Forecasting Anomaly Precursors via Uncertainty-Aware Time-Series Ensembles

Hyeongwon Kang; Jinwoo Park; Seunghun Han; Pilsung Kang

cs.LGFeb 19, 2026

Forecasting Anomaly Precursors via Uncertainty-Aware Time-Series Ensembles

Authors: Hyeongwon Kang, Jinwoo Park, Seunghun Han, Pilsung Kang

Organizations: Department of Industrial & Management Engineering, Korea University, 126-16 Anam-dong 5-ga, Seongbuk-gu, Seoul, Republic of Korea · Department of Industrial Engineering, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul, Republic of Korea · LG CNS, 71, Magokjungang 8-ro, Gangseo-gu, Seoul, Republic of Korea

Abstract

Detecting anomalies in time-series data is critical in domains such as industrial operations, finance, and cybersecurity, where early identification of abnormal patterns is essential for ensuring system reliability and enabling preventive maintenance. However, most existing methods are reactive: they detect anomalies only after they occur and lack the capability to provide proactive early warning signals. In this paper, we propose FATE (Forecasting Anomalies with Time-series Ensembles), a novel unsupervised framework for detecting Precursors-of-Anomaly (PoA) by quantifying predictive uncertainty from a diverse ensemble of time-series forecasting models. Unlike prior approaches that rely on reconstruction errors or require ground-truth labels, FATE anticipates future values and leverages ensemble disagreement to signal early signs of potential anomalies without access to target values at inference time. To rigorously evaluate PoA detection, we introduce Precursor Time-series Aware Precision and Recall (PTaPR), a new metric that extends the traditional Time-series Aware Precision and Recall (TaPR) by jointly assessing segment-level accuracy, within-segment coverage, and temporal promptness of early predictions. This enables a more holistic assessment of early warning capabilities that existing metrics overlook. Experiments on five real-world benchmark datasets show that FATE achieves an average improvement of 19.9 percentage points in PTaPR AUC and 20.02 percentage points in early detection F1 score, outperforming baselines while requiring no anomaly labels. These results demonstrate the effectiveness and practicality of FATE for real-time unsupervised early warning in complex time-series environments.

Figures & tables

Fig. 1: Comparison between traditional anomaly detection and Precursor-of-Anomaly (PoA) detection. (a) Traditional methods detect anomalies after their occurrence, limiting the ability to prevent failures. (b) PoA detection identifies early warning signals prior to anomaly onset, enabling proactive intervention.

Fig. 2: Overview of the proposed FATE framework. The input sequence is fed into an ensemble of forecasting models to predict future time steps. Uncertainty-based precursor detection is performed using the ensemble outputs, and early detection performance is quantitatively evaluated using the PTaPR metric.

Fig. 3: Example of predicting anomaly precursors at future time steps based on input at time $t$ . The third window ( $w=2$ ) forecasts $L_{y}=5$ future steps from current time $t+L_{x}-1=11$ , and a precursor is detected at time step 13.

Fig. 4: Illustration of early detection, partial detection, and ambiguous instances in the PTaPR metric. Anomalies and predictions are represented as instance-level segments along the x-axis. For example, anomaly $a_{1}$ spans indices 1 to 6, while early prediction $p^{\prime}_{3}$ detects an anomaly between indices 13 and 16.

Fig. 5: Example of PTaPR computation for anomaly segments ( $a_{1},a_{2}$ ) and prediction segments ( $p_{1},p_{2}$ ). The overlap score $O(a,p,p^{\prime})$ is the sum of detected anomalies $|a\cap p|$ , early predictions $|a\cap p^{\prime}|$ , and the ambiguous instance score $S(a^{\prime},p)$ . For $a_{1}$ , the overlap score is 3 with an early detection reward of 0.29. For $a_{2}$ , the overlap score is approximately 5.88, reflecting the contribution of the sigmoid-weighted ambiguous instances.

	SWaT	PSM	SMD	MSL	SMAP
Variables	51	25	38	55	25
Number of entities	1	1	28	27	54
#Train (0.7)	346,500	115,921	495,884	40,822	96,603
#Valid (0.3)	148,500	49,680	212,521	17,495	41,401
#Test (labeled)	449,919	87,841	708,420	73,729	427,617
Anomaly (%)	11.98	27.8	4.16	10.72	13.13

TABLE I: Details of Benchmarks

Method	Metric	PSM	SWaT	MSL	SMAP	SMD	Average
Transformer	MSE	0.0080	728.0698	0.0146	0.0224	0.0084	145.6227
Transformer	MAE	0.0601	7.1352	0.0618	0.0719	0.0271	1.4712
Informer	MSE	0.0056	639.0894	0.0177	0.0235	0.0096	127.8273
Informer	MAE	0.0449	6.6135	0.0680	0.0774	0.0356	1.3679
Reformer	MSE	0.0090	756.6053	0.0190	0.0222	0.0088	151.3318
Reformer	MAE	0.0657	7.3256	0.0694	0.0661	0.0275	1.5109

TABLE II: Time-series forecasting performance (MSE and MAE) across five datasets. Best scores are in bold and underlined.

Dataset	Metric	LSTM-AE	LSTM-VAE	USAD	DAGMM	OmniAnomaly	AT	VT-SAT	VT-PAT	FATE
PSM	$\text{F1}_{0}$	38.56	40.15	38.89	39.36	39.88	19.45	37.12	36.91	53.41
	$\text{F1}_{1}$	16.67	16.52	16.19	15.86	15.93	4.09	14.91	15.72	34.31
	AUC	28.59	28.64	28.34	28.52	28.74	7.90	25.93	26.66	50.64
SWaT	$\text{F1}_{0}$	29.64	30.79	32.62	29.83	32.36	15.06	26.61	26.76	36.29
	$\text{F1}_{1}$	19.01	18.04	17.62	17.18	17.97	0.68	18.09	17.00	30.47
	AUC	26.22	26.61	27.46	26.25	27.22	0.93	25.43	24.91	32.81

TABLE III: Experimental results of the PTaPR metric on five time-series datasets. The best scores are in bold and underlined.

Dataset	Metric	LSTM-AE	LSTM-VAE	USAD	DAGMM	OmniAnomaly	AT	VT-SAT	VT-PAT	FATE
PSM	P	54.92	72.04	57.87	72.96	74.48	18.94	50.47	45.76	42.85
	R	18.92	17.84	19.32	17.80	18.11	5.12	17.52	17.98	56.57
	F1	28.15	28.59	28.96	28.61	29.14	8.06	26.01	25.81	48.76
SWaT	P	51.97	42.74	52.47	49.20	51.08	9.44	44.50	76.94	73.03
	R	19.97	19.45	18.64	18.01	18.68	0.74	18.84	15.13	27.26
	F1	28.85	26.74	27.51	26.37	27.36	1.37	26.47	25.29	39.66

TABLE IV: Experimental results for early detection on five time-series datasets. The best scores are in bold and underlined.

Dataset	Metric	LSTM-AE	LSTM-VAE	USAD	DAGMM	OmniAnomaly	AT	VT-SAT	VT-PAT	FATE
PSM	$\text{F1}_{0}$	51.42	52.36	50.16	50.89	50.17	29.18	50.15	49.68	65.72
	$\text{F1}_{1}$	17.99	19.10	18.26	18.83	19.02	6.13	17.48	16.89	28.92
	AUC	35.30	37.41	35.82	36.81	37.27	11.85	34.23	33.01	56.95
SWaT	$\text{F1}_{0}$	32.33	27.25	33.36	29.79	32.01	22.58	33.19	33.31	44.80
	$\text{F1}_{1}$	15.06	12.88	13.51	13.19	13.03	1.02	15.06	15.26	13.47
	AUC	30.02	25.66	26.91	26.34	26.38	1.39	30.09	30.50	27.27

TABLE V: Experimental results of the TaPR metric for anomaly detection on five time-series datasets. The best scores are in bold and underlined.

Dataset	Metric	LSTM-AE	LSTM-VAE	USAD	DAGMM	OmniAnomaly	AT	VT-SAT	VT-PAT	FATE
PSM	$\text{F1}_{\text{PA}}$	92.94	94.51	92.22	92.33	92.24	97.78	92.68	91.84	96.01
	F1	35.96	37.88	34.98	35.91	35.30	2.31	30.26	33.80	46.79
	AUC	39.39	41.73	37.85	40.15	39.23	3.80	33.58	36.14	63.80
SWaT	$\text{F1}_{\text{PA}}$	86.26	86.46	87.28	85.55	87.33	96.65	84.65	84.63	88.99
	F1	77.13	76.57	76.57	76.57	76.57	3.45	78.00	78.19	74.73
	AUC	82.25	81.38	81.38	81.35	81.39	5.50	83.28	83.42	80.20

TABLE VI: Experimental results of the PA%K metric for anomaly detection on five time-series datasets. The best scores are in bold and underlined.

Fig. 6: Sensitivity analysis and ablation results of the FATE framework. (a) Sensitivity to the sharpness parameter $k$ on the PSM dataset. (b) Sensitivity to the optimal lead time $\epsilon$ on the PSM dataset. (c) Effect of uncertainty normalization in FATE, showing consistent PTaPR improvement across both PSM and SWaT datasets.

Fig. 7: Visualization of anomaly detection results by different models on the SWaT dataset. Ground-truth anomalies are shown in red, with detected segments overlaid for comparison.

Fig. 8: Visualization of Precursors-of-Anomaly (PoA) detected by FATE on the PSM and SWaT datasets. The blue line shows the uncertainty scores, red regions indicate detected PoA segments, and yellow regions mark ground-truth anomalies.

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Anomaly detection methods often have uncertain behavior with respect to samples near the distribution boundary, limiting their ability to anticipate future anomalies. This work introduces the concept of near-anomalies that, while not yet anomalous, lie close to the boundary and are likely to transition into anomalies in the near future. To address this, we propose an unsupervised method, named Christoffel-based ANomaly Anticipation for eaRly dIscovery (CANARI), which leverages the strong theoretical foundations of the Christoffel function to detect near-anomalies. The method is validated on industrial in-circuit testing data from printed circuit boards, with synthetically generated near-anomaly samples due to the lack of real-world data labeling. Experimental results show that CANARI outperforms the compared baselines that generally use a dual-threshold mechanism (one for anomalies and one for near-anomalies). It therefore provides a proactive solution for anticipating anomalies before they occur, offering a promising approach for resilience, predictive maintenance, and quality control.

Abstract

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