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TAIL-MIL: Time-Aware and Instance-Learnable Multiple Instance Learning for Multivariate Time Series Anomaly Detection
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Proposes TAIL-MIL, a two-level (time-point and variate) multiple instance learning model with T- and V-attention and conjunctive pooling that detects anomalies at bag, time-point, and variate levels using only bag-level labels.
Problem
Multivariate time series anomaly detection where anomalies must be localized at bag (multi-sensor sequence), time-point, and individual-variate levels, but instance-level labels are costly to obtain.
Approach
Two-dimensional MIL with two attention mechanisms (T-Attention across time-point instances, V-Attention across variates using recurrent features of previous time points) combined with conjunctive pooling applied at both levels, so instance-level predictions feed directly into bag-level prediction without external positional or RNN features.
Key results
- On the SOH dataset, TAIL-MIL reaches 0.9539 AUROC for TPIM detection and 0.9290 AUROC for VI-TPIM detection, far above the best MIL baselines (Nested 0.7272 for VI-TPIM).
- On 5-ECK-2022, TAIL-MIL achieves 0.9709 AUROC for bag-level (TAB) detection versus 0.9038 for the best 1D baseline (MILNET).
- TAIL-MIL matches or approaches fully supervised instance-level learning, e.g. 0.9458 VI-TPIM AUROC on 5-ECK-2022 vs 0.9283 supervised.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TAIL-MIL instead of Nested | SOH TAB detection · SOH | AUROC: 0.9513 -> 0.9574 | Helped |
| Use TAIL-MIL instead of MILNET | SOH TAB detection · SOH | F1-Score: 0.9824 -> 0.9844 | Helped |
| Use TAIL-MIL instead of MILNET | 5-ECK-2022 TAB detection · 5-ECK-2022 | AUROC: 0.9038 -> 0.9709 | Helped |
| Use TAIL-MIL instead of TimeMIL | 5-ECK-2022 TAB detection · 5-ECK-2022 | F1-Score: 0.8951 -> 0.9529 | Helped |
| Use TAIL-MIL instead of Nested | SOH TPIM detection · SOH | AUROC: 0.9513 -> 0.9539 | Helped |
| Use TAIL-MIL instead of Nested | SOH TPIM detection · SOH | F1-Score: 0.9808 -> 0.9812 | Helped |
| Use TAIL-MIL instead of Nested | 5-ECK-2022 TPIM detection · 5-ECK-2022 | AUROC: 0.7891 -> 0.9075 | Helped |
| Use TAIL-MIL instead of supervised learning | 5-ECK-2022 TPIM detection · 5-ECK-2022 | F1-Score: 0.9041 -> 0.8978 | Hurt |
| Use TAIL-MIL instead of Nested | SOH VI-TPIM detection · SOH | AUROC: 0.7272 -> 0.9290 | Helped |
| Use TAIL-MIL instead of supervised learning | SOH VI-TPIM detection · SOH | F1-Score: 0.9472 -> 0.9454 | Hurt |
| Use TAIL-MIL instead of Nested | 5-ECK-2022 VI-TPIM detection · 5-ECK-2022 | AUROC: 0.7386 -> 0.9458 | Helped |
| Use TAIL-MIL instead of Nested | 5-ECK-2022 VI-TPIM detection · 5-ECK-2022 | F1-Score: 0.7078 -> 0.9204 | Helped |
Surprising findings
- Conventional 1D-MIL methods such as MILLET and TimeMIL perform near chance on instance-level (TPIM/VI-TPIM) detection in the SOH dataset, with AUROC around 0.5-0.6.
Limitations
- Instance-level evaluation relies on baselines adapted from bag-level MIL, and the comparison uses only two datasets.
- Recurrent-feature window n is fixed to 2 and not explored in the main text.
- Theoretical claims (Shapley-proportionality) are stated but the proofs are deferred to an appendix not fully shown.
Experimental setup
Datasets: State of Health (SOH) dataset 5-ECK-2022
Benchmarks: SOH dataset 5-ECK-2022
Metrics: AUROC F1-Score
Baselines: mi-Net AMIL MILNET Additive MIL MILLET TimeMIL Nested MIL Supervised learning
Builds on: MILLET TimeMIL Nested MIL Attention-based MIL Shapley value explanation
Closest papers by meaning
- TimeMIL: Advancing Multivariate Time Series Classification via a Time-aware Multiple Instance Learning (ICML 2024 · similarity 0.88)
- Structured Temporal Causality for Interpretable Multivariate Time Series Anomaly Detection (NeurIPS 2025 · similarity 0.88)
- The Elephant in the Room: Towards A Reliable Time-Series Anomaly Detection Benchmark (NeurIPS 2024 · similarity 0.87)
- Detect, Explain, Interpret: An End-to-End Benchmark for Time Series Anomaly Detection, Explainability and Interpretability. (NeurIPS 2026 · similarity 0.86)
- UP2ME: Univariate Pre-training to Multivariate Fine-tuning as a General-purpose Framework for Multivariate Time Series Analysis (ICML 2024 · similarity 0.86)
- COMET: Codebook-based Online-adaptive Multi-scale Embedding for Time-series Anomaly Detection (NeurIPS 2026 · similarity 0.86)
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