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TimeInf: Time Series Data Contribution via Influence Functions

ICLR 2025 · Time series › Anomaly detection · approach: Multivariate anomaly detection

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Proposes TimeInf, a model-agnostic influence-function method that attributes loss/predictions to individual time points by integrating block influences over all overlapping time blocks containing the point, and uses self-influence for time series anomaly detection.

Problem

Estimating how individual time points contribute to a time series model's predictions is under-explored because standard influence functions assume i.i.d. data and temporal dependencies complicate attribution.

Approach

Extends influence functions to m-dimensional time blocks and defines TimeInf as the integral of block influence over all contiguous blocks containing a time point (contaminating distribution as a mixture of point masses), giving per-time-point attributions that preserve temporal structure and do not require a specific model class.

Key results

• On UCR, TimeInf reaches 0.79 AUC versus at most 0.65 for competing data contribution baselines, and it has the best AUC on SMAP (0.73), MSL (0.72), NAB-Traffic (0.64), and SMD (0.87).
• Compared with TranAD and DCdetector, TimeInf improves AUC by 7-30% and 3-17% respectively across datasets.
• In data pruning for forecasting on Traffic, removing 30% of blocks with TimeInf drops R^2 by more than 10%, whereas other methods drop less than 2%.

Measured effects reported in the paper

Surprising findings

• TimeInf performs comparably to or worse than Isolation Forest on several problematic datasets (PSM, NAB-Tweets, SWaT, KDD-Cup99), which the authors attribute to mislabeled ground truth annotations.
• Using a time stride greater than 1 reduces anomaly detection AUC on SMAP and SMD.

Limitations

• Focuses on validation loss as the quantity of interest; other metrics are left for future work.
• Performance gains are marginal on high-dimensional data, and many data attribution methods perform poorly there.
• Several benchmark datasets have unreliable ground-truth labels, which hurts measured performance.

Experimental setup

Datasets: UCR SMAP MSL NAB-Traffic SMD NAB-Tweets NAB-Taxi PSM SWaT WADI KDD-Cup99 NAB-AdExchange

Benchmarks: UCR SMAP MSL NAB-Traffic SMD NAB-Tweets NAB-Taxi PSM SWaT WADI KDD-Cup99 NAB-AdExchange

Metrics: AUC F1 runtime (s) R^2 RMSE

Baselines: Isolation Forest LSTM ARIMA / VAR TranAD DCdetector Anomaly Transformer Block LOOCV Conditional Influence LWCV

Builds on: influence functions conditional influence leave-within-structure-out cross-validation TracIn

Closest papers by meaning

• Channel Matters: Estimating Channel Influence for Multivariate Time Series (NeurIPS 2025 · similarity 0.87)
• MOMENT: A Family of Open Time-series Foundation Models (ICML 2024 · similarity 0.86)
• Structured Temporal Causality for Interpretable Multivariate Time Series Anomaly Detection (NeurIPS 2025 · similarity 0.85)
• Explain Temporal Black-Box Models via Functional Decomposition (ICML 2024 · similarity 0.85)
• OATS: Online Data Augmentation for Time Series Foundation Models (NeurIPS 2026 · similarity 0.85)
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