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arxiv: 2606.18729 · v3 · pith:HPJX2RGMnew · submitted 2026-06-17 · 📊 stat.ML · cs.LG

TimeLAVA: Learning-Agnostic Valuation for Time Series Data

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

Pith reviewed 2026-06-30 11:24 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords data valuationtime seriesWasserstein distancewavelet transformmodel-agnosticanomaly detectiondata pruninglabel noise
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The pith

TimeLAVA values time series segments by their marginal contribution to minimizing 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 data in a way that does not depend on any particular downstream learning model. It quantifies each segment's contribution to closing the distributional gap with a reference set through a new discrepancy measure that applies wavelet transforms at multiple scales and uses unbalanced optimal transport. This matters for domains such as healthcare and finance, where time series exhibit temporal dependencies and non-stationarity that break methods designed for independent samples. Values are obtained via sensitivity analysis on the discrepancy, and the paper supplies generalization bounds plus robustness results. Experiments on anomaly detection, data pruning, and label noise detection show these scores are more informative than those from prior approaches on real datasets.

Core claim

TimeLAVA is a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing the Selective Wavelet-based Wasserstein discrepancy between evaluated and reference data. Segment values are computed efficiently via sensitivity analysis without requiring model training and aggregated into point-wise scores. The method supplies theoretical guarantees that link the resulting valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination.

What carries the argument

Selective Wavelet-based Wasserstein discrepancy, formed by combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to shifts; values are extracted from sensitivity analysis on this measure.

If this is right

  • Time series data curation and quality control become possible without dependence on any specific model architecture or training procedure.
  • Value scores support more effective anomaly detection by identifying segments that contribute least to distributional alignment.
  • Data pruning guided by these scores yields higher performance on downstream tasks than pruning guided by existing valuation methods.
  • Label noise detection improves because noisy segments produce larger increases in the wavelet-Wasserstein discrepancy.
  • Valuation remains stable under moderate outlier contamination due to the bounded sensitivity result.

Where Pith is reading between the lines

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

  • The wavelet component suggests straightforward extensions to other multi-scale sequential signals such as audio or video streams.
  • Sensitivity analysis on the discrepancy could enable incremental valuation updates for streaming time series without recomputing from scratch.
  • Direct comparisons between TimeLAVA scores and model-dependent valuation scores on identical datasets would clarify when the model-agnostic property is most advantageous.
  • The framework may generalize to irregularly sampled or multivariate time series by adjusting the wavelet basis accordingly.

Load-bearing premise

The marginal contribution of a temporal segment to minimizing the Selective Wavelet-based Wasserstein discrepancy serves as a reliable proxy for its intrinsic quality or utility across downstream learning tasks.

What would settle it

A controlled experiment on a held-out time series dataset in which selecting or retaining segments ranked highest by TimeLAVA produces no improvement (or produces worse performance) on a downstream task such as forecasting or classification compared with selecting low-ranked segments or random subsets.

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

3 major / 2 minor

Summary. The paper introduces TimeLAVA, a learning-agnostic framework for time series data valuation. Temporal segments are valued by their marginal contribution to minimizing a novel Selective Wavelet-based Wasserstein discrepancy that combines multi-scale wavelet transforms with unbalanced optimal transport. The method requires no model training, supplies theoretical guarantees linking the scores to generalization and bounded outlier sensitivity, and is evaluated on anomaly detection, data pruning, and label noise detection tasks where it is claimed to outperform prior methods on real-world datasets.

Significance. If the theoretical links and empirical superiority hold, the work would address a clear gap in model-independent valuation methods that respect temporal structure, multi-scale patterns, and non-stationarity, with direct utility for data curation in healthcare, finance, and monitoring applications. The explicit positioning as learning-agnostic and the provision of sensitivity bounds are positive features.

major comments (3)
  1. [Abstract and §3] Abstract and §3 (Theoretical Analysis): the manuscript asserts 'theoretical guarantees linking valuation to model-agnostic generalization' and 'bounded sensitivity to outlier contamination,' yet the provided text contains no derivations, proof sketches, or statements of the relevant lemmas, which are load-bearing for the central contribution.
  2. [§5] §5 (Experiments): the claim that TimeLAVA 'produces significantly more informative value scores' is unsupported by any reported dataset sizes, error bars, ablation studies, or quantitative tables comparing value-score informativeness, rendering the superiority assertion impossible to assess.
  3. [§4] §4 (Method): the core modeling choice—that marginal contribution to the Selective Wavelet-based Wasserstein discrepancy serves as a reliable proxy for downstream utility—is load-bearing for all empirical claims but is not tested against direct task-specific utility or alternative discrepancy measures.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'Selective Wavelet-based Wasserstein discrepancy' is introduced without a one-sentence gloss of its two constituent ideas (wavelet localization and unbalanced OT).
  2. [§4] Notation: the aggregation step from segment values to point-wise scores is described only at a high level; a short equation or pseudocode line would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will revise the manuscript to improve clarity and completeness where the points are valid.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (Theoretical Analysis): the manuscript asserts 'theoretical guarantees linking valuation to model-agnostic generalization' and 'bounded sensitivity to outlier contamination,' yet the provided text contains no derivations, proof sketches, or statements of the relevant lemmas, which are load-bearing for the central contribution.

    Authors: We agree that the main text would benefit from explicit proof sketches. The full proofs appear in the appendix, but to address this, we will insert concise statements of the key lemmas and proof outlines directly into Section 3, making the theoretical links to generalization and outlier sensitivity self-contained in the body. revision: yes

  2. Referee: [§5] §5 (Experiments): the claim that TimeLAVA 'produces significantly more informative value scores' is unsupported by any reported dataset sizes, error bars, ablation studies, or quantitative tables comparing value-score informativeness, rendering the superiority assertion impossible to assess.

    Authors: The experimental section requires expanded reporting. In revision we will add explicit dataset sizes, standard-error bars from repeated trials, ablation tables, and quantitative comparisons of value-score informativeness to support the superiority claims. revision: yes

  3. Referee: [§4] §4 (Method): the core modeling choice—that marginal contribution to the Selective Wavelet-based Wasserstein discrepancy serves as a reliable proxy for downstream utility—is load-bearing for all empirical claims but is not tested against direct task-specific utility or alternative discrepancy measures.

    Authors: The choice is grounded in the theoretical connection between the discrepancy and generalization established in Section 3. While downstream-task results provide indirect validation, we will add targeted comparisons against alternative discrepancy measures in the revised experiments to further substantiate the modeling decision. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper presents TimeLAVA as a learning-agnostic framework that computes segment values via marginal contribution to a Selective Wavelet-based Wasserstein discrepancy, with aggregation into point-wise scores and theoretical guarantees on generalization and sensitivity. No equations, fitting procedures, or derivations are described that reduce a claimed result to its inputs by construction (e.g., no fitted parameters renamed as predictions, no self-definitional loops, and no load-bearing self-citations on uniqueness theorems). The method is explicitly positioned as independent of model training, with empirical validation on downstream tasks, rendering the derivation chain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only review supplies no explicit free parameters, background axioms, or independent evidence for new entities; the central technical object is the introduced discrepancy measure.

invented entities (1)
  • Selective Wavelet-based Wasserstein discrepancy no independent evidence
    purpose: Core measure combining multi-scale wavelet transforms and unbalanced optimal transport to value temporal segments
    Described as the novel core of TimeLAVA in the abstract.

pith-pipeline@v0.9.1-grok · 5750 in / 1179 out tokens · 46115 ms · 2026-06-30T11:24:21.788229+00:00 · methodology

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