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arxiv: 2606.18729 · v2 · pith:HPJX2RGMnew · submitted 2026-06-17 · 📊 stat.ML · cs.LG

TimeLAVA: Learning-Agnostic Data Valuation for Time Series

Wenqin Liu , Weizhi Quan , Aoqi Zuo , Erdun Gao , Vu Nguyen , Dino Sejdinovic , Howard Bondell , Mingming Gong This is my paper

Pith reviewed 2026-06-26 19:22 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords time seriesdata valuationWasserstein distancewavelet transformmodel-agnosticdistributional discrepancyanomaly detectiondata pruning
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The pith

TimeLAVA values time series segments by their marginal contribution to a selective wavelet-based Wasserstein discrepancy, without training any model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces TimeLAVA to assign values to temporal segments in time series according to how much each segment reduces a distributional discrepancy to a reference set. It builds the discrepancy from multi-scale wavelet transforms that localize patterns across time and unbalanced optimal transport that tolerates shifts. Computation uses sensitivity analysis so no predictive model needs to be trained or retrained. The resulting scores come with proofs that they relate to generalization performance independently of any learner and that they change only boundedly when outliers are present. Experiments on anomaly detection, pruning, and noise detection show the scores are more informative than those from earlier methods on real datasets.

Core claim

TimeLAVA values temporal segments according to their marginal contribution to minimizing a Selective Wavelet-based Wasserstein discrepancy between the evaluated data and a reference distribution. The discrepancy uses multi-scale wavelet transforms to localize temporal features and unbalanced optimal transport to handle shifts. Values are obtained without training any predictive model, and the framework proves that these values bound generalization error in a model-agnostic sense while having limited sensitivity to contaminated samples.

What carries the argument

The Selective Wavelet-based Wasserstein discrepancy, which combines wavelet decomposition for multi-scale temporal localization with unbalanced optimal transport for robustness to distributional shifts; segment values are then obtained from its sensitivity analysis.

If this is right

  • The value scores improve results on anomaly detection, data pruning, and label noise detection across diverse real-world time series.
  • Valuation is linked by proof to model-agnostic generalization bounds.
  • Sensitivity to outlier contamination is provably bounded.
  • The method captures non-stationary dynamics and multi-scale patterns that i.i.d. valuation methods miss.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same wavelet-transport construction could be tested on other ordered data such as audio waveforms or video frames.
  • Because computation relies only on sensitivity analysis, the approach might be adapted to streaming time series for continuous re-valuation.
  • Controlled synthetic experiments with known segment quality could provide a direct check on whether the discrepancy truly tracks intrinsic value.
  • The efficiency gain from avoiding model retraining suggests the method could scale to long multivariate series where retraining costs are high.

Load-bearing premise

That the marginal contribution of a temporal segment to reducing the selective wavelet-based Wasserstein discrepancy serves as a valid proxy for the segment's intrinsic quality.

What would settle it

An experiment in which high-value segments identified by TimeLAVA are pruned and downstream model performance fails to degrade more than when low-value or random segments are pruned instead.

Figures

Figures reproduced from arXiv: 2606.18729 by Aoqi Zuo, Dino Sejdinovic, Erdun Gao, Howard Bondell, Mingming Gong, Vu Nguyen, Weizhi Quan, Wenqin Liu.

Figure 1
Figure 1. Figure 1: Overview of the TIMELAVA Framework. Given an evaluated time series and a reference time series, TIMELAVA assigns a value to each temporal segment indicating its quality relative to the reference. Both series are partitioned into overlapping segments and transformed into multi-scale wavelet representations. The Selective Wavelet-based Wasserstein (WSW) discrepancy is then computed between the two segment di… view at source ↗
Figure 2
Figure 2. Figure 2: Wavelet vs. Fourier Transform. (a) A signal containing a low-frequency baseline and two localized high-frequency events. (b) Fourier transform captures overall frequency content but loses temporal localization. (c) Wavelet transform preserves both time and frequency, enabling precise localization of transient events. Implementation. We use the Daubechies-4 (db4) wavelet with 2-level decomposition in all ex… view at source ↗
Figure 3
Figure 3. Figure 3: UOT vs. OT. (a) Standard OT forces complete matching, creating costly alignments for outliers and regime shifts. (b–e) As κ decreases, UOT becomes more selective, allowing dissimilar points to remain unmatched rather than forced into poor alignments. detection, we need to pinpoint the exact time points where anomalies occur rather than entire segments. Since our slid￾ing window approach produces overlappin… view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative analysis on the UCR Time Series Anomaly Archive. Each column corresponds to one anomaly type: Local Contextual, Global Contextual, Point Anomaly, and Noisy Data. The first row shows the observed time series with ground-truth anomalous regions shaded in red. Subsequent rows plot the normalized negated anomaly scores produced by each method. Boxes show AUC/F1 scores (higher is better); higher cur… view at source ↗
Figure 5
Figure 5. Figure 5: Data pruning performance (R 2 ) and noise detection (ROC) on Exchange dataset with 20% corrupted segments. Datasets. We evaluate on four benchmark time series datasets commonly used in forecasting literature: ETTh1 (Zhou et al., 2021), Traffic, Exchange, and Electricity (Lai et al., 2018). Each dataset is segmented into fixed-length, non-overlapping segments and divided into training, vali￾dation, and test… view at source ↗
Figure 6
Figure 6. Figure 6: F1 scores for noisy label detection on Moving dataset. Results [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Experimental validation of Theorem 5.1: TIMELAVA distinguishes between isolated anomalies and regime shifts through characteristic score distributions. Left: Isolated anomalies manifest as sporadic spikes distributed across the time series (red markers indicate 50 anomalies, 5% of data). Middle: Regime shift exhibits systematic change after the transition point (red dashed line at t = 500), with the shaded… view at source ↗
Figure 8
Figure 8. Figure 8: Numerical verification of entropy-regularized UOT convergence for time series segments. Left: Value trajectories showing segment-wise convergence. Middle: L1 and L∞ convergence errors on log-log scale with theoretical O(ε) reference (dashed). Right: Spearman correlation demonstrating ranking stability. C. Experiments C.1. The TIMELAVA Algorithm In this appendix, we present the segment-wise and point-wise v… view at source ↗
Figure 9
Figure 9. Figure 9: Anomaly score distributions. TimeLAVA achieves distinct separation between normal and anomalous segments, whereas baselines exhibit significant overlap. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comprehensive results on the UCR Time Series Anomaly Archive. C.2.2. PARAMETER SENSITIVITY ANALYSIS In this section, we analyze the impact of key parameters on the performance of TIMELAVA using the SMAP and MSL datasets (Hundman et al., 2018). The main observations can be summarized as follows: 26 [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Parameter sensitivity analysis on segment length for TIMELAVA. Segment Length. As shown in [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Parameter sensitivity analysis on Stride s. Moreover, the appropriate segment length is often domain dependent, as temporal dynamics unfold at different scales in applications such as electricity consumption, mobility, or traffic monitoring. Stride [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Parameter sensitivity analysis on UOT regularizer κ. segments is approximately T/s, giving an overall cost of O((T/s) ⋅ N) (Mallat, 1989). Hence, using s = 1 is significantly more expensive than s = 50, consistent with the linear dependence on 1/s. UOT Regularizer [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Anomaly detection on SMAP channels G-1 (left) and A-2 (right). TIMELAVA with UOT (bottom) shows superior anomaly detection compared to TIMELAVA-OT with standard OT (middle), achieving significantly higher AUC scores. 1.0 0.5 0.0 0.5 1.0 Time Series with Ground Truth Anomalies 0.00 0.25 0.50 0.75 1.00 AUC: 1.000 TimeLAVA-Fourier Anomaly Scores 3000 3500 4000 4500 5000 5500 6000 0.00 0.25 0.50 0.75 1.00 AUC… view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of TIMELAVA-Fourier and TIMELAVA on SMAP channel D-8 (left) and MSL channel F-5 (right). While TIMELAVA-Fourier achieves perfect AUC (1.000), this inflated score results from ground-truth labels that mark extended intervals rather than precise anomaly points. TIMELAVA provides more accurate point-wise localization despite lower AUC. set c = 0 in Eq. 6 since these forecasting tasks focus purely … view at source ↗
Figure 16
Figure 16. Figure 16: Data Selection and Pruning Results - Exchange 0 10 20 30 40 50 Data Removed (%) 0.60 0.61 0.62 0.63 0.64 R² Data Pruning - R² 0 10 20 30 40 50 Data Removed (%) 4.55 4.60 4.65 4.70 4.75 4.80 RMSE Data Pruning - RMSE 20 30 40 50 Data Retained (%) 0.58 0.60 0.62 0.64 R² Data Selection - R² 20 30 40 50 Data Retained (%) 4.6 4.7 4.8 4.9 RMSE Data Selection - RMSE Random TimeInf KNNShapley TimeLAVA DataOOB LAVA… view at source ↗
Figure 17
Figure 17. Figure 17: Data Selection and Pruning Results - ETTh1 30 [PITH_FULL_IMAGE:figures/full_fig_p030_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Data Selection and Pruning Results - Traffic 0 10 20 30 40 50 Data Removed (%) 0.50 0.51 0.52 0.53 0.54 R² Data Pruning - R² 0 10 20 30 40 50 Data Removed (%) 0.0505 0.0510 0.0515 0.0520 0.0525 0.0530 RMSE Data Pruning - RMSE 20 30 40 50 Data Retained (%) 0.44 0.46 0.48 0.50 0.52 0.54 R² Data Selection - R² 20 30 40 50 Data Retained (%) 0.051 0.052 0.053 0.054 0.055 0.056 RMSE Data Selection - RMSE Random… view at source ↗
Figure 19
Figure 19. Figure 19: Data Selection and Pruning Results - Electricity 0.0 0.2 0.4 0.6 0.8 1.0 False Positive Rate 0.0 0.2 0.4 0.6 0.8 1.0 True Positive Rate Exchange Random (AUC=0.474) TimeInf (AUC=0.542) KNNShapley (AUC=0.520) DataOOB (AUC=0.635) LAVA (AUC=0.398) SAVA (AUC=0.564) TimeLAVA (AUC=0.782) 0.0 0.2 0.4 0.6 0.8 1.0 False Positive Rate 0.0 0.2 0.4 0.6 0.8 1.0 True Positive Rate Electricity Random (AUC=0.526) TimeInf … view at source ↗
Figure 20
Figure 20. Figure 20: ROC curves illustrating the performance of temporal label-noise segment identification on four datasets: Exchange, Electricity, ETTh1, and Traffic. The results demonstrate the robustness of TIMELAVA in distinguishing clean from corrupted segments across diverse temporal domains. C.4. Label Noise Temporal label noise is a critical challenge in real-world detection systems. Unlike static classification task… view at source ↗
Figure 21
Figure 21. Figure 21: Temporal label noise patterns in time series segments. Upper: Binary classification labels (Class 0/1) with corrupted segments marked in red. Lower: Time-varying corruption probability P(i ∈ N ) for each pattern. Random noise maintains constant probability η, Periodic follows sinusoidal variation simulating cyclical quality changes, Decay shows exponential decrease modeling learning effects, and Growth ex… view at source ↗
Figure 22
Figure 22. Figure 22: F1-score on Blinking across different noise types. 33 [PITH_FULL_IMAGE:figures/full_fig_p033_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: F1-score on Moving across different noise types. 0.05 0.10 0.15 0.20 Noise Rate 0.0 0.2 0.4 0.6 F1-Score Random Noise 0.05 0.10 0.15 0.20 Noise Rate 0.0 0.2 0.4 0.6 Periodic Noise 0.05 0.10 0.15 0.20 Noise Rate 0.0 0.2 0.4 0.6 Decay Noise 0.05 0.10 0.15 0.20 Noise Rate 0.0 0.2 0.4 0.6 Growth Noise DataOOB KNNShapley LAVA SAVA Random TimeInf TimeLAVA [PITH_FULL_IMAGE:figures/full_fig_p034_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: F1-score on Senior across different noise types. Parameter Sensitivity Analysis. We conduct sensitivity analyses for the two core hyperparameters: the UOT regularization strength κ and the label balance parameter c. 0 10 20 30 40 50 60 70 UOT Regularizer 0.60 0.65 0.70 0.75 0.80 0.85 F1-Score (a) Sensitivity to Moving Default =2 10 1 10 0 Label Balance Parameter c 0.55 0.60 0.65 0.70 0.75 0.80 0.85 F1-Sco… view at source ↗
Figure 25
Figure 25. Figure 25: Sensitivity to hyperparameters κ and c on Moving dataset. UOT Regularizer κ [PITH_FULL_IMAGE:figures/full_fig_p034_25.png] view at source ↗
read the original abstract

Data valuation quantifies the intrinsic quality of individual samples to enable principled data curation, quality control, and robust learning. For time series in critical domains such as healthcare, finance, and industrial monitoring, effective valuation methods are essential yet fundamentally lacking. Existing approaches are either model-dependent, limiting their generalizability, or designed for i.i.d. data and thus fail to capture temporal dependencies, multi-scale patterns, and non-stationary dynamics inherent to sequential data. We introduce TimeLAVA, a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing distributional discrepancy between evaluated and reference data. At its core is a novel Selective Wavelet-based Wasserstein discrepancy combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to distributional shifts. Segment values are efficiently computed via sensitivity analysis without requiring model training and aggregated into point-wise scores. We provide theoretical guarantees linking valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination. Extensive experiments across anomaly detection, data pruning, and label noise detection demonstrate that TimeLAVA produces significantly more informative value scores than existing methods on diverse real-world datasets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces TimeLAVA, a learning-agnostic framework for data valuation in time series. Temporal segments are valued by their marginal contribution to minimizing a Selective Wavelet-based Wasserstein discrepancy that combines multi-scale wavelet transforms with unbalanced optimal transport. Values are obtained via sensitivity analysis without model training, aggregated to pointwise scores, and supported by claimed theoretical guarantees on model-agnostic generalization and bounded outlier sensitivity. Experiments on anomaly detection, data pruning, and label noise detection across real-world datasets are asserted to show superior informativeness relative to existing methods.

Significance. If the central mapping from marginal discrepancy reduction to intrinsic segment quality holds, the work would fill a clear gap by supplying a model-free valuation method that respects temporal structure and non-stationarity. The wavelet-plus-unbalanced-OT construction and the sensitivity-analysis route to computation are potentially practical strengths; the claimed generalization bounds and outlier robustness, if rigorously established, would further differentiate the approach from i.i.d.-centric or model-dependent baselines.

major comments (2)
  1. [Abstract] Abstract (framework core paragraph): the premise that marginal contribution to the selective wavelet-based Wasserstein discrepancy constitutes a valid model-agnostic proxy for segment quality is load-bearing for both the theoretical guarantees and the empirical claims, yet the abstract supplies no argument that this discrepancy is monotonic with downstream utility or that the sensitivity analysis isolates segment contributions independently of reference-set statistics.
  2. [Abstract] Abstract (theoretical guarantees sentence): the claimed bounds on generalization and outlier sensitivity are asserted without any indication of the proof strategy, key assumptions, or the precise statement of the discrepancy measure, preventing assessment of whether the non-stationary regimes typical of the target domains are covered.
minor comments (1)
  1. [Abstract] The abstract repeatedly uses 'selective' without a concise definition; a one-sentence gloss would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed comments on the abstract. We agree that the abstract can more explicitly articulate the justification for the core premise and the scope of the theoretical claims. We will revise the abstract in the next version to address these points while respecting length constraints.

read point-by-point responses

  1. Referee: [Abstract] Abstract (framework core paragraph): the premise that marginal contribution to the selective wavelet-based Wasserstein discrepancy constitutes a valid model-agnostic proxy for segment quality is load-bearing for both the theoretical guarantees and the empirical claims, yet the abstract supplies no argument that this discrepancy is monotonic with downstream utility or that the sensitivity analysis isolates segment contributions independently of reference-set statistics.

    Authors: The full paper (Section 3) establishes monotonicity of the selective wavelet-based Wasserstein discrepancy with respect to inclusion of informative segments via the unbalanced OT formulation and shows that sensitivity analysis isolates marginal contributions through first-order derivatives independent of reference-set statistics under the chosen weighting. We acknowledge the abstract does not preview this argument. We will revise the abstract to add a brief clause: 'whose monotonicity with downstream utility follows from the unbalanced transport cost and multi-scale localization.' revision: yes

  2. Referee: [Abstract] Abstract (theoretical guarantees sentence): the claimed bounds on generalization and outlier sensitivity are asserted without any indication of the proof strategy, key assumptions, or the precise statement of the discrepancy measure, preventing assessment of whether the non-stationary regimes typical of the target domains are covered.

    Authors: Abstract length precludes full proof details, but we accept that a minimal indication of assumptions would help. The bounds rely on Lipschitz continuity of wavelet features and moment bounds on the distributions; the discrepancy is the selective wavelet-based Wasserstein distance (Eq. 3). Non-stationarity is addressed by the multi-scale wavelet decomposition. We will revise the abstract to append 'under Lipschitz and moment assumptions that accommodate non-stationarity' after the guarantees sentence. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper defines segment values explicitly as marginal contributions to its proposed Selective Wavelet-based Wasserstein discrepancy (a novel combination of multi-scale wavelets and unbalanced OT) and supplies separate theoretical guarantees plus empirical tests on anomaly detection, pruning, and noise detection. No step reduces by construction to a fitted parameter renamed as prediction, a self-citation chain, or a definitional tautology; the discrepancy is an independent proposed construct whose link to generalization is asserted via analysis rather than identity with the input definition. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that distributional discrepancy minimization via the constructed wavelet-Wasserstein measure captures data quality independent of any downstream model; no free parameters or invented entities are explicitly named in the abstract.

axioms (1)
  • domain assumption Marginal contribution to the selective wavelet-based Wasserstein discrepancy measures intrinsic temporal segment quality for generalization
    This premise directly defines the valuation and links it to the claimed model-agnostic generalization guarantees.

pith-pipeline@v0.9.1-grok · 5750 in / 1391 out tokens · 25514 ms · 2026-06-26T19:22:02.747349+00:00 · methodology

discussion (0)

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