES 2 . The results show that CADES outperforms state-of-the-art methods with respect to both detection performance and FPR control.