IMPACT: Influence Modeling for Open-Set Time Series Anomaly Detection

Xiaohui Zhou; Yijie Wang; Hongzuo Xu; Weixuan Liang; Xiaoli Li; Guansong Pang

cs.LGMar 31, 2026

IMPACT: Influence Modeling for Open-Set Time Series Anomaly Detection

Authors: Xiaohui Zhou, Yijie Wang, Hongzuo Xu, Weixuan Liang, Xiaoli Li, Guansong Pang

Organizations: National Key Laboratory of Parallel and Distributed Computing · College of Computer Science and Technology, National University of Defense Technology · Intelligent Game and Decision Lab (IGDL) · Information Systems Technology and Design, Singapore University of Technology and Design · School of Computing and Information Systems, Singapore Management University

Abstract

Open-set anomaly detection (OSAD) is an emerging paradigm designed to utilize limited labeled data from anomaly classes seen in training to identify both seen and unseen anomalies during testing. Current approaches rely on simple augmentation methods to generate pseudo anomalies that replicate unseen anomalies. Despite being promising in image data, these methods are found to be ineffective in time series data due to the failure to preserve its sequential nature, resulting in trivial or unrealistic anomaly patterns. They are further plagued when the training data is contaminated with unlabeled anomalies. This work introduces $\textbf{IMPACT}$ , a novel framework that leverages $\underline{\textbf{i}}$ nfluence $\underline{\textbf{m}}$ odeling for o $\underline{\textbf{p}}$ en-set time series $\underline{\textbf{a}}$ nomaly dete $\underline{\textbf{ct}}$ ion, to tackle these challenges. The key insight is to $\textbf{i)}$ learn an influence function that can accurately estimate the impact of individual training samples on the modeling, and then $\textbf{ii)}$ leverage these influence scores to generate semantically divergent yet realistic unseen anomalies for time series while repurposing high-influential samples as supervised anomalies for anomaly decontamination. Extensive experiments show that IMPACT significantly outperforms existing state-of-the-art methods, showing superior accuracy under varying OSAD settings and contamination rates. Code is available at https://github.com/mala-lab/IMPACT.

Figures & tables

Figure 1: (a) Contaminated anomalies and low-quality pseudo anomalies significantly affect the learned boundary. (b) IMPACT addresses these issues by i) accurately flipping the contaminated unlabeled anomalies into labeled ones through influence modeling and ii) the influence-score-guided generation of high-quality pseudo anomalies from the perspective of reducing the test risk.

Figure 2: The overall framework of IMPACT. TIS first quantifies the influence of training samples on test risk, then RADG leverages these influence scores from the risk-reduction perspective to decontaminate the training set via label flipping and synthesize realistic unseen anomalies through feature perturbation. A dual-head architecture is finally trained to effectively detect both seen and unseen anomalies.

	Methods	UCR	ASD	PSM	SMD	CT	SAD	PTBXL	TUSZ
Unsupervised	TCN-AE	$\text{50.63}_{\pm\text{0.46}}$	$\text{58.73}_{\pm\text{0.49}}$	$\text{58.49}_{\pm\text{0.79}}$	$\text{64.76}_{\pm\text{0.19}}$	$\text{50.02}_{\pm\text{0.05}}$	$\text{50.01}_{\pm\text{0.02}}$	$\text{58.74}_{\pm\text{0.28}}$	$\text{64.17}_{\pm\text{0.06}}$
	THOC	$\text{52.75}_{\pm\text{0.56}}$	$\text{55.74}_{\pm\text{1.57}}$	$\text{58.02}_{\pm\text{1.51}}$	$\text{62.55}_{\pm\text{0.47}}$	$\text{74.50}_{\pm\text{3.16}}$	$\text{57.76}_{\pm\text{3.14}}$	$\text{62.89}_{\pm\text{1.97}}$	$\text{62.45}_{\pm\text{1.92}}$
	TranAD	$\text{49.26}_{\pm\text{0.73}}$	$\text{56.86}_{\pm\text{0.68}}$	$\text{60.34}_{\pm\text{0.40}}$	$\text{64.40}_{\pm\text{0.25}}$	$\text{29.28}_{\pm\text{3.12}}$	$\text{49.10}_{\pm\text{1.09}}$	$\text{58.51}_{\pm\text{1.18}}$	$\text{62.82}_{\pm\text{0.73}}$
	DCdetector	$\text{51.40}_{\pm\text{1.43}}$	$\text{47.94}_{\pm\text{1.05}}$	$\text{50.51}_{\pm\text{0.72}}$	$\text{50.23}_{\pm\text{0.85}}$	$\text{49.20}_{\pm\text{1.80}}$	$\text{49.02}_{\pm\text{1.15}}$	$\text{51.28}_{\pm\text{0.78}}$	$\text{50.55}_{\pm\text{1.10}}$
	GPT4TS	$\text{54.60}_{\pm\text{0.87}}$	$\text{62.42}_{\pm\text{2.06}}$	$\text{61.14}_{\pm\text{0.63}}$	$\text{66.20}_{\pm\text{0.31}}$	$\text{60.32}_{\pm\text{0.80}}$	$\text{48.09}_{\pm\text{3.59}}$	$\text{47.82}_{\pm\text{0.78}}$	$\text{66.31}_{\pm\text{0.31}}$
	COUTA	$\text{53.44}_{\pm\text{1.14}}$	$\text{61.74}_{\pm\text{2.67}}$	$\text{58.29}_{\pm\text{3.90}}$	$\text{60.93}_{\pm\text{1.36}}$	$\text{51.09}_{\pm\text{0.00}}$	$\text{50.00}_{\pm\text{0.00}}$	$\text{56.71}_{\pm\text{1.86}}$	$\text{62.45}_{\pm\text{0.89}}$

Table 1: Detection accuracy (AUC

\pm

standard deviation) of IMPACT and its competing methods under the unsupervised and open-set general settings. All results are in %. The best ones are boldfaced and the second best are

\underline{\text{underlined}}

Dataset	seen anomaly	DevNet	DSAD	NCAD	DRA	MOSAD	InvAD	WSAD-DT	IMPACT
CT	Letter-G	$\text{49.54}_{\pm\text{1.03}}$	$\text{73.56}_{\pm\text{3.41}}$	$\text{63.27}_{\pm\text{0.65}}$	$\text{68.79}_{\pm\text{3.43}}$	$\underline{\text{75.64}}_{\pm\text{1.50}}$	$\text{75.43}_{\pm\text{0.52}}$	$\text{68.83}_{\pm\text{1.77}}$	$\textbf{80.90}_{\pm\text{1.03}}$
	Letter-M	$\text{50.75}_{\pm\text{1.52}}$	$\underline{\text{75.67}}_{\pm\text{1.41}}$	$\text{64.28}_{\pm\text{0.58}}$	$\text{74.93}_{\pm\text{2.22}}$	$\text{75.15}_{\pm\text{0.69}}$	$\text{75.60}_{\pm\text{0.89}}$	$\text{72.51}_{\pm\text{2.35}}$	$\textbf{81.65}_{\pm\text{0.38}}$
	Letter-Q	$\text{50.91}_{\pm\text{1.68}}$	$\text{74.46}_{\pm\text{1.16}}$	$\text{64.52}_{\pm\text{0.77}}$	$\text{71.85}_{\pm\text{3.11}}$	$\underline{\text{76.37}}_{\pm\text{0.84}}$	$\text{75.01}_{\pm\text{0.77}}$	$\text{74.01}_{\pm\text{2.17}}$	$\textbf{82.50}_{\pm\text{0.37}}$
	Letter-W	$\text{51.40}_{\pm\text{3.83}}$	$\text{74.23}_{\pm\text{3.22}}$	$\text{63.71}_{\pm\text{0.39}}$	$\text{73.02}_{\pm\text{1.57}}$	$\text{75.75}_{\pm\text{0.48}}$	$\text{75.74}_{\pm\text{0.62}}$	$\underline{\text{76.20}}_{\pm\text{1.07}}$	$\textbf{80.87}_{\pm\text{1.05}}$
	Letter-Z	$\text{49.54}_{\pm\text{1.05}}$	$\underline{\text{79.46}}_{\pm\text{2.10}}$	$\text{64.22}_{\pm\text{0.35}}$	$\text{75.11}_{\pm\text{1.38}}$	$\text{78.70}_{\pm\text{0.81}}$	$\text{75.33}_{\pm\text{0.67}}$	$\text{74.94}_{\pm\text{1.36}}$	$\textbf{83.58}_{\pm\text{0.97}}$
	Mean	$\text{50.43}_{\pm\text{0.76}}$	$\text{75.48}_{\pm\text{2.11}}$	$\text{64.00}_{\pm\text{0.45}}$	$\text{72.74}_{\pm\text{2.32}}$	$\underline{\text{76.32}}_{\pm\text{1.25}}$	$\text{75.42}_{\pm\text{0.25}}$	$\text{73.30}_{\pm\text{2.54}}$	$\textbf{81.90}_{\pm\text{1.03}}$

Table 2: Detection accuracy (AUC

\pm

standard deviation) of IMPACT and its competing methods under the open-set hard settings. All results are in %. The best ones are boldfaced and the second best are

\underline{\text{underlined}}

Dataset	Ours	w/o $\mathcal{D}_{con}^{\prime}$	w/o $L_{seen}$	w/o $L_{unseen}$	w/o $s_{f}$	w/ $\mathcal{D}_{con}$	w/ rnd $\mathcal{D}_{ref}$	w/ rnd $\mathcal{D}_{con}^{\prime}$	w/ rnd $\mathcal{W}_{per}^{\prime}$
General Setting
UCR	$\text{59.21}_{\pm\text{1.34}}$	$\text{58.95}_{\pm\text{1.86}}$	$\text{50.14}_{\pm\text{4.26}}$	$\textbf{59.27}_{\pm\text{1.55}}$	$\text{54.25}_{\pm\text{2.24}}$	$\text{55.74}_{\pm\text{1.21}}$	$\text{52.12}_{\pm\text{3.14}}$	$\text{53.47}_{\pm\text{4.22}}$	$\text{53.63}_{\pm\text{3.05}}$
ASD	$\textbf{65.76}_{\pm\text{2.17}}$	$\text{64.34}_{\pm\text{2.97}}$	$\text{57.39}_{\pm\text{3.25}}$	$\text{65.60}_{\pm\text{2.73}}$	$\text{64.67}_{\pm\text{4.13}}$	$\text{60.23}_{\pm\text{1.44}}$	$\text{58.43}_{\pm\text{3.56}}$	$\text{57.89}_{\pm\text{2.54}}$	$\text{58.14}_{\pm\text{2.41}}$
PSM	$\textbf{64.24}_{\pm\text{1.67}}$	$\text{63.37}_{\pm\text{2.37}}$	$\text{61.67}_{\pm\text{2.49}}$	$\text{63.47}_{\pm\text{2.35}}$	$\text{62.38}_{\pm\text{3.43}}$	$\text{62.44}_{\pm\text{0.96}}$	$\text{60.13}_{\pm\text{3.76}}$	$\text{59.82}_{\pm\text{2.35}}$	$\text{60.47}_{\pm\text{1.97}}$
SMD	$\textbf{75.97}_{\pm\text{3.03}}$	$\text{74.07}_{\pm\text{2.80}}$	$\text{72.28}_{\pm\text{2.24}}$	$\text{75.63}_{\pm\text{1.39}}$	$\text{69.02}_{\pm\text{3.34}}$	$\text{73.13}_{\pm\text{1.25}}$	$\text{67.49}_{\pm\text{3.44}}$	$\text{69.34}_{\pm\text{1.31}}$	$\text{71.82}_{\pm\text{2.22}}$
CT	$\text{91.96}_{\pm\text{2.32}}$	$\text{91.81}_{\pm\text{2.05}}$	$\text{90.24}_{\pm\text{2.78}}$	$\textbf{92.16}_{\pm\text{1.84}}$	$\text{91.32}_{\pm\text{2.12}}$	$\text{90.42}_{\pm\text{1.51}}$	$\text{87.75}_{\pm\text{2.76}}$	$\text{86.13}_{\pm\text{1.36}}$	$\text{87.54}_{\pm\text{2.41}}$

Table 3: Ablation study results (as %) of ours and its variants under both general and hard settings. The best results are boldfaced .

Figure 3: Sensitivity analysis results (AUC performance w.r.t. different hyperparameters) under the hard setting.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	#lens	#dims	#classes	#train	#test	#anom
UCR	100	1	1	54,106	70,512	172
ASD	100	19	1	1,043	468	78
PSM	100	25	1	1,351	798	272
SMD	100	38	1	7,228	6,084	528
CT	205	3	5	889	1,715	412
SAD	93	13	4	4,040	2,200	880

Appendix

Table 4: Details in eight datasets. #lens and #dims indicate the length of a time interval, and the number of variables. #classes represents the number of anomaly classes. #train and #test denote the number of training and test samples. #anom is the number of anomalies over all the test samples.

Dataset	seen anomaly	Seen				Unseen
Dataset	seen anomaly	MOSAD	InvAD	WSAD-DT	Ours	MOSAD	InvAD	WSAD-DT	Ours
CT	Letter-G	$\text{53.67}_{\pm\text{5.80}}$	$\text{51.94}_{\pm\text{2.74}}$	$\underline{\text{97.12}}_{\pm\text{0.31}}$	$\textbf{99.60}_{\pm\text{0.22}}$	$\underline{\text{74.53}}_{\pm\text{0.38}}$	$\text{72.18}_{\pm\text{0.75}}$	$\text{60.70}_{\pm\text{2.32}}$	$\textbf{75.53}_{\pm\text{3.90}}$
	Letter-M	$\text{94.47}_{\pm\text{0.78}}$	$\text{85.33}_{\pm\text{3.75}}$	$\underline{\text{98.39}}_{\pm\text{0.31}}$	$\textbf{99.82}_{\pm\text{0.01}}$	$\text{71.26}_{\pm\text{0.84}}$	$\underline{\text{73.88}}_{\pm\text{1.07}}$	$\text{67.93}_{\pm\text{2.78}}$	$\textbf{75.04}_{\pm\text{5.16}}$
	Letter-Q	$\text{75.06}_{\pm\text{2.25}}$	$\text{71.78}_{\pm\text{2.87}}$	$\underline{\text{96.00}}_{\pm\text{1.02}}$	$\textbf{99.89}_{\pm\text{0.04}}$	$\text{73.11}_{\pm\text{1.11}}$	$\textbf{75.73}_{\pm\text{1.25}}$	$\text{69.12}_{\pm\text{2.69}}$	$\underline{\text{73.27}}_{\pm\text{4.11}}$
	Letter-W	$\text{74.21}_{\pm\text{2.13}}$	$\text{68.23}_{\pm\text{2.30}}$	$\underline{\text{81.65}}_{\pm\text{2.89}}$	$\textbf{95.52}_{\pm\text{0.53}}$	$\underline{\text{78.50}}_{\pm\text{0.31}}$	$\text{77.33}_{\pm\text{0.85}}$	$\text{65.73}_{\pm\text{1.86}}$	$\textbf{79.16}_{\pm\text{2.95}}$
	Letter-Z	$\text{97.22}_{\pm\text{1.57}}$	$\text{91.43}_{\pm\text{1.75}}$	$\underline{\text{99.91}}_{\pm\text{0.01}}$	$\textbf{99.99}_{\pm\text{0.01}}$	$\underline{\text{71.87}}_{\pm\text{0.95}}$	$\text{69.39}_{\pm\text{1.00}}$	$\text{65.73}_{\pm\text{1.86}}$	$\textbf{74.34}_{\pm\text{2.70}}$

Appendix

Table 5: Detection accuracy (AUC

\pm

standard deviation) of IMPACT and its competing methods w.r.t sample types (seen and unseen anomalies). All results are in %. The best ones are boldfaced and the second best are

\underline{\text{underlined}}

Figure 4: AUC performance of IMPACT w.r.t different number of labeled anomalies under the general setting.

Figure 5: AUC performance of IMPACT w.r.t different number of labeled anomalies under the hard setting.

Figure 6: AUC performance of IMPACT and its competing baselines w.r.t different contamination rates under the general setting.

Figure 7: AUC results w.r.t. various methods to create pseudo anomalies under the hard setting.

Figure 8: Kullback-Leibler Divergence (KLD) of anomaly features from various datasets under the hard setting.

KLD({\Phi}_{unseen}||{\Phi}_{pseudo})

is given, which implies distribution discrepancies of unseen anomaly features and the generated pseudo anomaly features.

Figure 9: Feature t-SNE visualization. The features are extracted under the condition that Letter-G serves as the seen anomaly class in the CT dataset.

Figure 10: Identified helpful and harmful training samples from CT. For the test samples from normal class and five distinct anomaly classes, each corresponds to three helpful training samples with the minimum influence estimates and three harmful training samples with the highest influence estimates.

Figure 11: A qualitative example from the PTBXL dataset to demonstrate how multi-channel strategy helps to identify channel-specific anomalies that may be missed in single-channel analysis. The first row displays three-dimensional visualizations of ground truth data distribution, multi-channel anomaly scores, and multi-channel deviation losses. The second row presents different plane projections, which indicate that some anomalies are difficult to distinguish from a single projection, thereby highlighting the importance of multi-channel anomaly discrimination.

Figure 12: AUC performance of IMPACT w.r.t different number of channels under the general setting.

	Methods	Affiliation-F1				VUS-ROC
	Methods	UCR	ASD	PSM	SMD	UCR	ASD	PSM	SMD
Unsupervised	TCN-AE	$\text{67.30}_{\pm\text{0.54}}$	$\text{70.50}_{\pm\text{0.05}}$	$\text{73.47}_{\pm\text{0.73}}$	$\text{64.76}_{\pm\text{0.19}}$	$\text{51.89}_{\pm\text{0.68}}$	$\text{62.62}_{\pm\text{0.17}}$	$\text{60.44}_{\pm\text{0.77}}$	$\text{64.17}_{\pm\text{0.06}}$
	THOC	$\text{67.34}_{\pm\text{0.11}}$	$\text{70.84}_{\pm\text{0.76}}$	$\text{72.50}_{\pm\text{1.53}}$	$\text{74.85}_{\pm\text{1.00}}$	$\text{53.48}_{\pm\text{0.51}}$	$\text{61.65}_{\pm\text{1.46}}$	$\text{55.35}_{\pm\text{2.56}}$	$\text{64.42}_{\pm\text{0.77}}$
	TranAD	$\text{66.93}_{\pm\text{0.18}}$	$\text{71.40}_{\pm\text{0.45}}$	$\text{76.32}_{\pm\text{0.44}}$	$\text{68.62}_{\pm\text{0.00}}$	$\text{50.20}_{\pm\text{0.56}}$	$\text{62.54}_{\pm\text{0.57}}$	$\text{63.72}_{\pm\text{0.35}}$	$\text{68.25}_{\pm\text{0.17}}$
	DCdetector	$\text{66.67}_{\pm\text{0.00}}$	$\text{69.78}_{\pm\text{0.00}}$	$\text{70.77}_{\pm\text{0.09}}$	$\text{68.43}_{\pm\text{0.11}}$	$\text{52.04}_{\pm\text{1.86}}$	$\text{54.85}_{\pm\text{0.17}}$	$\text{52.21}_{\pm\text{0.14}}$	$\text{54.89}_{\pm\text{0.47}}$
	GPT4TS	$\text{67.92}_{\pm\text{0.30}}$	$\text{71.50}_{\pm\text{0.63}}$	$\text{72.78}_{\pm\text{0.41}}$	$\text{70.43}_{\pm\text{0.21}}$	$\underline{\text{61.09}}_{\pm\text{0.36}}$	$\text{66.20}_{\pm\text{0.41}}$	$\text{59.80}_{\pm\text{0.46}}$	$\text{72.71}_{\pm\text{0.30}}$

Appendix

Table 6: Point-level anomaly detection results (Affiliation-F1/VUS-ROC

\pm

standard deviation) of IMPACT and its competing methods under the unsupervised and open-set general settings. All results are in %. The best ones are boldfaced and the second best are

\underline{\text{underlined}}

Figure 13: Visualization of point-level anomaly scores in comparison with SOTA baselines on the UCR dataset. The first row displays the testing time series, while the remaining rows show the point-level anomaly scores generated by each method. Red regions highlight the ground truth anomaly intervals.

Figure 14: Visualization of point-level anomaly scores in comparison with SOTA baselines on the multivariate datasets with several selected dimensions. The first four rows display the selected dimensions of the testing time series, which represent the major anomaly patterns in the data. The last three rows show the point-level anomaly scores generated by each method. Red regions highlight the ground truth anomaly intervals.

Figure 15: Computational efficiency results across different dimensionality and sample sizes.

Explore similar work

ASTER: Latent Pseudo-Anomaly Generation for Unsupervised Time-Series Anomaly Detection
Apr 15, 2026Romain Hermary, Samet Hicsonmez, Dan Pineau +2Time-Series Anomaly Detection Unsupervised Anomaly Detection
University of Luxembourg, Luxembourg
ChronosAD: Leveraging Time Series Foundation Models for Accurate Anomaly Detection
May 31, 2026Uzair Khan, Luigi Capogrosso, Francesco Biondani +4Industrial Anomaly Detection Time-Series Anomaly Detection
University of Verona · Interdisciplinary Transformation University of Austria · ETH Zurich
PaAno: Patch-Based Representation Learning for Time-Series Anomaly Detection
Feb 1, 2026Jinju Park, Seokho KangSelf-Supervised Time Series Representation Learning Time Series Representation Learning
Department of Industrial Engineering, Sungkyunkwan University

Apr 15, 2026J/K move · Enter open · S save

ASTER: Latent Pseudo-Anomaly Generation for Unsupervised Time-Series Anomaly Detection

Romain Hermary, Samet Hicsonmez, Dan Pineau, Abd El Rahman Shabayek+1

University of Luxembourg, Luxembourg

Time-Series Anomaly Detection Unsupervised Anomaly Detection Synthetic Anomaly Generation

Open paper AskPDF arXiv

Time-series anomaly detection (TSAD) is critical in domains such as industrial monitoring, healthcare, and cybersecurity, but it remains challenging due to rare and heterogeneous anomalies and the scarcity of labelled data. This scarcity makes unsupervised approaches predominant, yet existing methods often rely on reconstruction or forecasting, which struggle with complex data, or on embedding-based approaches that require domain-specific anomaly synthesis and fixed distance metrics. We propose ASTER, a framework that generates pseudo-anomalies directly in the latent space, avoiding handcrafted anomaly injections and the need for domain expertise. A latent-space decoder produces tailored pseudo-anomalies to train a Transformer-based anomaly classifier, while a pre-trained LLM enriches the temporal and contextual representations of this space. Experiments on three benchmark datasets show that ASTER achieves state-of-the-art performance and sets a new standard for LLM-based TSAD.

Abstract

Explore similar work

ASTER: Latent Pseudo-Anomaly Generation for Unsupervised Time-Series Anomaly Detection

ChronosAD: Leveraging Time Series Foundation Models for Accurate Anomaly Detection

PaAno: Patch-Based Representation Learning for Time-Series Anomaly Detection