Correlation-Aware Reconstruction for Multivariate Time Series Anomaly Detection

Md. Johir Raihan; Zahra Zamanzadeh Darban; Yueyang Liu; Flora D. Salim; Levin Kuhlmann; Mahsa Salehi

cs.LGOct 11, 2026

Correlation-Aware Reconstruction for Multivariate Time Series Anomaly Detection

Authors: Md. Johir Raihan, Zahra Zamanzadeh Darban, Yueyang Liu, Flora D. Salim, Levin Kuhlmann, Mahsa Salehi

Organizations: Monash University, Melbourne, Victoria, Australia · University of New South Wales, Sydney, New South Wales, Australia

Abstract

Reconstruction-based detectors for multivariate time series anomaly detection typically learn a single entangled representation of normal behavior and flag anomalies based on reconstruction error. However, real-world anomalies are not only isolated spikes in a single channel but also disruptions in the relationships between channels, where each sensor individually appears normal, but their joint behavior deviates from the norm. Because these models compress both temporal evolution and inter-channel structure into this single space, they lack an explicit mechanism to isolate such inter-channel dependencies from normal temporal dependencies, leading to lower detection rates for cross-channel anomalies. We propose CARMA (Correlation-Aware Reconstruction for Multivariate Time Series Anomaly Detection), which is a reconstruction-based variational autoencoder with two complementary latent spaces: a temporal latent that captures sequential dynamics, and a correlation latent that is trained to reconstruct the window's pairwise Pearson correlations. Both representations are fused in the signal decoder, and anomalies are detected from the reconstruction error. We evaluate CARMA on the TSB-AD-M benchmark suite (17 datasets, 180 series) against 29 baseline methods, and show that it significantly outperforms all of them across multiple threshold-free and range-aware metrics, achieving a VUS-PR of 0.4929. Ablations show that removing the correlation branch degrades performance, that adding a second latent without supervision recovers only part of the gain, and that supervising the correlation latent with an explicit correlation target accounts for the rest and produces a sharper error response at anomalies.

Figures & tables

Figure 1: Top panel shows GHL sensor data with the ground truth anomaly shaded. Middle panel displays $\log(1+\mathrm{MSE})$ for CARMA without correlation conditioning, which misses the anomaly with spurious errors in normal regions. Bottom panel shows full CARMA achieving low reconstruction during normal segments with localized multichannel error increase at the anomalous interval.

Figure 2: Overview of CARMA. A multivariate window is encoded into temporal and correlation latents. The concatenated latents reconstruct the input series, while the correlation latent reconstructs window-level channel dependencies.

Method	AUC-PR	AUC-ROC	VUS-PR	VUS-ROC	Standard-F1	PA-F1	Event-based-F1	R-based-F1	Affiliation-F
HYDRA [ 19 ]	0.3933	0.7727	0.4409	0.8068	0.4509	0.6783	0.5669	0.4303	0.8556
StreamVAE [ 29 ]	0.3881	0.7578	0.4277	0.7740	0.4551	0.5390	0.4757	0.4162	0.8311
PaAno_PAI [ 31 ]	0.3992	0.7834	0.4049	0.8059	0.4345	0.7732	0.6109	0.3804	0.8679
USAD [ 2 ]	0.3625	0.7366	0.4026	0.7652	0.4329	0.6229	0.5189	0.4227	0.8366
TimesNet [ 40 ]	0.3375	0.6697	0.3910	0.7103	0.4115	0.6691	0.5336	0.4076	0.8476
PatchTST [ 28 ]	0.3360	0.6746	0.3902	0.7167	0.4067	0.7097	0.5355	0.3777	0.8460

Table 1: Results on the TSB-AD-M benchmark. Mean of each metric over 180 series and three seeds. The best and second-best results in each column are given in bold and underlined, respectivel. Where AT and AE refer to Anomaly Transformer and AutoEncoder, respectively.

Figure 3: Critical difference diagrams on TSB-AD-M for VUS-PR (left) and domain-specific performance (right). Models connected by a horizontal bar are not significantly different (Wilcoxon signed-rank test, 0.05). Lower average rank indicates better performance.

Method	AUC-PR	AUC-ROC	VUS-PR	VUS-ROC	Standard-F1	PA-F1	Event-based-F1	R-based-F1	Affiliation-F
StreamVAE [ 29 ]	0.9716	0.9962	0.9858	0.9982	0.9245	0.9389	0.9375	0.9213	0.9838
HYDRA [ 19 ]	0.8681	0.9382	0.8681	0.9500	0.8180	0.9200	0.9183	0.7785	0.9376
PaAno_PAI [ 31 ]	0.7336	0.9300	0.7559	0.9451	0.6797	0.9807	0.9361	0.3342	0.9358
TimesNet [ 40 ]	0.5300	0.7588	0.5510	0.7849	0.5417	0.8408	0.6504	0.5473	0.8432
USAD [ 2 ]	0.5104	0.7402	0.5322	0.7638	0.5287	0.8785	0.6003	0.4479	0.8337
CARMA (Ours)	0.9768	0.9968	0.9888	0.9986	0.9259	0.9426	0.9411	0.9329	0.9859

Table 2: Comparison with the main benchmark’s five strongest baselines on synthetic datasets.

Method	AUC-PR	AUC-ROC	VUS-PR	VUS-ROC	Standard-F1
CARMA + Pearson lag=5	0.3468 $\pm$ 0.0069	0.7985 $\pm$ 0.0023	0.4042 $\pm$ 0.0057	0.8376 $\pm$ 0.0018	0.4315 $\pm$ 0.0067
CARMA w/o $z_{c}$	0.4180 $\pm$ 0.0047	0.8041 $\pm$ 0.0034	0.4620 $\pm$ 0.0032	0.8287 $\pm$ 0.0036	0.4936 $\pm$ 0.0053
CARMA w/o $\mathcal{L}_{\text{corr}}$	0.4243 $\pm$ 0.0060	0.8157 $\pm$ 0.0032	0.4719 $\pm$ 0.0055	0.8424 $\pm$ 0.0031	0.5033 $\pm$ 0.0084
CARMA + Spearman corr	0.4302 $\pm$ 0.0033	0.8218 $\pm$ 0.0007	0.4780 $\pm$ 0.0035	0.8488 $\pm$ 0.0006	0.5102 $\pm$ 0.0030
CARMA $\sigma_{t,0}=1$	0.4384 $\pm$ 0.0021	0.8313 $\pm$ 0.0059	0.4881 $\pm$ 0.0033	0.8575 $\pm$ 0.0066	0.5271 $\pm$ 0.0038
CARMA (Ours)	0.4425 $\pm$ 0.0009	0.8330 $\pm$ 0.0017	0.4929 $\pm$ 0.0027	0.8598 $\pm$ 0.0010	0.5301 $\pm$ 0.0032

Table 3: CARMA ablation study reported as mean

\pm

standard deviation over seeds. The best and second-best results in each column are given in bold and underlined, respectively.

Figure 4: Paired pointwise VUS-PR on TSB-AD-M for CARMA and single latent model. Panel (a) compares scores for all 180 series, with points above the diagonal favoring the correlated model. Panel (b) shows the paired differences.

Method	AUC-PR	AUC-ROC	VUS-PR	VUS-ROC	Standard-F1
HYDRA [ 19 ]	0.3933 $\pm$ 0.3208	0.7727 $\pm$ 0.2245	0.4409 $\pm$ 0.3409	0.8068 $\pm$ 0.2144	0.4509 $\pm$ 0.3112
StreamVAE [ 29 ]	0.3881 $\pm$ 0.3539	0.7578 $\pm$ 0.2382	0.4277 $\pm$ 0.3635	0.7740 $\pm$ 0.2363	0.4551 $\pm$ 0.3367
PaAno_PAI [ 31 ]	0.3992 $\pm$ 0.3370	0.7834 $\pm$ 0.2133	0.4049 $\pm$ 0.3520	0.8059 $\pm$ 0.2070	0.4345 $\pm$ 0.3130
USAD [ 2 ]	0.3625 $\pm$ 0.3392	0.7366 $\pm$ 0.2562	0.4026 $\pm$ 0.3490	0.7652 $\pm$ 0.2459	0.4329 $\pm$ 0.3227
TimesNet [ 40 ]	0.3375 $\pm$ 0.3119	0.6697 $\pm$ 0.3028	0.3910 $\pm$ 0.3373	0.7103 $\pm$ 0.2968	0.4115 $\pm$ 0.3128
PatchTST [ 28 ]	0.3360 $\pm$ 0.3101	0.6746 $\pm$ 0.3049	0.3902 $\pm$ 0.3357	0.7167 $\pm$ 0.2992	0.4067 $\pm$ 0.3119

Table 4: Results on the TSB-AD-M benchmark. Mean

\pm

standard deviation over all evaluated series (spread). The best and second-best results in each column are given in bold and underlined, respectively. Where AT and AE refer to Anomaly Transformer and AutoEncoder, respectively.

Method	AUC-PR	AUC-ROC	VUS-PR	VUS-ROC	Standard-F1
HYDRA [ 19 ]	0.3933 $\pm$ 0.0056	0.7727 $\pm$ 0.0029	0.4409 $\pm$ 0.0052	0.8068 $\pm$ 0.0028	0.4509 $\pm$ 0.0014
StreamVAE [ 29 ]	0.3881 $\pm$ 0.0021	0.7578 $\pm$ 0.0021	0.4277 $\pm$ 0.0023	0.7740 $\pm$ 0.0017	0.4551 $\pm$ 0.0006
PaAno_PAI [ 31 ]	0.3992 $\pm$ 0.0000	0.7834 $\pm$ 0.0002	0.4049 $\pm$ 0.0001	0.8059 $\pm$ 0.0002	0.4345 $\pm$ 0.0000
USAD [ 2 ]	0.3625 $\pm$ 0.0004	0.7366 $\pm$ 0.0016	0.4026 $\pm$ 0.0008	0.7652 $\pm$ 0.0021	0.4329 $\pm$ 0.0005
TimesNet [ 40 ]	0.3375 $\pm$ 0.0027	0.6697 $\pm$ 0.0011	0.3910 $\pm$ 0.0042	0.7103 $\pm$ 0.0012	0.4115 $\pm$ 0.0029
PatchTST [ 28 ]	0.3360 $\pm$ 0.0013	0.6746 $\pm$ 0.0002	0.3902 $\pm$ 0.0010	0.7167 $\pm$ 0.0002	0.4067 $\pm$ 0.0008

Table 5: Results on the TSB-AD-M benchmark. Mean

\pm

standard deviation over three seeds. The best and second-best results in each column are given in bold and underlined, respectively. Where AT and AE refer to Anomaly Transformer and AutoEncoder, respectively.

Panel of Figure 5 — Figure 5: Side-by-side comparison of CARMA and single latnet model (w/o $z_{c}$ ) on one TSB-AD-M series. Each column shows the raw multivariate series, the normalized input, per-channel reconstruction error as log(1 + MSE), and anomaly score. Red bands mark ground-truth anomalies. CARMA (Ours) shows a clearer score peak at the event and a higher VUS-PR (0.48 vs 0.30).

Panel of Figure 6 — Figure 6: t-SNE visualization of latent representations for series SMD_id_10_Facility_tr_2634_1st_2734 . (a) CARMA (Ours): Panels show the per-timestep temporal latent $z_{t}$ , the window-level correlation latent $z_{c}$ , and their concatenation $[z_{t},z_{c}]$ . (b) Singel latent (w/o $z_{c}$ ) The per-timestep temporal latent $z_{t}$ obtained when the correlation branch is ablated.

Explore similar work

Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation
Mar 29, 2026Jun Liu, Ying Chen, Ziqian Lu +2Time-Series Anomaly Detection Anomaly Detection
Zhejiang University, Hangzhou, China · Zhejiang Sci-Tech University, Hangzhou, China
LEARN-TS: LLM-Enhanced Alignment and Reconstruction with Normality Guidance for Multivariate Time-Series Anomaly Detection
Sep 30, 2026Jahyeob Koo, Kio Yun, Byoungmo Koo +1Anomaly Localization Reconstruction-Based Anomaly Detection
Department of Industrial and Management Engineering, Korea University Seoul, Republic of Korea
CALAD: Channel-Aware contrastive Learning for multivariate time series Anomaly Detection
May 22, 2026Jaehyeop Hong, Youngbum HurContrastive Learning Self-Supervised Time Series Representation Learning
Department of Industrial Engineering, Inha University, Incheon, Republic of Korea

Mar 29, 2026J/K move · Enter open · S save

Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation

Jun Liu, Ying Chen, Ziqian Lu, Qinyue Tong+1

Zhejiang University, Hangzhou, China · Zhejiang Sci-Tech University, Hangzhou, China

Time-Series Anomaly Detection Anomaly Detection Reconstruction-Based Anomaly Detection

Open paper AskPDF arXiv

Multivariate Time Series Anomaly Detection (MTSAD) is critical for real-world monitoring scenarios such as industrial control and aerospace systems. Mainstream reconstruction-based anomaly detection methods suffer from two key limitations: first, overfitting to spurious correlations induced by an overemphasis on cross-variable modeling; second, the generation of misleading anomaly scores by simply summing up multivariable reconstruction errors, which makes it difficult to distinguish between hard-to-reconstruct samples and genuine anomalies. To address these issues, we propose DBR-AF, a novel framework that integrates a dual-branch reconstruction (DBR) encoder and an autoregressive flow (AF) module. The DBR encoder decouples cross-variable correlation learning and intra-variable statistical property modeling to mitigate spurious correlations, while the AF module employs multiple stacked reversible transformations to model the complex multivariate residual distribution and further leverages density estimation to accurately identify normal samples with large reconstruction errors. Extensive experiments on seven benchmark datasets demonstrate that DBR-AF achieves state-of-the-art performance, with ablation studies validating the indispensability of its core components.

Abstract

Explore similar work

Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation

LEARN-TS: LLM-Enhanced Alignment and Reconstruction with Normality Guidance for Multivariate Time-Series Anomaly Detection

CALAD: Channel-Aware contrastive Learning for multivariate time series Anomaly Detection