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
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 Ly=5 future steps from current time t+Lx−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 a1 spans indices 1 to 6, while early prediction p3′ detects an anomaly between indices 13 and 16.
Fig. 5: Example of PTaPR computation for anomaly segments ( a1,a2 ) and prediction segments ( p1,p2 ). The overlap score O(a,p,p′) is the sum of detected anomalies ∣a∩p∣ , early predictions ∣a∩p′∣ , and the ambiguous instance score S(a′,p) . For a1 , the overlap score is 3 with an early detection reward of 0.29. For a2 , 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
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
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
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
F10
38.56
40.15
38.89
39.36
39.88
19.45
37.12
36.91
53.41
F11
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
F10
29.64
30.79
32.62
29.83
32.36
15.06
26.61
26.76
36.29
F11
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
F10
51.42
52.36
50.16
50.89
50.17
29.18
50.15
49.68
65.72
F11
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
F10
32.33
27.25
33.36
29.79
32.01
22.58
33.19
33.31
44.80
F11
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
F1PA
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
F1PA
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 ϵ 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.
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.
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LAAS, INSA Toulouse · LAAS-CNRS, University of Toulouse, CNRS, Toulouse, France · LAAS-DISCO, Comue de Toulouse +1
Time series anomaly detection is a crucial task in various domains, including finance, healthcare, and industry. However, existing methods often struggle to generalize across different datasets, especially when anomalies are subtle or context-dependent. To solve this issue, we introduce ChronosAD, a novel architecture for anomaly detection that uses a time series foundation model as a feature extractor. Specifically, it employs a two-stage pipeline: first, it uses the foundation model to extract embeddings for each time series in a zero-shot manner. Then, a custom-developed Temporal Block, composed of Bidirectional Long Short-Term Memory (BiLSTM) and Multi-Head Attention, refines these embeddings to capture temporal dependencies and highlight salient patterns. Unlike previous approaches, our model requires minimal task-specific tuning and demonstrates robust generalization across a wide range of domains, including industrial, medical, cyber-physical, and automotive systems. Extensive experiments on 11 benchmarks show that ChronosAD outperforms existing methods by 4.72% in AUC and 6.60% in AP on average. The source code is available at https://github.com/intelligolabs/ChronosAD.
Uzair Khan, Luigi Capogrosso, Francesco Biondani +4
University of Verona · Interdisciplinary Transformation University of Austria · ETH Zurich
Although recent studies on time-series anomaly detection have increasingly adopted ever-larger neural network architectures such as transformers and foundation models, they incur high computational costs and memory usage, making them impractical for real-time and resource-constrained scenarios. Moreover, they often fail to demonstrate significant performance gains over simpler methods under rigorous evaluation protocols. In this study, we propose Patch-based representation learning for time-series Anomaly detection (PaAno), a lightweight yet effective method for fast and efficient time-series anomaly detection. PaAno extracts short temporal patches from time-series training data and uses a 1D convolutional neural network to embed each patch into a vector representation. The model is trained using a combination of triplet loss and pretext loss to ensure the embeddings capture informative temporal patterns from input patches. During inference, the anomaly score at each time step is computed by comparing the embeddings of its surrounding patches to those of normal patches extracted from the training time-series. Evaluated on the TSB-AD benchmark, PaAno achieved state-of-the-art performance, significantly outperforming existing methods, including those based on heavy architectures, on both univariate and multivariate time-series anomaly detection across various range-wise and point-wise performance measures.
Jinju Park, Seokho Kang
Department of Industrial Engineering, Sungkyunkwan University