TAIL-MIL: Time-Aware and Instance-Learnable Multiple Instance Learning for Multivariate Time Series Anomaly Detection

Abstract This study addresses the challenge of detecting anomalies in multivariate time series data. Considering a bag (e.g., multi-sensor data) consisting of two-dimensional spaces of time points and multivariate instances (e.g., individual sensors), we aim to detect anomalies at both the bag and instance level with a unified model. To circumvent the practical difficulties of labeling at the instance level in such spaces, we adopt a multiple instance learning (MIL)-based approach, which enables learning at both the bag- and instance- levels using only the bag-level labels. In this study, we introduce time-aware and instance-learnable MIL (simply, TAIL-MIL). We propose two specialized attention mechanisms designed to effectively capture the relationships between different types of instances. We innovatively integrate these attention mechanisms with conjunctive pooling applied to the two-dimensional structure at different levels (i.e., bag- and instance-level), enabling TAIL-MIL to effectively pinpoint both the timing and causative multivariate factors of anomalies. We provide theoretical evidence demonstrating TAIL-MIL's efficacy in detecting instances with two-dimensional structures. Furthermore, we empirically validate the superior performance of TAIL-MIL over the state-of-the-art MIL methods and multivariate time-series anomaly detection methods.