ShapeX: Shapelet-Driven Post Hoc Explanations for Time Series Classification Models
Authors: Bosong Huang
Ming Jin
Yuxuan Liang
Johan Barthelemy
Debo Cheng
Qingsong Wen
Chenghao Liu
Shirui Pan
Venue: NeurIPS 2025 poster ()
Keywords: Explainability
Time Series Classification
Shapelet
Primary area: deep_learning

Abstract: Explaining time series classification models is crucial, particularly in high-stakes applications such as healthcare and finance, where transparency and trust play a critical role. Although numerous time series classification methods have identified key subsequences, known as shapelets, as core features for achieving state-of-the-art performance and validating their pivotal role in classification outcomes, existing post-hoc time series explanation (PHTSE) methods primarily focus on timestep-level feature attribution. These explanation methods overlook the fundamental prior that classification outcomes are predominantly driven by key shapelets. To bridge this gap, we present ShapeX, an innovative framework that segments time series into meaningful shapelet-driven segments and employs Shapley values to assess their saliency. At the core of ShapeX lies the Shapelet Describe-and-Detect (SDD) framework, which effectively learns a diverse set of shapelets essential for classification. We further demonstrate that ShapeX produces explanations which reveal causal relationships instead of just correlations, owing to the atomicity properties of shapelets. Experimental results on both synthetic and real-world datasets demonstrate that ShapeX outperforms existing methods in identifying the most relevant subsequences, enhancing both the precision and causal fidelity of time series explanations.

SHAPEX : Shapelet-Driven Post Hoc Explanations for Time Series Classification Models
Bosong Huang', Ming Jin'; Yuxuan Liang", Johan Barthelemy Debo Cheng', Qingsong Wen Chenghao Liu", Shirui Pan
Griffith University Hong Kong University Science and Technology (Guangzhou) NNVIDIA
*Hainan University Squirrel Ai Learning, USA "Saeesforce Research Asia
bosong hhung@griffithie edu. au, mingj inedu@gmail. com, s. pan@griffiih edu. au
Abstract
Explaining time series classification models is crucial, particularly in high-stakes applications such healthcare and finance, where transparency and trust play critical role. Although numerous time series classification methods have identi- fied key subsequences, known as shapelets, core features for achieving state- of-the-art performance and validating their pivotal role in classification outcomes, existing post-hoc time series explanation (PHTSE) methods primarily focus on timestep-level feature attribution. These explanation methods overlook the fun- damental prior that classification outcomes are predominantly driven by key shapelets. To bridge this gap. we present SHAPEX, an innovative framework that segments time series into meaningful shapelet-driven segments and employs Shapley values to assess their saliency. At the core of SHAPEX lies the Shapelet Describe-and- Detect (SDD) framework, which effectively learns a diverse of shapelets essential for classification. We further demonstrate that SHAPEX pro- duces explanations which reveal causal relationships instead of just correlations, owing to the atomicity properties of shapelets. Experimental results both syn- thetic and real-world datasets demonstrate that SIIAPXX outperforms existing methods in identifying the most relevant subsequences, enhancing both the preci- sion and causal fidelity of time series explanations. Our code made available at https://gi //gthbbb com CommBBooonwaangShappee
Introduction
Time series classification plays critical role across various domains [[]]. While deep learning mod- els have significantly advanced classification performance in this area, their black-box nature often compromises explainability. This limitation becomes particularly critical in high-stakes applica- tions such as healthcare and finance, where reliability and accuracy are paramount. Most research on time-series model explainability focuses on post-hoe time-series explanation (PHTSE), predom- inantly via perturbation- bbaed methods at the timestep level. For example, Dynamask [ generates instance-specific importance scores through perturbation masks. Similarly, TIMEX rogate model to mimic pretrained model behavior, whereas TIMEX+ leverages information bottleneck to deliver robust explanations.
[ trains sur-
Despite these advancements, existing methods neglect an essential aspect of time series classifi- cation: the classification outcomes often driven by key subsequences rather than individual timesteps. Recently, several classification methods [5L K [7]l have emphasized the significance of utilizing these crucial subsequences, known shapelets. Take some examples for intuitive under- standing: In electrocardiogram (ECG) signal classification, specific segments like the QRS com-
*Corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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plex are critical for accurate diagnostics [8] In human activity recognition (HAR), patterns like gait cycles play a decisive role in classifying activities [M] Recent methods have expanded upon this foundational knowledge, exploring diverse strategies to incorporate shapelets into classification frameworks. For instance, ShapeFormer [6] employs a discovery algorithm to extract specific shapelets and incorporates them into a transformer-ban
model to enhance classification perfor- mance. Wen et al. [[]] generalizes shapelets into symbolic representations, enhancing flexibility and expressiveness. Similarly, Qu et al. [S]] demonstrates that convolutional kernlls can naturally func- tion as shapelets, offering both strong discriminative power and interpretability, Together, these approaches underscore growing consensus that shapelets are not only interpretable but also central to the performance of modern time series classification models.
Although shapelets are widely recognized as key features time series classification,, ex- isting explanation methods primarily rely on
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perturbing individual timesteps to compute saliency scores. This disrupts local tempo- ral dependencies and fails to capture the holis- tic influence of key subsequences, resulting in fragmented and less interpretable explanations. As shown in Figure M (b), timestep-level per- turbations are scattered, making it difficult to align with true saliency patterns. While equal- length segment perturbations (Figure MI (c)) may further reduce interpretabilltty by splitting meaningful patterns or merging unrelated sub- sequences. To overcome these limitations, an ideal approach should perturb segments aligned with meaningful shapelets, as illustrated in Fig- ure M (d). This preserves the atomicity of key subsequences, potentially leading to more faithful and interpretable explanations. However, exist- ing time series segmentation methods primarily detect statistical change points [III, [I]] or extract subsequences unrelated determining classification outcomes [[2]] making them unsuitable for explaining model behaviors.
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ECG example. (a) shows the original signal with saliency labels derived from QRS complexes clinically critical regions for arrhythmia classifi- cation. (b)-(d) apply timestep-level, equal-length, and shapelet-driven perturbations, respectively. Only (d) maintains alignment with the salient re- gions.
Figure 1: Perturbation strategies
To fill the gaps, introduce SHAPEX, a novel approach that segments the time series into mean- ingful subsequences and computes Shapley value [|K]]] as saliency scores. Instead of distributing im- portance across individual timesteps, SHIPPX aggregates timesteps into cohesive, shapelet-driven segments that serve as "players" in the Shapley value computation. By measuring each segment's marginal contribution the black-box model's prediction, this method clearly identifies which sub- sequences significantly influence classification outcomes. Specifically, the Shapelet Describe-and Detect (SDD) framework within SHAPEX efficiently discovers representative and diverse shapelets most critical for classification. Subsequently, SHAPEX segments the time series to align closely with these dominant temporal patterns, yielding more accurate and interpretable explanations. Our key contributions are summarized as follows:
SHAPEX pioneers PHTSE at the shapelet-driven segment level, offering a precise and prin- cipled alternative to timestep-level methods. Its SDD framework is the first shapelet learn- ing approach designed specifically for PHTSE, enforcing representativeness and diversity.
2. We provide a theoretical justification for interpreting the Shapley value computed by SHAPEX as an approximation of the model-level Conditional Average Treatment Effect (CATE), thereby enabling more trustworthy and robust interpretations across diverse real- world datasets.
3. Our experiments demonstrate that SHAPEX consistently outperforms the baseline models, delivering more accurate and reliable explanations in critical applications. To our knowl- edge, it is also the first approach to conduct large-scale, occlusion- evaluation across the entire UCR archive of 100+ datasets, establishing a more comprehensive benchmark for explanation quality.

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2
Related Work
The field of time series explainabilityy has gained increasing attention, aiming to interpret the decision process of black-box models applied to temporal data [I [S]. Existing methods are commonly cate- gorized into in-hoc and post-hoc approaches. In-hoc methods embed interpretability directly into the model, typically via transparent representations such as Shapelets or self-explaining architectures, as seen TIMEVIEW [TB]] and VQShape [[Z)]. contrast, post-hoe methods generate explanations after the model has been trained and are further divided into gradient-based based and perturbation- techniques. The former includes Integrated Gradients (IG) [[X]] and SGT+GRAD [[.)] while the lat- ter observes prediction changes under input perturbation, in CoRTX [20] and other related work.
For convenience, and following prior literature focused specifically on temporal data, we refer to post-hoc explainability methods in the time series domain Post-Hoc Time Series Explainability
(PHTSE).
Several foundational studies have underscored the unique challenges of explaining time series mod- els, such as the limitations of standard saliency techniques [[S]], the use of KL-divergence to quantify
temporal importance [2I0], and the development of symbolic shapelet-based explanation rules [22]].
These works laid a foundation for understanding the temporal nature of model explanations.
Building on these insights, a major line of recent work has focused on PHTSE. Unlike generic saliency methods, PHTSE methods are explicitly designed for time-dependent inputoutput map- pings. Representative approaches include Dynamask [2],, which learns instance-specific perturba- tion masks; WinIT [23]], which models varying temporal dependencies via windowed perturbation; and the TIMEX family [G], BI], which ensures faithfulness through interpretable surrogate models and information bottleneck regularization. For a broader discussion of deep learning explainability methods, see Appendix R
3 Methodology
Figure D shows the two major phases of SHAPEX. Training: the Shapelet Describe-ande meteet (SDD) framework learns a compact set of shapelets. Inference: these shapelets align segments that are (i) perturbed at the Shapelet-Driven Segment Level (SDSL.) and (ii) assessed with Shapley value Attribution, producing faithful post-hoc explanations. To keep the discussion self-contained, we begin by introducing the necessary background and notation.
3.1 Background & Notation
We address the task of explaining time series classification models in a post-hoc manner. Given a trained black-box model that predicts class labels from time series data, our goal is to analyze its behavior by identifying which input components contribute most to the prediction.
Formally, let each input be time series of length T, where each timestep has a D-dimensional feature vector X, E R forming dimensional space, Y E R The objective of time series classification is to learn classifier f(-)
= [X,, X2,..., Xy). The associated label Y lies in C-
that maps X to its predicted label y =(X).
To provide PHTSE, we employ an explanation method E(-) that produces saliency scores E TKD,, where each element Re, E [0,1] quantifies the importance of the input feature X,,d for the predicted label Ý Higher values of Re, indicate stronger influence the classification outcome. In this work, we focus on the univariate setting, i.e., D = 1, and omit the feature dimension d for clarity; all subsequent discussions assume univariate time series unless otherwise specified. Furthermore. the evaluation of (-) depends on the availability of ground-truth saliency labels: when available, they serve direct supervision or evaluation references; otherwise, occlusion-based perturbation used to assess the quality of the generated R.
In the realm of PHTSE methods, perturbation-base explanation methods represent the most pri- mary category. We briefly present the essential background here; for a more detailed discussion of perturbation paradigms, saliency granularity, see Appendix Al
The concept of shapelets has played a central role time series interpretability. It was originally introduced short, classdiisermminative subsequences directly extracted from raw time series [
3

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(a) Shapelet Describe-and-Detect (SDD) Framework: Training Phase
Descriptor- Deteettrr Layer
Projection Layer
Expressiveness
Y I
Shapelet Encoder
Series
Loss
Time Sories Clasificatioon
Training
Descriptor
Sn Initislization
Diversity Loss
Compute
Similarity
Activation Maps
Instance Narm Patching
Map
Detector
Matching Loss
MHSA
X
detecttd
Shapelets Sn
Uinear Head
(b) Shapley Value (SV) Attribution for Sravelet- Segments: Inference Phase
Shapelet-Driven Segmentation
SV-based Saliency Attribution
Saliency
Test Time Series
Shapley Value
Segment Extraction
Trained SDD
P(X, (17"))
S.S
Shapelets Sn from (a)
Black- Box Model
Perturbation
Figure 2: Overview of SHAPEX. In the training phase, given time series from dataset and the initial- ized shapelets, ! descriptor generates activation maps by 3 taking shapelets as the convolution kernel, demonstrating which extent the input time series aligns with each shapelet. Meanwile, @ detector locates key subsequences for the morphological matching of shapelets. Simultancously, the shapelets are optimized using three loss functions. In inference, the learned shapelets first trigger shapelet-driven segmentation the test series; the resulting segments are next perturbed by SDSL to obtain ① P(X, Mg.). Finally, Shapley value is applied to compute the final saliency scores.
These subsequences served as intuitive and interpretable building blocks, revealing characteristic temporal patterns most indicative of specific classes. Under this classical definition, each shapelet corresponded to an explicit segment of the input series and was closely tied to a particular class identity. Over time, however, this notion has evolved into more flexible and abstract representa- tion. Modern approaches no longer require shapelets to be literal subsequences of the data; instead, they can be viewed as prototypical temporal patterns learned through optimization representation learning [25), 26, 27 M] These learned shapelets are typically not class-specific but rather aim to capture generalizable and semantically meaningful features shared across the dataset.
3.2 Shapelet Describe-and-Deter (SDD) Framework
This section introduces the SDD framework used during training to learn a compact set of discrimi- native shapelets segmenting time series into interpretable units.
Inspired by the Deseribe-and-Deted paradigm from image anomaly detection [2X] we adapt this idea to time series by designing shapelets that both activate strongly on discriminative regions and serve as semantic prototypes. The SDD framework consists of a descriptor-detecte layer to localize nigh-activation regions, shapelet encoder to enhance representation quality, and multi-objective training strategy that promotes classification relevance and diversity. In contrast to prior methods that rely on large shapelet banks, SHAPEX emphasizes conciseness and discriminativeness through joint optimization.
Descriptor-Detecee Layer. To identify regions in the input time series that align with key patterns, we apply two-step matching mechanism consisting of descriptor and a delector.
The descriptor uses of shapelets S {Si, S2,..., ). where each S,, E RR is fixed-length prototype, and N is the number of shapelets. For an input X E RT,, we compute a similarity map I E IR T'N using valid-width ID convolution:
= X
(I)

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where * denotes ID convolution with same padding (i.e., zero padding on both sides), and b is learnalle bias term. Each 4.n represents the similarity between shapelet Sn and the local subse- quence centered at position I.
We then apply softmax across the shapelet dimension each timestep obtain activation map A E IR T
A
m=1 e
Here, Ar, reflects the normalized alignment strength between Sn and X time t.
The detector identifies the peak activation position 1 = arg max, Ar, and extracts subsequence of length I. centered at :
Xddelected x - [L/2] 1 + [L/2]]
This segment Xddetectdd RL captures the region in X most strongly aligned with shapelet Sn. forming the basis for downstream segmentation and attribution.
Shapelet Encoder and Training Losses. We apply lightweight patch-based encoder refine the temporal structure of each shapelet; see Appendix O for details.
To jointly optimize shapelet quality, we define composite loss training samples (X, Y), target- ing three objectives: expressiveness, aligmment accuracy, and diversity. Let = {S1, S ................................ SN} denote the set of learnable shapelets. The expressiveness loss encourages shapelets to be discrimina- tive with respect to the target label. For each training mini-batch of size K, we obtain the predicted probabilities Y; for each input by applying a projection layer to its activation map A. The expres- siveness loss is defined
K
Las Σ i=1
(Kilog Y; (1 Y2) log(1 - 8:1)
The matching loss promotes alignment between each S, E S and its most responsive segment X deteecte encouraging each shapelet to closely match the local temporal shape of the input. The di- versity loss encourages non-redundancy by penalizing shapelet pairs with high similarity, promoting angular diversity and preventing redundant patterns [29]]. The two losses are defined as:
N
N
N
Lmatch
d(Sn, detected)
Laiv
Σ
Σ
max (0, - (i,,S, S;)),
(5)
2=1 j-i+1
where d(-) denotes the Euclidean distance, sim(..) the cosine similarity, and is a distance margin. The total objective is a weighted combination of the above components:
= Lets + Amatch Cranch + Adiv faiv;
where Amatch and Aaiv balance alignment and diversity.
3.3 Shapley Value Attribution for Shapelet-Driven Segments
To perform post-hoe time series explanation, SHAPEX evaluates the importance of shapelet-alignes segments through Shapley value analysis. These segments correspond to regions aligned with the learned shapelets. Since this framework relies on marginal contributions over different coalitions, we simulate segment inclusion or exclusion via perturbation: retaining a segment corresponds to including it in the coalition, while perturbing it simulates its removal. This enables the computation of saliency scores reflecting each segments contribution to the model output.
Shapelet- Driven Segmentation. To extract these segments, SHAPEX utilizes the shapelets learned during training to extract interpretable segments that correspond to key morphological pat- terns. These segments are derived from shapelet activation maps computed on the test input, abling a structured and semantically meaningful decomposition of the time series.
Specifically, for time series X E RT from the test set and each learned shapelet S, S (Si,..., SN), ), we compute the activation map A, R using the trained SDD from Section 3.2 indicating alignment strength between X and S, across timesteps.
5

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To extract high-activation regions, we apply threshold & to obtain:
T(s.) = { {I...., An. > 5
(7)
The corresponding segment is:
(s.) = (X, T(s.))
(8)
capturing the region in X that is morphologically aligned with shapelet Sn..
Let 9 = {1, . .N index set of shapelet-aligned segments {X(s.)) each corresponding
shapelet Sn E S. For any subset g' _ G. the union of activated timesteps is defined as:
T
U T(s.). EE
These shapelet-driven segments serve explanation units in the Shapley value analysis that follows.
Shapelet-driven Segment-Level (SDSL) Perturbation. We define binary perturbation mask Mig') E IR" for any subset of segment indices G' C = (L........
[1, t T(g) Mig = 10 TET
(10)
where the perturbation function defined in Equation 14 is instantiated as P(X,, M(g)). However, the current baseline valuing approach, whether zero-filling averaging. often introduces abrupt changes at boundaries. These changes may prevent the value function in Shapley value from fully climinating the influence of segments outside the coalition. To address this, we propose linear perturbation, where the baseline value B, is set as:
Exturt (X
B, X
X(an), t E [tstarts fend],
(11)
tead
Estart
where X Xt,g are the values at the boundaries of the perturbed region. This design isolates the contribution of X (G') and enables Shapley value computation. Intuitively, this linear interpolation creates a smooth transition between the two boundaries, preventing artificial discontinuities when segment is masked.
Shapley Value Computation. by () as:
We compute the Shapley value Φh, for each segment X X(S.) (indexed
1I (
19'1 - 1)!
on Σ ('C
(
(12)
9
where Xiaa and Xty are the values the boundaries of the perturbed region, and P(X, M(g.) de- notes the perturbed input defined in Equation [4 The coefficient gives the probability that segment is added after the subset G' in random ordering of all segments, and f(-) denotes the black-box classifier.
To further reduce the complexity in computation and based the assumption of temporal depen- dency, we apply a temporary-relation subset extract strategy, which to restrict the range of coalitions in Shapley value to subset of segments that are directly indirectly connected to the current X(s_)- This modification reduces the computational complexity of each segments Shapley value from ONN) to O(N). Ultimately, the saliency score is computable using Equation [ (see Appendix A for the detailed formulation).
4 ShapeX as Approximate Causal Attribution
In this section, we present a theoretical analysis of SHAPEX as a method for approximate causal attribution in time series models.
Most host-hoc explainers for time series models merely expose correlations: they estimate the asso- ciations between input regions and model predictions, often by training proxy models computing

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correlation- coreelation-bsed importance scores. However, these methods do not guarantee that the highlighted regions are causal drivers of the model's predictions. In contrast, SHAPEX is designed provide model-level causal insight by explicitly conducting causal intervention [30]] Specifically, SDSL perturbation interprets the actions of "keeping vs. masking a segment" as an intervention in the mod- els input space, while shapelet-driven segmentation isolates semantically coherent subsequences for calculating Shapley value. By framing perturbations as interventions, SHAPEX moves beyond corre- lational explanations to provide causal attributions that are more robust to confounding noise, more stable across re-training, and better aligned with practitioners needs in sensitive domains such as medical triage.
To formalize the causal semantics of SHAPEX, we demonstrate that its attribution mechanism ap- proximates the concept of the CATE [T B2]. The CATE quantifies the expected change in an outcome resulting from a specific intervention, conditioned on given context. our setting, the outcome is the model prediction f(X), the intervention is whether a shapelet-aligned segment X(s.) is retained or masked, and the context is defined by the remaining segments indexed by G" C giin) where 9 = (l...... N is the set of all segment indices. Shapelet-driven segmentation naturally pro- vides localized and semantically coherent regions, making it particularly well-suited for modeling such conditional interventions. Importantly, the resulting CATE in this setting is defined with respect to the model prediction, not the true outcome Y. Hence, we refer to this quantity as the model- level CATE, denoted by model measuring the causal strengths of X (s.) on [(X). We formalize this relationship in the following proposition:
Proposition 1 (Shapley Value as Model-Level CATE). Let J(X) denote the models prediction for imput X, and let X(S.) denote the segment aligned with shupelet n E G, where G = {1....; ., N) is the index set of all segments. Then, under the intervention defined by retaining or masking segment (ss)). the Shapley value on computed
On = Eg (((X)))))--(((X)
(13)
is equivalent to the model-level CATE model, conditioned on context G' C (n).
detailed proof is provided Appendix D This equality holds exactly when all coalitions G are exhaustively enumerated. Under subset sampling, the estimator remains unbiased given valid surrogate randomization mechanism.
We further conduct case study in Figure + to un- derline this mechanism, see Appendix G for de- tails: T-MeX++ maps scatter importance across many timesteps, hinting only at loose association with the outcome. SIIAPEX, however, concentrates saliency on the growth plate transition region, the true biomechanical determinant of class labels, providing visually plausible evidence a causal structure.
TIMEX+ PhalangesOuttinssCCreee Shawex
MWM
Figure 3: The saliency scores generated by SHAPEX and TIMEX++ on PhalangesOut- lineCorrect dataset.
Experiments
The explanatory effectiveness of SHAPEX is assessed across four synthetic datasets and compre- hensive suite of real-world datasets, considering two different perspectives: (I) For datasets with ground-truth saliency scores, we conduct saliency score evaluation experiments. (2) For datasets without ground-truth saliency scores, we perform occlusion experiments [2]]. The best and second- best results in all experiments are highlighted in bold and underlined, respectively. In terms of the black-box models to be explained, we select four of the most widely used time series classification models: Transformer [33], LSTM [[=]] CNN [B5]] and MultiRocket [66]. The experimental results presented in the main body are all based on vanilla Transformer [ل]] as black-box models. Further
experimental details can be found in Appendix D.
Datasets. We evaluate on both synthetic and real- world time series. The synthetic data includes four basef binary classification datasets: (i) MCC-E, (ii) MTC-L, (iii) MCC-L, and (iv) MTC- E, following [37]]. Each sample is annotated with ground-truth saliency for evaluating explanation quality. For real-world data, we use the ECG dataset [38], which similarly provides ground-truth labels, and the full UCR Archive [3%], comprising over 100 univariate classification datasets across diverse domains. Further details are provided in Appendix +
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Table 1: Saliency evaluation synthetic datasets using Trans- Table 2: Saliency score the ECG dataset.
formers as black-box. box model. Dark blue marks better values.
AUMPAC
Massop
AUURC
AUF
AUR.
AUTBC
ALD
A2TA
241.2044 2048
1UFFT12 11200 2028
6J15225H 6623
1234422000 1800
8011
3:5444:9 1411
CORTX BCD
MILLET
0.3017 8248
BAT22 E.JANN
3.508--23
Mil Am
8847
121
8-3644:20
Tox
10.999 14.
Taank 1101
SA0NE4 9696
SHORY
072286619134
SHoPa
8.508800 BOOS
36799 019058
6TDS 2055
NTC
MITC B
Table 3: Ablation ECG.
MUTDOO
AUTRC
AUF
AUTSIC
AUD
Albrimn
AIP
AFR
1166780.20
0L-45BUD MX27
82/009
220668000005
Pal
8:7225-000224
10005=1100112
COREES Br3
P90ESBA 2001
8:20152H 1143
3
612894-000022
(19733
0.3115 109399
8:7117-10041
TiacN BB
23479660300 5835
1300000 0003
05153 2010
Wh SR
WI
0.3777200001
0220852002030
9
00231
SHaPP SP SHAPIX
BATIO 10.204
0.396200 2007
178 1976
009IIISSONE 0024
179RE52 2010
Mansata low: diSEnE 2o0: SE, sigssa/aaAa
LIN:
SEGMENT.
Benchmarks. The proposed methods compared with multiple benchmark approaches (see Ap- pendix EN for benchmark details and metric definitions.): Perturbation- basedd methods: TimeX++
H. TIMEX Dynamask [2] and CoRTX [2M]. cradieet-based methods: Integrated Gradients
(IG)
[T
WinIT [23]] MILLET [0O]
FACESUCR
UWAVEGEST
FACEALL
UWANEGESTURELUBRAAAL
1:00
1.00
AUROC
AUROC
3.60
0.00
0.30
0.20
3.50
0.50
Tal Proportion Parturbed
Proportion 12t sie
2.40
Proporti Perturbed
0.40
Proportion Perturbed
2:15 1.12
Figure 4: Occlusion results under different per- turbation ratios, where higher AUROC indicates
Figure 5: Ablation study on SHAPEX by replac- ing SDSL with squal-length segmentation, lead- ing to performance drop.
better saliency.
Average AUROC with Error Bars Across Datasets
dyna
shapex
Average AUROF
0.90
0.65
0.80
0.53
8:48
0.70
0.35
0.60
0.60
Propartion Perturbed
Dest Model per Dataset
(a)
(b)
Figure 6: Occlusion evaluation results on the full UCR archive. (a) Average AUROC with stan-
dard deviation across all datasets under varying perturbation ratios. (b) Distribution of the best-
performing explainability method across datasets under varying perturbation ratios. Each row cor- responds to a perturbation level, and each colored dot represents the method achieving the highest performance on specific dataset at that level.
5.1 Saliency Score Evaluation on Synthetic Datasets and Real-world Datasets
In this section, we directly evaluate the generated saliency score by each model on the synthetic dataset and the real-world dataset. We also report SHAPEX_SS ___, using ShapeFormer [6]] in place of SDD (see Subsection 5.3 for details). In Table M. SHAPEX surpasses the second-best method in AUPRC by an average of 58.12%. with the largest gain of 146.07% on MTC-E. For AUR, it achieves an average improvement 21.09% However, AUP, SHAPEX shows a slight performance decline. We make the following observations: The consistent enhancement of SHAPEX in AUPRC indicates that it effectively balances the identification of complete salient sequences while maintaining high accuracy. Notably, TIMEX and TIMEX++ perform significantly worse on the MCC-E and MTC-E datasets, where the motif amplitude is equal to the baseline waveform, compared to the MCC-H and MTC-H datasets, where motifs exhibit higher amplitudes. This suggests that these methods
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tend to label outliers or anomalies as key features. In contrast, SHAPEX remains stable across all datasets, demonstrating its ability identify key time series patterns relevant to classification rather than relying on extreme amplitude variations. Table Q shows that SHAPEX also consistently out- performs all baselines, with a notable AUR improvement in ECG dataset. To explore how different black-box classifiers affect saliency outcomes, we also conduct further evaluations using range of models, from standard LSTM [33]] and CNN [<]] to the state-of-the-ar MultiRocket [36]]. Results are presented in Appendix E.
5.2 Occlusion Experiments on Real-world Datasets
We follow the occlusion protocol from [BI, which perturbs the bottom-k timesteps ranked by saliency scores generated from explanation methods. By progressively perturbing less important regions, observe how quickly the model's classification accuracy degrades. A reliable explanation model should exhibit a slow and smooth performance capture the key discriminative patterns, while a steep drop suggests poor alignment between the saliency map and the underlying predictive logic.
inpicaaiin that high saliency regions truly
Figure E illustrates occlusion results on two typical UCR datasets, serving as visual examples of the evaluation process rather than highlighting best-case performance. Full occlusion results for all datasets are included in Appendix F2 Figure summarizes occlusion results across 112 datasets from the UCR archive. Subfigure (a) presents the average AUROC under different perturbation ratios, where SHAPEX consistently achieves the highest scores and exhibits the most stable degrada- tion curve, indicating superior robustness. Subfigure (b) reports the frequency with which each method ranks first across all datasets and occlusion levels, further confirming the reliability of SHAPEX.
To our knowledge, this is the first PHTSE work to conduct explanation evaluation over the entire UCR archive, covering a wide range of real-world domains, sequence lengths, and class granularities. The results not only validate the strong generalization ability of SHAPEX but also demonstrate its unmatched consistency and reliability across diverse conditions.
5.3 Ablation Study
We conduct ablation studies on both real-world and synthetic datasets to assess the contributions of different components in SHAPEX. The results on the ECG dataset are shown in Table E. while additional results synthetic datasets are provided in Appendix E. As the trends are consistent, we focus our discus- sion on the ECG setting.
Shopabet kamed Shapek
Stapelomer
We first evaluate SHAPEX SF, a variant that replaces the pro- posed SDD module with ShapeFormer [6]] for shapelet learn- ing, while keeping the downstream explanation pipeline un- changed. Despite ShapeFormer's ability to model local pat- terns, this variant performs worse in saliency evaluation, high- lighting that shapelets must be learned in explanation-aware manner to be effective for post-hoc interpretation. Next, we ab- late key components of the SDD module. Specifically, remove the loss functions that guide morphological learningthe matching loss and the diversity lossas well as the shapelet encoder. w/o LINEAR replaces the linear perturbation with zero-mask perturbation, and w/o SEGMENT directly uses the shapelet activation map as the saliency score without segment-based aggregation.
Figure 7: Visualization of learned shapelets in ECG dataset.
From the results, observe that the loss components have the most significant impact model performance, confirming that the learned shapelets must be well-aligned with the input, temporally smooth, and morphologically diverse. Furthermore, the sharp drop in AUR for w/o SEGMENT validates the necessity of segment-level aggregation for capturing complete key subsequences.
To assess the impact of shapelet-driven segmentation, we perform ablation study involving oc- clusion experiments on two real-world datasets. Specifically, we replace the SDSL perturbation in SHAPEX with equally spaced segments of length N, denoted as F_ N. The results are shown in

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Figure E SHAPEX significantly outperforms other variants. These results indicate that the effective- ness of SHAPEX is fundamentally dependent on SDSL perturbation.
5.4 Shapelet Visualization and Case Study
Visualization. ShapeFormer [6] is leading shapelet learning method. We visualize and compare the shapelets generated by ShapeFormer and SHAPEX, as shown in Figure M In accordance with the initial configuration of ShapeFormer, we choose the shapelets it generates that have the highest PSD scores within the dataset. The results show that ShapeFormers shapelets primarily match sub- sequences within the time series, while SHAPEX learns shapelets critical for classification. Specif- ically, SHAPEX's shapelets align with saliency labels, emphasizing their relevance to classification. This indicates that only SHAPEX's shapelets effectively support downstream explanations.
Case Study. Additionally, case studies on three real-world datasets (Appendix ( further vali- date SHAPEXs causal fidelity and interpretive precision. In each case, SHAPEX produces saliency distributions that align closely with the ground-truth causal regions verified by domain knowledge or prior annotations. For example, on the PhalangesOuttineSCoree dataset, the model accurately high- lights the transitional growth plate region that determines bone maturity, while other baselines yield dispersed and noisy saliency maps without semantic correspondence. Similarly, for the FaceAll dataset, SHAPEX concentrates attention around facial boundaries and expression-related areaskey morphological cues for class discrimination, demonstrating its ability to capture meaningful shape transitions rather than texture noise. Finally, in motion-related datasets such as UWaveGestureLi braryAll [.] SHAPEX highlights subsequences with decreasing acceleration, which correspond to the transitional phases of gestures such as sharp turns or circular motions. Overall, SHAPEX identifies truly causal segments, while other methods focus on random or uninformative regions.
Conclusion
SHAPEX introduces an innovative shapelet-driven approach for explaining time series classification. By leveraging the SDD framework, SHAPEX effectively learns representative and diverse shapelets, integrating Shapley value to assess their contribution to classification outcomes. Experimental re- sults demonstrate that SHAPEX not only enhances precision in identifying key subsequences but also provides explanations with stronger causal fidelity. Its effectiveness across synthetic and real- world datasets highlights its potential for improving interpretability in critical applications such as healthcare and finance.
However, several limitations remain. The framework involves few user-defined hyperparametters. such as the number and length of shapelets and the threshold that determines their selection. These parameters control the granularity and diversity of extracted shapelets, which in turn influence both interpretability and quantitative performance. While they offer flexibility across tasks, they may also require datasct- tuning and manual calibration to achieve optimal results, limiting the methods plug-and-play usability unseen domains.
Meanwhile, SHAPPX relies on separate training phase learn shapelets and optimize the SDD module, which introduces additional computational overhead compared to purely mruieent-based methods. This two-stage design ensures interpretability and robustness but sacrifices some efficiency and adaptability. Future work could address these limitations through automated hyperparameter selection, lightweight or joint-training strategies, and generalized formulations for multivariate and irregular time series.
Acknowledgments
Pan was partially funded by Australian Research Council (ARC) under grants FT210100097 and DP240101547 and the CSIRO National Science Foundation (US) AI Research Collaboration Pro- gram. This work was also partially supported by the NVIDIA Academic Grant Higher Education and the NVIDIA Developer Program.
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: SHAPEX is a post-hoc explanation framework for time series classification that segments inputs by learned shapelets and attributes importance using Shapley val- ues, consistently outperforming existing methods across extensive synthetic and real-world benchmarks in both precision and causal fidelity.
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A Supplementary Background: Perturbation Paradigms and Shapelets
A.1 Perturbation-based Explanation Methods
Perturbation- ciauubbatioo-bsedd methods derive the saliency of input features by analyzing how perturbations to those features affect the models output. Let P(X, MM) represent perturbation function that modifies the input X using a mask M = [M,, M2, Mr], where Mr E [0, 1]. The perturbed X is defined as:
x = P(X,, M,) M2 X, + (1 M,) Bi,
(14)
where B₁ denotes a baseline value (e.g., zero, mean, or noise). A general formulation of perturbation- based explanation methods to evaluate saliency is given by:
R x EM ( - [(P(X
(15)
where je is the distribution of the perturbation mask, and G(-) represents some transformation func- tion. Two primary subclasses can be utilized to instantiate this method: the Optimized Mask and Fixed Mask methods.
A.1.1 Two Primary Subclasses of Perturbation- Explanation Methods
Optimized Mask Perturbation Methods. In these methods, mask M is treated learnable parameter. The optimal mask M is obtained by solving an optimization problem [D, A M and the optimized mask M directly represents the saliency score, with Rg M,.
wherein M is a predefined, fixed mask (e.g., masking one time step segment). The saliency score R is defined as:
Fixed Mask Perturbation Methods.
( [lx(x) ((P(X.M))]]
R = EM-
(16)
where M is the distribution of the mask M, and the change in the models output.
denotes norm, typically L1 or L2, measure
Within this field, the Shapley value is frequently employed to determine the marginal contribution of each unmasked element (as a player in Shapley value) model's behavior, which can then be converted to the saliency score. This branch primarily focuses on Perturbing equal-length segments [22 43 Refer to Appendix AA.2 for additional information on using equal-length perturbed segments to compute Shapley value.
A.2 Applying Shapley Value to Fixed Mask Perturbation
Shapley value [|ت]]] offers a principled approach to measure the importance of each segment by averaging their marginal contributions across all possible subsets of segment indices. In fixed mask perturbation methods, segments of the time series are treated as participants, and the Shapley value is computed using the model's 's output as the value function. The saliency scores derived from Shapley value provide interpretable and consistent importance measures for segments or individual time steps within the time series.
Under the fixed mask perturbation framework, suppose the time series X {XI...... X7} is equally divided into segments E Es.... E,.,,,,,,, }. Each segment Eg acts as a "participant" that can either be retained (unmasked) masked with a baseline value. Define the mask M E {0, 13", where Mj = 1 indicates that segment E, is retained, and M; 0 indicates it is masked. For a subset of segment indices S N, the value function is defined as:
u(u)=
(17)
where M, is a mask that retains segments with indices in u and masks all other segments.
The Shapley value d; for each segment E, is then computed as:
Juit (n
u0 1)!
Φ = Σ
(X,
(18)
m!
(C
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This equation captures the average marginal contribution of segment E; across all possible subsets segment indices that do not include The resulting o, serves as the saliency score for segment Fg To obtain saliency scores for individual time steps I, distribute the segment-level Shapley value uniformly across the time steps within each segment:
Ad E,
R₂
for t. E Eg-
(19)
As the general form of fixed mask perturbation methods is given by:
R2 = EM-M - (P(X,
where M is the distribution over masks. By leveraging the Shapley value, the distribution M can be interpreted considering all possible subsets of segment indices with equal probability. Thus, the Shapley value-based saliency scores Φ; provide a theoretically grounded method to estimate the importance of each segment in the fixed mask perturbation framework.
A.3 Timestep-level and Segment-level Perturbation
based on whether the mask was fixed. From another perspective, we classify them by the minimal element in the perturbation mask: timestep-level and segment-level, indicating whether the mask is applied to individual timesteps segments. All the optimized mask methods are timestep-level, while most fixed mask methods are segment-level.
Previously, we categorized perturbation-base explanation methods [L. C. 12 3
However, timestep-level perturbation directly disrupts the local dynamic dependencies, while equal length segment-level perturbation may disrupt the integrity of critical subsequences by splitting them across adjacent segments or combining unrelated subsequences into single segment, refer to Figure This can lead to fragmentation meaningful patterns and generation of spurious segments, yielding suboptimal explanations.
B Additional Related Works and Discussion
Explainable Artificial Intelligence. Explainable Artificial Intelligence (XAI) aims to make AI systems' decisions understandable and auditable [A5]]. The growing complexity of deep learning models necessitates XAI methods to address safety, fairness, and accountability concerns. XAI is generally categorized into in-hoc and post-hoe explainability methods.
In-hoc explainability methods are inherently interpretable by design. In the field of computer vi- sion, in-hoe methods include such interpretable representation learning [+ 97 and model ar- chitectures with intrinsic interpretability [[N]]. Mcan while, transparent generative models, such as interpretable Generative Adversarial Networks (GANs), are also used to provide visual explanations for image generation processes [49]] In natural language processing, in-hoc methods leverage inter- pretable attention mechanisms to reveal the relationship between input text and output predictions [50]] For tabular data, in-hoc methods often rely on comprehensible models like decision trees or linear models [[]]].
Post-hoe explainability methods provide explanations for complex models after training, making them applicable to various data modalities. Among these, Shapley value, derived from game theory, widely used in XAI to quantify the contribution each feature to model predictions [224]. The ad-
vantage of Shapley value lies in its adherence to principles of fairness, equitability, and consistency. Methods based on Shapley value, such as SHAP (SHapley Additive cxPlanations), approximate Shapley value to offer both global and local explanations for complex models [[2]. In computer vision, SHAP identifies the pixels or regions in an image that have the greatest influence on classifi- cation outcomes, helping understand the key areas the model focuses on [533]. In natural language processing, Shapley value are used to evaluate the contribution of each word to text classification or generation tasks, revealing the basis for the model's 's decisions [[4]].
Besides Shapley value, post-hoe methods include techniques such as LIME [55], Grad-CAM [[66], Layer-wise Relevance Propagation (LRP) [57], and Integrated Gradients | These methods pro-
23

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vide fine- -hneigraindd explanations without altering the original model structure, aiding in the understand- ing of feature extraction and decision- becision-making processes.
Through these methods, the application of XAI across various data modalities not only enhances the trust in Al systems, laying
transparency and interpretability of models but also strengthens solid foundation for their deployment and adoption in real-world applications.
Time Series Explainability. Explainability methods for time series models are broadly categorized into in-hoc and ad-hoc approaches. Early survey and benchmarking studies have established the foundation of this field. Theissler al. [68] provided comprehensive taxonomy of explainable Al for time series classification, grouping methods into time-point- subsequence- and instance-based explanations, while Ismail et al. [TS)] systematically benchmarked saliency-basee baaeed interpretability techniques, revealing their limitations in capturing temporal importance.
In-hoc methods embed interpretabilitty directly into the model, typically via transparent represen- tations such as Shapelets or self-explaining architectures. For instance, TIMEVIEW adopts a top- down transparency framework to understand both high-level trends and low-level properties, leverag- ing static features and visualization tools for interpretability [T6]), while VQShape introduces a novel representation learning approach based vector quantization, enabling shapelet-based interpretable classification [ل Spinnato et al. [59]] further advanced this direction by developing a subsequence- based explainer capable of generating saliency, instance-level, and rule-based explanations for any Black-box time series classifier.
Ad-hoc methods are typically divided into two main categories. Gradient-Bass Baaded Methods are mainly derived from IG [[8]] For instance, SGT+GRAD refines gradient-based saliency maps by iteratively masking noisy gradient features to improve interpretability [T Perturbation- -ased Methods de-
rive the saliency by observing the effect of perturbation. Tonekaboni et al. [60] proposed FIT, a framework quantifying instance-wise feature importance via KL-divergence to identify when and where a models decision changes over time, Dynamask creates dynamic perturbation masks to yield feature importance scores specific each instance [ CoRTX enhances real-time model explana- tions using contrastive learning to reduce reliance on labeled explanation data [20]]. WinIT improves perturbation- based explainability by explicitly accounting for temporal dependence and varying fea- ture importance over time [23]. TIMEX learns an interpretable surrogate model that maintains con- sistency with a pretrained models behavior ensure faithfulness [3] TIMEX+ builds the infor- mation bottleneck principle to generate label-preserving explanations while mitigating distributional
shifts [+]]
The principal distinction between these methods lies in their interpretability strategies: in-hoc ap- proaches seek intrinsic transparency of the model itself, whereas ad-hoc strategies aim to provide explanations for the behaviors of the model, with perturbation bbased techniques currently prevailing in the domain.
C Shapelet Econder
The shapelets S used in descriptor and detector are not fixed but learned jointly with the model. To ensure their internal consistency and expressive capacity, we introduce a dedicated encoder that models their temporal structure. Each shapelet is segmented into local patches, which are embedded with positional encoding as in [61]]. A multi-head self-attention mechanism is then applied to model temporal dependencies across patches, promoting smoothness and internal consistency in shapelet representations. This encoder helps shapelets act as both expressive and stable morphological proto- types.
We first divide the input shapelet sequence 8m E RR into several equal-length patches, where each patch captures continuous segment of temporal features and is mapped into representation y through a linear transformation combined with positional encoding. Specifically, the representation of each patch given by
P: = Linear(s:) + PE(i),
(20)
where Linear(-) denotes the linear mapping operation and PF( the positional encoding that preserves the position information of the patch. Next, we apply a multi-head attention module to
24

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perform information exchange and fusion among all patch representations. For the set of patch representations P...... PN obtained after the linear transformation, the attention computed using the following formula:
QK" Vae
Attention(Q,A K, V) softmax
V,
(21)
where Q, K, and V are the query, key, and value matrices, respectively, obtained through linear pro- jections of Ps. The multi-head attention mechanism utilizes multiple sets of these linear projections to capture different feature patterns in parallel, which can be expressed as
MultiHeadd(,,K, w [heady; head2; ... heada],
(22)
with each individual attention head computed as
head, Attention(QW, KW., vw.),
(23)
where index i refers to different attention heads. This design enables the Shapelet Encoder to not only preserve the fine-grained information of local patches but also to integrate global temporal dependencies through multi-head attention, thus aiding in the learning of more precise and stable shapelets.
D Theoretical Justification for Approximate Causal Attribution
D.I Theoretical Analysis
In this section, we provide theoretical justification for interpreting the Shapley value computed by SHAPEX as an approximation of the model-level CATE. We begin by introducing the necessary notation. Let
{0, 1} indicate whether a segment indexed by n is retained (z or masked (z = 0). and let g' C {n} denote a coalition of other retained segments, where G = {I..... N} the index set of all shapelet-aligned segments in the input.
We define the potential model outcomes under each intervention as follows:
- = ((Xoum)),, = ((
(24)
(25)
where (11 G') represents the models output when segment n is retained alongside the coalition g', and YO,, G') represents the output when segment masked, with only g' retained.
To establish the causal interpretability of SHAPEX at the model level, we reinterpret classical identi-
fication assumptions from causal inference in the space of model inputs [60, BT. 62). Specifically:
Consistency & SUTVA: Each shapelet-aligned segment is perturbed independently. and the effect of given segment does not depend the perturbation status of others. That is, the potential model output under a given intervention depends only on the subset of included segments, consistent with the SUTVA.
Ignorability: Given a subset of retained segments G', the assignment variable = E {0,1), 1}. representing whether segment n is retained (z = 1) or masked (2 0), is independent of the potential model outcomes. This holds because is controlled deterministically through our synthetic perturbation policy.
For any G', both interventions 0 and 1 occur with non-zero probability, ensured by our random sampling over subsets.
Positivity:
Under these assumptions, the model-level CATE model is identifiable.
We now proceed to prove Proposition 1, which establishes the equivalence between the Shapley value computed by SHAPEX and the model-level CATE.
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Proposition 1 (Shapley Value Model-Level CATE). Let f(X) denote the models prediction for input X, and let (S.)) denote the segment aligned with shapelet n G. where 9 = [l.....N. is the index set of all segments. Then, under the intervention defined by retaining or masking segment (S)), the Shapley value on computed as
On E (f(Xou(m))
(26)
is equivalent to the model-level CATE T r-moded, conditioned on context G' C {m).
Proof. Given the validity of the three identification assumptions, the model-level CATE Tinddd identifiable. Its definition is given by:
model is
model In
Egg (Y(1g9)) Y(0,
(27)
Substituting the definitions of Y (1, g") and (") obtain:
model
Egg [f(X)u(m) ((Xg))] On
(28)
Thus, the Shapley value on is equivalent to the model-level CATE 7
modee
D.2 Practical Estimation via Coalition Averaging
Using the cyypoorally-elattion subset strategy, we estimate:
model
1 M
Σ [f(X).)um)) - f(Xgm)),
where each 9m S 9 {n} is sampled from segments temporally connected to n. This estimator is unbiased within the restricted coalition space, and reduces complexity from O([gl!) to O([g)).
Approximation Caveat. When only subset of coalitions used, the estimated CATE converges to conditional average over a restricted support. We refer to this as a shapelet-local CATE, ac- knowledging that this is an approximation of the full-coalition effect.
Table 4: Overview of Datasets
Calearey
Dutaact Name
Classes
Testing Samples
Training Sample
Leugt of Scries
Description
True Sationcy Soore
UCR Arduve (128 dassen))
vadles
varies
vañes
vaies
Benchnaak stite diesse tiee series tacks
No
BCG
Bonadial signds with expent ovaotation
Yes
MDC-B
2,000
10,001
5(0
Skopulnt chactictton equal amplinate
Yoe
Systhzis
MTC-E
MC3-41
3/000
2,000
180401
10/001
$00
500
Stapelo count fir doeiiicatinn higher amppinads
Shupple type claariiation, apual amplttace
Yec
Yec
MTC-H
10.000
Stapelt type for elssiitttioo hights ampilitude
E Experimental Details
E.1 Dataset Details
Following the experimental setup of previous PHTSE methods [3] H] we evaluate the explanation model using both synthetic and real-world datasets. The statistical details of the datasets are pre- sented in Table
Synthetic Datasets. Previous PHTTS methods [RL [] have used synthetic dataset generation ap- proaches such as SeqComb and FreqShapes, that derive from the data generation method in [63]. However Geirhos et al. [b3] generates datasets by injecting highly salient features as shortcuts into the original data to test whether deep neural networks rely on them for classification. Accordingly, methods like FreqShapes inject time series segments with significantly higher amplitudes than the mean serve as class- discríminative features. Therefore, this approach more similar to synthetic data generation methods in time series anomaly detection, which primarily evaluate whether an explanation model can highlight timesteps with extreme amplitude variations. real-world time se- ries classification tasks, class-disciiminative features are often defined by specific temporal patterns rather than simple amplitude differences. For example, ECG data [8]] the dass-discriminatiee fea- tures P-waves and T-waves do not necessarily exhibit higher amplitudes than surrounding regions.
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Based on this observation, we propose new approach for synthetic data generation for the PHTSE problem. Inspired by the time series motif insertion methods in [3Z]], we generate four different motif-based binary classification datasets: Motif Count Classification Equal (MCC-E), Motif Type Classification Large (MTC-L), Motif Count Classification Large (MCC-L), and Motif Type Classification Equal (MTC-E). Here, "type" and "count" refer to datasets where classifi- cation is determined by either the type of inserted motif's or their count, respectively. The terms "Equal" and "Large" indicate whether the inserted motif has the same amplitude the baseline waveform or significantly exceeds it.
These dataset synthetic methods better align with the mechanisms of the generation real data, allow- ing us to better assess whether an explanation method can effectively identify time series patterns that are crucial for classification.
Real-world Datasets. To further evaluate the explanation methods, we conduct experiments on several real-world time series datasets across diverse domains. ECG [38] is a physiological dataset used for binary classification of atrial fibrillation (AF), where each instance corresponds to a raw ECG segment annotated by clinical experts. UCR Archive [39] is a large-scale benchmark suite containing time series from a wide range of application domains such as image outlines, motion sen- sors, and astronomical observations. Since most datasets in the archive do not provide ground-truth saliency labels, they are primarily used our occlusion based evaluation. Additionally, datasets with variable-length sequences are excluded for consistency. We select 114 fixed- datasets from the archive that span wide spectrum of domains and difficulty levels. To the best of our knowledge, this is the first work in Post Hoc Time Series Explanation (PHTSE) that performs such comprehensive and diverse evaluation on the UCR archive.
E.2 Benchmarks
We evaluate explanation methods using multiple benchmark approaches designed for interpreting deep learning models on time series data.
Perturbation-based methods: TimeX++ + applies an information bottleneck principle to gen- erate label-preserving, in-distribution explanations by perturbing the input while addressing trivial solutions and distributional shift issues. TimeX [3]] trains an interpretable surrogate model to mimic a pretrained classifier while preserving latent space relations, ensuring faithful and structured expla- nations. Dynamask [2] generates dynamic perturbation masks to produce instance-wiss importance scores while maintaining temporal dependencies. WinIT [2 captures feature importance over time by explicitly modeling temporal dependencies and summarizing importance over past time windows.
Gradient-based methods: Integrated Gradients (IG) [18] computes feature attributions by in- tegrating gradients along path from a baseline input to the actual input, ensuring sensitivity and implementation invariance. SGT GRAD [T_]]] enhances saliency-based explanations by reduc- ing noisy gradients through iterative feature masking while preserving model performance. MIL- LET [50]] enables inherent interpretability for time series classifiers by leveraging Multiple Instance Learning (MIL) to produce high-quality, sparse explanations without sacrificing performance.
Metrics: We follow the evaluation metries from [3], adopting AUP (Area Under Perturbation Curve), AUR (Area Under Recall), and AUPRC (Area Under Precision-Recall Curve) in the saliency evaluation experiment to assess the discrepancy between the generated saliency scores and the ground truth. A metric value closer to 1 indicates higher accuracy. In the occlusion experiment, we use the prediction AUROC (Area Under the Receiver Operating Characteristic Curve) of the black- box classifier as the evaluation metric, measuring the impact of removing important subsequences on classification performance.
E.3 Experimental Settings
All experiments were conducted on a machine equipped with an NVIDIA RTX 4090 GPU and 24 GB of RAM. The black-box classifiers used in our evaluation (e.g.. Transformer, CNN) are trained independently using standard cross-entropy loss until convergence, with early stopping based on validation accuracy. Unless otherwise specified, default training settings from each baselines original implementation are followed.
27

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Table 5: Saliency score evaluation synthetic datasets (CNN the black-box model).
MCC-B
MCC-H AUP
METHOD
AUPRC
ALP
AUR
AUPRC
AUR
0.3394:10. 0045
0.3966:1.00000
0.0000
0.4689 1.0. 0024 0.0004
0.4097
0.4896.10.000
0.4960
DYNAMASK
0,3488=20.008
0.2277+:00004 000447
0.1008++0.002 00.2
0.4017=0.0073
0.2633=00.00
0.0510:+0.0012
WINIT
0.1513+0 0028
0.0625+0.000 0010
0.46364+0 0074
0.1659=0.0033
0.0628:20. 001
0,4481 1200 9063
TIMEX
0.2608-000000 0029
0.25711:0
00.32
0.5505-400.005
0.3107=0.003
0.3147=0.000
0.4493::00000
TIMEX++
0.3179.10.000
0..055
0..960000.0023
0.4900.10.
SHAPEX
0.6197=:000037
0.5157=10.0078
0.2775
0.8100=0.0014
0.6144:1.0045
0.7041=0.0005
MTC-E
MTC-H
AUPRC
AUP
AUPRC
AUR
0,3427:40.000
0.7233+00000
0.2616::0.00P
0.2531=0.0022
0.6482:#0.00 0066
0.3664::0. 0065
DYNAMASK
0.2869:00 0016
0,5252400 0026
0.0857::0.000 0014
0,3300=0.003
0.6177:00.000 0068
0.0798:20. 0011
WINIT
0,1511=:0.003
0.0632+:0.000 000118
0.4522:+00008 0068
0.0021=0.0021
0,0614=0.0008
0.4790:+0.000 0066
TIMEX
0.1413++0 0015
0.1197=0.000 0012
0.57874:0 0022
0.2315=0.0033
0.2293=00. 0040
0.5184400 9027
TIMEX+
0.1157:40:000 0009
0.08774:0.. 0008
0.4845:200008.
0.1174=0.0010
D. 0.11166:0.000
0.5456:10.000 0026
0.6954110.002
0.508410.0051
0.66631.0.066
0.6793_.0.0014
0.8933-10.0045
To ensure robustness and account for variability in training and explanation outputs, we repeat each experiment across five random seeds, reporting the mean and standard deviation as error bars. The random seeds affect both model initialization and data shuffling. For methods involving sampling- based perturbation (e.g., TIMEX++), the same set of seeds is applied to ensure fair comparison.
All models and explanation methods are implemented in Py Torch, and our codebase supports effi- cient parallel evaluation across datasets and seeds.
For dataset splits, we follow the standard training/test partitions provided in each dataset. A valida- tion set comprising 20% % of the training set is held out tune hyperparameters and perform early stopping.
F
Additional Experiments
F.1 Saliency Experiments
To further examine the impact of black-box models on explainability, we conducted saliency evalu- ation experiments on both synthetic and real-world datasets using LSTM [A4], CNN [35]] and Multi- Rocket [36] as classifiers. The results are presented in Tables EL & K. EL and A
We observe that other baseline methods whereas SHAPEX consistently achieves the best performance with remarkable stability. This in- dicates that SHAPEX provides highly robust explanations, benefiting from its ability to preserve true causal relationships.
significantly affected by changes in the classifier,
Table 6: Saliency score evaluation on ECG dataset (CNN as the black-box model).
BCG
METHOD
AUPRC
ALP
AUR
0.49492:00011
0,5374-1:
0.53066::..0m D010
0.459820.00
0.72162:0 0027
0.131450
WISIT
0.3963+0.001
0.3292=0.0m
0.351x=0
TIMEX
0.640110 0010
0.7458::0.00
0.418111: 0008
TIMEX++
0.6726:10.0010
0.7570::0.0011
0.43192000011
SHAPEX
0.7198 1:000229
0.8321 10.0051
0.6948 1:0.0032
Table 9: Saliency score evaluation on ECG dataset (LSTM as the black-bor model).
BCG
METRON
AUPRCC
ACP
AIR
0.5037=:0.001
0.612910.0126
0.4026+-0.000
DYNAMASK
0.3730L1.0.00 0012
0.5299 0.0000
0.1102.10 0007
WINIT
0 0.5628+00000 0013
0.3805 0002
0.4055 8009
TIMEX
O 0.60571:0000 0018
0.54162:0000 0024
0.44362-0000 0017
TIMEX++
0.651220.0011
0.74321-0.0011
0.44512-.0008
SHAPEX
10.0028
10.0032
28

---

Table 7: Saliency score evaluation on synthetic datasets (MultiRocket as the black-box model).
MCC-E ALIP
MCC-H
METHOO
AUPRC
AUPRC
0.2871
0.4013:40..013
0.3415=10.00$6
0.3091::0.0048
0.4215-0.0038
0.52144::
DYNAMASK
0.4141 0004
0.4726-20 0058
0.4142:10.0011
0.4150:20.00
0. 0.157200.005
0.2113220 I013
WINIT
0.1974
0.2411+000112
0.3250=0.0055
0.1528=20.0024
0.0925=0.0075
0.5101 0078
CORTX
0.3109:000007
0.4762:400.011
0.4317=000019
0.5031
0.5107=0.0011
0
MILLET
0.2358::0.0026
0.2513:2000071
D.2147:2 0.0866
0:3147:40.000
0.251110.0061
0.31255: 0061
TIMEX
0.403240.0000
0.3140:1.000822
0.6490 0.0044
0.4513:40.0077
0.6712-0.0051
0.3500 0.0092
TIMEX++
0.3509:000000
0.4851:4:0000 0066
D.2631::00000
0.6351400.0051
0.6524=00000
0,5120+:0 0023
SHAPEX SF
0.2715=0.0072
0.2231:1-0.003
0.2690=0.00
0.0001
0.2016=00000 00004
0.7135
SHAPEX
0.0025
0.0009310.0023
0.351 00000033
0.8245
0.694400.0070
0.7714
MTC-E
MTC-H
METHOD
AUPRC
AUP
AUR
AUPRC
AUP
AUR
IG
0.2081=0.0023
0.1125+:0.0070
0.5721=100034
0.3152:40.0051
0.3513 #0.0034
0.4742:::0 0075
DYNAMASK
0.1409:0.0003
0.1266--:0.0056
0.2519:10.008
0,2760:1:0.004
0.3937=0000076
0.2175:::0 0044
WINIT
0.1539:0.000 0076
0.1072:4:0000 00023
0.0417:0.000 00000
0.14344::0 0076
0:0821 0023
0.4728:1:0
CORIX
0.1841=0.0056
0.1851++0.0001
0.5152:20.000
0.2153:40.0023
0.2307=0.001 0.005
0 0016
MILLET
0.1846:00.0027
0.1252:::0.0009
0.1952 0.0024
0.2194::00000
0.2474=00000 0.0089
0,38 0.0032
0.2011
0.6249:1:00001
0.1250:10.00
0.2856:10.0008
0.3745=0.001
0
TIMEX++
0.2165:50.0022
0,4301 0.000097
0.2250 0.0022
0.3521:::00000
0. 0.3504=0.0057
0.1149 0.0055
SHAPEX NF SHAPEX
0.3840=0000022
0.1677:4:0.00 6021
D. 0.4699:2000001
D.38W0=500000 00041
0.4600=000041
0. 0 0082
0.6705:00.001
0.6558:10.0041
0.0008
0.6859:+0.0031
0.4262=0.0051
0,9122::0.0322
Table 8: Saliency score evaluation synthetic datasets (LSTM as the black-box model).
MCC-E AUP
MCC-I AUP
METHOD
AUPRC
AUR
AUPRC
AUR
0.4752:1:000 0.0878
0.5282:10.000
0.4622:1.0000 00.5
0.5144=0.0009
0.5297:10.009)
0.4965:10.0055
DYNAMASK
0,3999=200000
0.4925=:0.00m 0099
0.0369:t:00011
0.4178=0.0068
0.3239=000007 0.003
0.0103++0.000
WINIT
0,20374:00 0076
0.1897:+0001 0.060
0.3355+:0 0085
0.2013=0.0057
0.1573=40.015
0.3472-40. 0.111
TIMEX
12400:=0000220
0,2139:::000 0025
0.5495:10.0000
0.5013=0.0052
0.5492: 0.22200.0000 0065
0.3482:#0.000
TIMEX++
0.3766 0.001
0.3356+t:.000
0040
0.5242+-0.000
0.4799=0.0044
0.2395=00.
0.5224=0..000
SHAPEX
0.7422:10.00 0.029
0.7507:10.008
0.5703 0.009
0.8166:00.000
0.6893.10.000 0054
0.7701
MTC-E
MTC-H
AUPRC
ALP
AUPRC
AUP
AUR
IG DYNAMASK
0.2469:10.000
0,3512::0.00 20633
0.4862:10 0.44
0.4453=000029
0.3938 0030
0.3652:10.00223
0.1243:10.001
0.0803:10.0033
0.00851:0. 0.0000
0.2044=0.0016
0.2398.10.000
0.0283-10.0000
WINIT
0.1395=20.002
0.0953+:0.00 00953+90.0098
0.3785+t0.009
0.1560=0.0046
0.1457=0.015
0.2519=+0.008
TIMEX
0,20124:0 0022
0,1500:::0000 0012
0.6780+t:0 0022
0.1874=0.0072
0.1556:20.00 0016
0.5216400 0013
TIMEX
0.1314:1:0D000
0. 0.11255::0.00 0011
0.
0.5070:10.0001 0012
0.3169=0.0027
0.2076 0.0000
0.46:2-10.0011
SHAPEX
0.60281000055.
0.4472.10.0080
0.5616110.0066
0..005
0.3952-10.0024
0.8549.100 0.00056
F.2 Details of the Occlusion Experiment
To enable a fair and comprehensive evaluation across diverse datasets, we first preprocessed the UCR Archive by excluding datasets with variable-length sequences, their inconsistent input shapes incompatible with fixed-length perturbation settings. Additionally, both TIMEX and TIMEX++ suf- fered from gradient explosion during training on small subset of datasets. For fairesss, we removed these failed runs from comparison.
Nevertheless, the remaining collection still covers a highly diverse and representative set of over 100 datasets, making it by far the most comprehensive occlusion- based evaluation conducted in the literature of PHTSE. The aggregated results are illustrated in Figure &. B. IT0. and [
Given the inherent diversity of UCR class cardinalities, generating accurate saliency scores remains a challenging task. Consequently, no single explanation model dominates across all datasets. However, SHAPEX demonstrates superior robustness compared to baseline methods: its performance degrades more gracefully on challenging cases, as reflected in the smoother drop of AUROC scores across datasets. The statistical comparison, with Figure ((a) reporting mean performance and Figure b(b) highlighting the best-case results, reinforces the advantage of SHAPEXX as the most consistently robust and reliable method for PHTSE tasks to date.
covering various domains, sequence lengths, and
29

---

Table 10: Computation Time (in seconds) of Different Explanation Methods
METHOO
MCC-H
MTC-E
MTC-H
TiMeX++
13.7306
13.5581
49.7619
22.9600
53.4244
910.0483
DYNAMASK
837.2252
851.3321
840.9815
WINIT
167-9887
1853
166. 166.8685
166.5799
SHAPEX
129.0921
132,8452
127.1463
115.3492
Table 11: Ablation analysis on synthetic datasets.
MCC-E
MOC-H
Ablations
AUPRC
AUP
AUR
AUPRC
AUP
AUR
Full
0.5614=0.0016 0.6407:t000036
0.3679::00000
0.8113++0.0013
0.683420.0054
0.7431=0.0005
w/o matching loss
0.1455:t:0.0112
0.1622=0.057
0.1347:10.0012
0.2612:1-0.0035
0.1792::0.011
0.3849=10.0023
w/o diversity loss
0.1309:t:00002
0.0450=0.0061
0.1103::0.033)
0.2630=t.0.0332
0.1849::0.0012
0.3542:+0.0035
w/o shapelet encoder
0.0933=000032 0.2407:+000013
0.4099::000023
0.2366::000030
0.3274::0.0077
0.7113+:0.0023
w/o LINEAR
0.5926::000036
0.5281=000011
0.3352+:0.0021
0.7633+t0.0024
0.6551=0.000
0.7084+0.0037
w/o segment
0.6104+000033
0.5274=000090
0000066
0.7030+:0.0023
0.6312=#0.099 0.3051
MTC-E
MTC-H
Ablations
AUPRC
AUP
AUR
AUPRC
AUP
AUR
Full
0.6100::000048
0.3962=0.0067
0.5472:10.0083
0.6792:t0.0014
0.4255=000004
0.9019
w/o matching loss
0.1273::0.0052
0.1135=0.0057
0.1043::00005
0.2153+::00034
0.1305=0.0044
0.3347:+0.0012
wlo diversity loss
0.1524=0.0012 0.0073
0.1042+:00023
0.2094=:0.0054
0.1053=#00022
0.49141:0.003
w/o shapelet encoder
0.1027=000076 0.2358:t0.0057
0.0982++0.0023
0.00000
0.2781=0.0012
0.8120=:000033
w/o LINEAR
0.5627:4:0.000
0.3991=0.0033
0.518411.0005 0055
0.6204:100005
0.3683=10.0042
0.7711
wlo segment
0.5792:4-000070
0.3518=000045
0.5371+0.0020
0.6347::0.0045
0.4014=200060
0.8820++0.0034
G Further Analysis Experiments
G.1 Computational Cost Analysis
It is well known that computing Shapley value is highly time-consuming. making computational cost a critical consideration in Shapley value analysis. We measure the inference time required for explanation generation across several datasets, with results presented in Table I[[
While SHAPEX is not the fastest method, it is significantly more efficient than Dynamask. This acceptable computational cost is primarily attributed to SHAPEX's segment-level design and its temporally relational subset extraction strategy. Consequently, SHAPEX not only achieves superior performance but also maintains practical feasibility.
G.2 Parameter Analysis
We further analyze the impact of shapelet-related parameters on the performance of SHAPEX. Specif- ically, we examine the interplay between shapelet length (L) and the number of shapelets (N). Fig- ure I2] presents the results on the ECG dataset.
Overall, we observe that AUP decreases as the number of shapelets increases, indicating that only shapelets corresponding key features contribute to improved accuracy. In contrast, AUR exhibits an opposite trend, suggesting that larger number of shapelets facilitates the discovery of more latent features. Additionally, optimal performance is achieved when the shapelet length is appropriately chosen, highlighting the importance of selecting a balanced length.
G.3
Case Study
To qualitatively assess the interpretability of SHAPEX, we present case studies on three represen- tative UCR datasets with well-defined domain semantics: PhalangesOutlinesCooee FaceAll, and These datasets span the domains of medical imaging, biometric contours, and motion sensors, respectively. In each case, we compare SHAPEX against existing baselines by visualizing the generated saliency scores.
UWaveGestureLibraryy
Dataset. The PhalangsSOutinesCoreer dataset 64 is one- dimensional time series derived from X-rays of the third phalanx through contour-based processing. First, the bone contour is extracted from the original radiograph. Then, the Euclidean distance from
PhalangeSOuttinssCorees
30

---

each point on the contour to the bones center is computed. By radially sampling these distances in clockwise direction, a polar distance sequence is formed, which captures the morphological profile of the bone outline in ID space.
As illustrated in Figure T.. the sequence may contain components: the shaft and the epiph- ysis. If a growth plate is present, the sequence includes a distinct transition region--bighlighted in greenbetween the bone shaft and the epiphysis. The dataset comprises two classes: Immature,, cor- responding to the early Tanner-Whitehone Whitchouse (TW) stages, and Mature, representing the later stages. In clinical practice, the key criterion for distinguishing between these two classes is the extent of epiphyseal development, particularly its fusion with the diaphysis. In the time series representation, the growth plate transition region typically corresponds the time interval between steps 40 and 60.
In Figure 14 we observe that, as the most advanced baselines, TIMEX and TIMEX ++ predominantly generate explanations focused the peaks valleys of the sequence. However, these features not the primary indicators of bone maturity. In contrast, SHAPEX highlights the sequence region between the 40th and 60th time steps. which critical for reflecting the developmental status of the epiphysis. This indicates that SHIPPX effectively identifies segments within the sequence that are medically significant, distinguishing it significantly from other baselines that focus on prominent values in the sequence.
The FaceAll dataset [39] sourced from the UCR archive. It consists of head contours collected from 14 graduate students, converted into one-dimensional time series through series of image processing algorithms. The first half of the sequence corresponds to the facial contour of the human head, while the second half corresponds to the contour of the hair. This dataset includes 14 classes, each representing one of the 14 graduate students. Due to the high variability in human hair shapes, the classification results are primarily determined by the facial contour portion of the time series.
FaceAll Dataset.
In the visualization of model predictions, as shown in Figure IS. we observe that only SHAPEX effectively highlights the facial contour regions, whereas other models merely focus a few peaks and fail to provide meaningful insights.
UWaveGestuueLiibaryyal Dataset. The UWaveGestureLibrrryAll dataset |||| generates se- quences by recording acceleration signals during user gestures, encompassing eight predefined ges- tures. Compared to the phases of increasing acceleration, the phases where acceleration begins to decrease often carry more gesture-specific information. This is because decreasing acceleration indicates the beginnings of gesture transitions, such as sharp turns circular motions.
In Figure II, we observe that SHIAPXX distinctly focuses on regions with negative slopes in the se- quence, which correspond to the phases where gestures begin to change. This demonstrates that our method can effectively identify sub- sequeeeses that are more valuable for sequence classification.
31

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random
timex
timex++
shapex
dyna
ACSF1
ADIAC
ARROWHEAD
DEEF
3.08
3.90
8.50
0.30
2.3
2-02
6.7
0.70
0.0
0.93
130
0.30
030
0.5
576
335
336
34
0.55
613 6.8
S
520
E33
6.5 9.85
0.33
0.30
Perture
BEETLEFLY
BIRDCHICKEN
BME
CAR
3.66
2.00
2.00
1.00
3.50
0.97
0.30
0.00
0.93
2.02
0.30
6.40
0.03
030 Paturbed
Prozottin Tutureed
Prozestion Pestur
Pariibedd
CHINATOWN
CHIORNECONCENTTATTONN
CINCECCTORE
110
1.01
ANNOC
038
Prozottin Fertuied
Prspertio Perturbez COMPUTERS
Proseition Ferturted
Preporiinn Persittes
COFFEE
CRICKETX
648
320
6.4
0.15
844
0.38
Prozertin Fertured
Propertin Perturbes
Prosortion Perturbed
Propartinn Perturbed
CRICKETZ
CROP
DIATOMSIZREDDCTTION
DETTAPPHHLANKKTTLEENNGGGGO
0.00
0.89
0.0
0.5
0.52
0.5
0:4
576
2.3
235
243
8.91
0:90
0.51
013
033
5.0
040
220
631
4.8
355
6:3
340
Prpprton
110 ANSTAUTAALNNOOUUTI INEEORRECT
DISTAL DISTALPHALANXTM
EARTHQUAKES
ECG200
2.00
2.00
1.00
8.58
5.5
1.10
6.0
0.0
2.62
630
637
035
0.3
648
576
3.5
310
281
0:2
811
0.0
2.2
231
0.31
ECG5080
ECGRIVEDAYS
ELECTRICDEVICES
EOGHORIZONTA.SEE SIGNAL
3.00
2.00
2.00
1.00
6.5
6.30
2.00
0.00
122
0.87
MUNOC
0.0 Plpprtion NaTuubed
Propettinn Futureed
Prozettion Potur
Figure 8: Occlusion experimental results UCR archive.
32

---

random
timex
timex+
shapex
dyna
SOGVERTICALSICNLL
ETHANOLLEVEL
FACEALL
FACEFOUR
Prozertion Returted
Prsporton Pemiited
Preportion Petuuber
Fropertion Pertubbe
1.30
1.30
1.00
AUBOC
0.60
0.20
6.40
0.15
E20 Returted
0.56
0.35
6.30
0.35
0.6
6A5
Perturbe
FORDB
FREEZERREGULARTRAN
FREEZERSMALLTRAIN
FUNGI
3.50
1.00
6:90
0.90
0.55
2.0
0.40
0.80
AURIC::
420
0.78
0.8
0.6
8.90
0.50
0.5
0:40
030
0.55
820
6-4
044
3.0
0.5
6.30
045
6.0
0.48
0.00
0.25
0.38
6-45
8.30
0.5
0.50
Prozertio in Rettrted
Propertion Pertutted
Priportion Perturbec
Frozentinn Perturber
GUNPOINT
GUNPOINTAGESPAN
GUNPOONTOODDEERSUUYYUNG
AUROC
Prosertion Returted
Priporton Perturted
Preportion Pertubee
Frosertion Petuuree
0.22
0.20
0.78
0.50
0.38
6.50
0.38
6.40
0.50
3.15
5:0
016
6.15
5.40
0.35
550
545
6.56
INLINE SKATE
INSECTEPGREGULA ARTRAIN
INSECTERGSMALLTTAIN
INSECTWINGBEATSOUR
3.30
1.35
1.60
1.0
0.00
0.90
AUnOe
AUROC
6.40
0.00
0.60
4.00
6.20
0.28
0.50
650
0:50
0.50
0311
8.50
0.48
0.58
326
0.35
8.30
0.21
6.00
0.42
800
615
0.50
6.5
8.50
640
8.50
015
0.35
6-85
0.50
Prosortion Nettured
Propertio Parturbed bed
Troportion Parturbus
Frozerton Pertuibes
ITALYPOWEDDEMNND
LARGEKTICEEWPPLIINCES
LIGHTNING2
LIGHTNING7
Prazert on Returted
Proportion Ferturted
Treportion Pertu
Frozertion Perlutber
Figure 9: Occlusion experimental results UCR archive.
33

---

random
timex++
shapex
dyna
644
660
025
6.33
3.43
0.25
0.30
0.0
0.25
6.50
0.0
0.25
8:23
0.45
Troporiinn Perutbed
Placeracn bed
Thapordon
MIDDL EPHALANKTW
MOXDSSHAPESREUUUAATTUII
MIXEESSHWESSMALLTIRN
MOTESTRAIN
6.5
2.00
3.93
0.80
2.10
0.2
0..0
6.08
3.0
0.50
669
830
331
0.90
0.5
640
516
388
0133
031
6-40
000
VON HOGTAAKK
OSULEAF
1.30
3.00
0.99
Tropories Pertuteed
Disportio Pettiibed
Prpprtion Perturbed
Prsportion Perturted
0.0
3.5
6.48
670
0.5
0.30
320
0.5
0.30
030
0.35
6.56
000
0.55
Troporier Penurbed
Prsportin Partutad
Prsporiin Parsutted
Proportion Farturted
PLANE
POWERCONS
PROKIMAIPHAI ARXOUTII WEAAGGGRRBOOOOOOO PHAI ANXIUTII INFCORRECT
4.0
3.83
0.30
1.10
3.75
646
3.2
0.60
600
828
359
0.50
0.9
648
325
0.33
042
128
0:3
0.30
845
0.83
330
6.5
6.6
3.55
661
000
0.5
0.5
PROXIMAI PHAL ANXTW
DEFFIGERAATIONEEVIEE
ROCK
SCREENTYPE
3.68
2.00
1.30
3.00
835
3.5
0.90
0.00
2.92
3.73
Irporion Penutee
Pmsporion Peturtel
Plperricnn Pertiibed
Argprrton Perturted
SEMGHANDGENDERCH2
SEMGHANDMOVEMENTCHH
SEMGRANDSUBBECCCH2
SHAPELETSIM
6.48
646
235
0.30
3.4
340
0.5
0.3
330
0.55
630
0.9 033
Triporinn Peruuthe
3mpprtion Pwrtuihedd
Prstertin Pertiihed
Rreportonn Pettureed
Figure 10: Occlusion experimental results on UCR archive.
34

---

random
timex
timex+
shapex
dyna
SHAPESALL
SHAILIKITCHEEAPPLINCCE
SMOOTHSUBSPICE
CONYABBOROBOTSURACCCO
3.50
3.00
1.00
0:30
0.58
0.3
0.30
8.00
0.3
XLROC
8.00
0.8
0.20
41.5
6-R
6.45
6:3
Propotion Purtabed
Froscrton Peturbed
Prsportion Purturbed
Propot on Pattrred
SONVABBOROBOTSURRCCE
STARLIGHTCURVES
SWEDISHLEAF
Autoo
0.30
0.50
0.0
0.30
6.30
6.30
0155
6:6
0.66
6.15
0.35
6.30
644
Pertured
Prozortion Rerturbed
Parturbed
Propett
SYMBOLS
SYNTHEETICCONTALL
TOESEGMENTATION
OBESEGMENTATIONA
1.30
1.0
1.00
1.00
6:90
0.50
0.90
5.50
AUROC
AURDE
6.00
6.68
0.58
8.50
6.90
0:0
0.28
8:30
6:00
4.5
635
5.50
0.3
0:4
0:31
0.5
6.15
6.5
0.22
0.82
220
6.5
0.56
545
5:40
0:00
0.22
0:35
5.00
031
662
Propotien
Neturbed
Iisprrtion Partabed
Propotton Puttared
TRACE
TWOLEADECG
TWOPATTERNS
UMD
Prozo on Pertrited
Proscrtion Pertrred
Resportion Perturbed
Propor Penurr
IBRARYY
6.90
0.40
612
0.42
0.50
6:40
0.50
633
0.30
044
E60
0.4
6.30
0.5
636
6
0.58
0.42
500
6:15
0.31
6.45
1.30
0:80
0.8
0.35
5:30
045
WAFER
WINE
WORDSYNONYMS
WORMS
3.50
3.00
1.00
1:00
0.90
8.5
0.32
8:00
0.30
0.00
0.32
0.72
0.00
0.08
0.40
2.22
644
0.42
8:40
Prosotion Parturbed
Frossition Perlubed
Irsportion Purturbed
Proport on Paturrod ood
WORMSTWOCLASS
0.50
Perturted
Frasortion Perturbed
Figure 11: Occlusion experimental results on UCR archive.
35

---

Figure 12: Saliency score generated by SHAPEX concerning various shapelet lengths and quantities on ECG Dataset.
Growith Plate Transition Region
Contour Projection
Polar Distance Sequence
Figure 13: Radial sampling from the center (a) yields a polar distance sequence (b), where the green region highlights the growth plate transition region. [64
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Reviews:
[{"review_id": "HzL5K3NS6G", "reviewer": "Reviewer_vy4B", "summary": "This paper presents ShapeX, a post-hoc time series explanation framework which segments time series into meaningful subsequences denoted as shapelets and uses shapley values to determine their saliency. The framework uses a describe and detect method which learns shapelets meaningful for classification. The framework is compared against benchmarks on 4 synthetic and 100+ real datasets from the UCR archive.", "questions": "1. How to guarantee the validity or “truthfulness” of the shapelets generated by the ShapeX framework compared to the implicit shapelets used by the classification model? What if these are not the same – i.e., the black box classification model uses a different set of shapelets than those identified by the ShapeX framework?\n\n2. How to guarantee that the shapelets actually represent subsequences from the real raw input time series? It looks like the generated shapelets may not even correspond to the real underlying time series (as seen in Figure 7 where the 4 shapelets do not directly match subsequences of the input time series.)\n\n3. The experimental results seem to use an apples to oranges comparison where the saliency at each timestep was derived from multiple timesteps in ShapeX and prior methods only have information from a single timestep. Can the authors justify this comparison?", "limitations": "Although Section 6 Conclusion briefly acknowledges a limitation, it appears to be a rather superficial and self-evident one (use for univariate time series only). Given the complexity of the proposed framework, a more thorough and insightful analysis of the framework's limitations would strengthen the paper.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Overall, this paper highlights an important gap in current research for explainability methods in time series classification but has fundamental issues in the methodology and results.\n\nThe premise of the paper is interesting and important, namely that the impact of time series subsequences i.e., shapelets, are more significant for explaining classification models than individual timesteps. All prior work focuses on individual timestep explanations, with nothing focusing on providing explanations for trace subsequences or shapelets. This is a very important gap in current literature. Therefore, the development of a new framework to address this gap is highly original with the potential for high significance and impact. \n\nHowever, I believe there are fundamental issues with the methodology and experimental results. I have concerns about the shapelet describe and detect framework in which shapelets are self-identified and generated *independently* from the black-box classification model. This appears to be an issue because there could be a mismatch between the shapelets identified by the ShapeX framework, and those actually used by the classification model. For example, the transformation of time series used in classification models (e.g., the convolutional kernels used in MultiRocket) may be different from the transformation used in the descriptor component of ShapeX (e.g., the generated activation maps). There is no guarantee that the generated shapelets actually correspond to the underlying subsequences used in the classification model; it seems these two should be directly tied to each other. (See Question 1). I am further concerned because it appears that the generated shapelets may not even correspond to the real underlying time series for example as seen in Figure 7 where the 4 shapelets do not directly match subsequences of the input time series. (See Question 2).\n\nThe experimental results do not appear technically sound. It seems there is an unfair comparison between ShapeX, that computes explainability/saliency for a *set* of timesteps, and other prior methods which compute explainability/saliency for a *single* timestep. In ShapeX according to Equation 19, to obtain saliency scores for each individual time step, the segment level shapley value is uniformly disturbed across the time steps within each segment. This means the learned explainability value at each timestep is derived from information it learned from *more* than one timestep, when compared to prior methods that only have knowledge about a *single* timestep (e.g., like in Dynamask which builds a perturbation for each feature at each individual timestep). This seems to be an apples to oranges comparison, where ShapeX has an unfair advantage (i.e., the saliency was given extra context from timesteps before or after the current one) compared to prior methods that only have knowledge about a *single* timestep. A fairer comparison might also aggregate the values from the same trace subsequences in the benchmarks so they can be more directly compared. (See Question 3). Moreover, while it's commendable that the authors evaluated their approach on 100+ datasets from the UCR archive, I have concerns about the validity of reporting results averaged across all datasets. This approach overlooks the unique characteristics of each dataset and may obscure important nuances, especially when large averages mask dataset-specific performance differences. This is further supported by the very high error in the presented results (for example Figure 6(a) has very large error bars across all methods including ShapeX).\n\nThe paper also has issues with clarity. The paper is extremely dense and hard to parse as a result of many important technical descriptions related to the methodology and the experiments being in the appendix (including description of encoder in Appendix C, saliency score calculation in equation 19 in Appendix A.2, metric definitions in Appendix E, testing on multiple black-box models in Appendix F). The large number of nonstandard abbreviations used (e.g., SV, SDD, SDSL, PHTSE) contribute to the paper being hard to parse as well. It is unclear to me the point of Section 4 – it seems this would be better removed or placed in the appendix and instead this space used to further describe important technical methodology and experimental choices that are currently in the appendix. Some figures and tables are confusing: Table 1 and 2 are confusing and hard to read with all of the blue shading; it is unclear what the expected conclusion we should draw from Figure 6 (b) is.", "was_revised": true, "final_justification": "Given the authors detailed rebuttal, and taking into account the other reviews and comments, my main concerns surrounding issues with selecting shapelets in the methods, validity of the experiments, and structural organization of the paper have been alleviated. Therefore I raise my score to a 4.", "rebuttal": "Thank you for these thoughtful suggestions. We believe **many of the concerns raised stem from our suboptimal separation of content between the main text and appendix**. We are confident that **through better organization and clearer presentation, we can resolve the majority of these concerns** and significantly improve the accessibility and clarity of the paper.\n\n> **Q1: How to Ensure the Validity of ShapeX Explanations When Its Learned Shapelets May Differ from the Implicit Representations Used by the Black-Box Model**\n\nA1: We sincerely appreciate your insightful question, which touches on the core of ShapeX's design philosophy. We acknowledge that this question appears very reasonable and likely stems from a **misunderstanding caused by not defining the problem setting in the clearest and most rigorous terms**.\n\nFirst, from a problem formulation perspective, the task we address is well-defined: given a time series input and a trained black-box classifier, we aim to assign importance scores to input time series, where a higher score indicates greater influence on the model's decision. In this paradigm, **the shapelets identified by ShapeX are not assumed to coincide with the internal representations of the black-box model.** Instead, they are treated as **intermediate constructs** to facilitate effective segment-level attribution.\n\nTo be transparent, ShapeX can be interpreted as hypothesizing what model-relevant shapelets might be. If these learned shapelets align well with the truly discriminative patterns used by the model, the resulting saliency score is accurate. **However, even if the guessed shapelets do not precisely match the model’s internal logic, the final saliency score can still remain robust.** This robustness stems from the flexible structure of ShapeX: **the learned shapelets guide the preliminary segmentation**, while the **final saliency scores are computed from perturbation-based outcomes**, independently of whether the segmentation is perfectly aligned with the model's actual reasoning.\n\n\nTo validate this claim, we designed a controlled experiment using ShapeFormer as the black-box model to be explained. We then created a variant of ShapeX, denoted **ShapeX-S**, in which we replaced the learned shapelets in ShapeX with the exact shapelets used internally by ShapeFormer for segmentation.\nIn this setup, ShapeX-S uses the **exact same shapelets as the black-box model**, ensuring full alignment between the segmentation patterns and the model's internal logic.\nThe experimental results show that **ShapeX-S often performs worse than the original ShapeX**, which uses independently learned shapelets. This finding suggests that our method **does not require perfect alignment with the black-box model’s internal representations** to produce accurate and faithful explanations.\nWe believe this supports our core hypothesis: ShapeX explanations rely more on the perturbation-based attribution mechanism than on precise imitation of the model’s internal structure.\n\n| Model       | MCC-E         |             |             | ECG       |             |             |\n|-|-|-|-|-|-|-|\n|            | AUPRC          | AUP         | AUR         |AUPRC           | AUP         | AUR         |\n| ShapeX  | 0.6407±0.0031  |0.5614±0.0076  |  0.3679±0.0050 |   0.7228±0.0028    |   0.8395±0.0030   | 0.6961±0.0032 |\n| ShapeX-S| 0.5782±0.0056  |0.6027±0.0007  |  0.2513±0.0009 |   0.6525±0.0044    |   0.7435±0.0075   | 0.5730±0.0021 |\n\n\n---\n\n> **Q2: How to Ensure That the Learned Shapelets Correspond to Real Subsections of the Raw Input Time Series**\n\nA2: This is a very natural and reasonable concern, and we thank the reviewer for the opportunity to clarify this point. In early shapelet-based literature (e.g., [40]), shapelets were indeed defined as **actual subsequences** extracted directly from the raw input time series. However, more recent advances—including our work—adopt a **more flexible and generalized definition**, in which **shapelets are learned representations obtained through optimization or deep neural networks** [41,42]. We note that the reference numbers are consistent with those in the main submission.\n\nUnder this modern formulation, the shapelets produced by ShapeX are **not intended to exactly replicate raw input subsequences**. Instead, they are **abstract, representative patterns** that best capture discriminative structures across multiple input samples. These learned shapelets act as **pattern templates** rather than literal time series fragments.\n\nWe acknowledge that **the confusion may stem from the fact that we placed this foundational clarification in Appendix A.4**, which may have made it less accessible to readers. This was an oversight on our part. In the revised manuscript, we will move the definition and conceptual framing of shapelets to the main methodology section to prevent similar misunderstandings.\n\n---\n\n> **Q3: Justification for Comparing ShapeX’s Segment-Level Saliency with Prior Per-Timestep Methods**\n\nA3: This is a very insightful and important observation. It raises a fundamental question that is rarely addressed in the time series explainability literature: **What exactly is the task formulation, and what types of temporal dependencies are permissible in computing saliency?**\n\nOur problem setting follows the formulation used in prior works such as DynaMask, TimeX, and TimeX++, as described in Section 3.1. This task formulation is deliberately broad—it specifies the overall input-output behavior of the explainer, but **does not restrict whether the saliency score for a specific timestep must be based solely on that timestep or can incorporate surrounding context.**\n\nIn fact, **several baselines already utilize temporal dependencies.** For example:\n- **TimeX** employs a Transformer-based encoder-decoder that takes the entire sequence as input to generate binary attribution masks for each timestep. It also introduces smoothness constraints to enforce local continuity in saliency scores.\n- **TimeX++** similarly uses a Transformer encoder to model cross-timestep dependencies, with its Smoothness Regularization explicitly encouraging temporally coherent attributions.\n\nTherefore, we believe that ShapeX’s segment-level attribution mechanism remains consistent with the problem setting adopted in existing methods. If anything, your question highlights a broader challenge in the field—the **lack of standardized assumptions** about how attribution across time should be formulated.\nIn response, we **will add a dedicated paragraph in the Related Work section of our revised manuscript to clarify how different methods interpret and implement this task formulation.** We greatly appreciate you bringing this issue to our attention.\n\n---\n\n> **Q4: Request for a More Thorough and Insightful Analysis of ShapeX’s Limitations Beyond the Univariate Setting**\n\nA4: We agree that the current manuscript’s treatment of limitations—focused only on the univariate setting—is relatively superficial. A more thorough discussion will certainly strengthen the clarity and scope of the work.\n\nIn addition to the univariate constraint, ShapeX has the following key limitations:\n\n- **Predefined hyperparameters**: The framework requires several user-defined parameters, including the threshold $\\Omega$, the number of shapelets, and their lengths. These hyperparameters may affect performance and require tuning for different datasets.\n\n- **Training requirement**: Like TimeX and TimeX++, ShapeX involves a separate training stage to learn shapelets and optimize the SDD module. This reduces flexibility compared to gradient-based methods like Integrated Gradients, which compute saliency scores directly without training.\n\n\nWe will explicitly incorporate these points into Section 6 of the revised manuscript to provide a more balanced and transparent evaluation of our framework.\n\n---\n\n> **Q5: Concern About Averaging Results Across UCR Datasets and Large Variance Obscuring Dataset-Specific Differences**\n\nA5: Thank you for highlighting this important concern. We agree that averaging performance across 100+ UCR datasets may obscure meaningful dataset-specific behaviors.\n\nWe **have provided** detailed results for **each individual UCR dataset in Figures 8–11**. These plots show the per-dataset perturbation curves, allowing readers to examine how ShapeX and other methods perform under varying datasets on a case-by-case basis.\n\nWe will also revise the caption of Figure 6 in the main text to explicitly direct readers to the appendix, ensuring that those interested in dataset-level granularity can easily locate and interpret the relevant figures. Thank you again for pointing this out.\n\n---\n\n> **Q6: Clarification Requested Regarding Presentation and Organization of Key Content**\n\nA6: We appreciate the reviewer’s feedback on presentation quality and acknowledge that certain important technical components were placed in the appendix, which may have inadvertently led readers to overlook critical context.\n\nIn the revised manuscript, we will reorganize the structure to surface essential elements—such as the definition of shapelets and the introduction of the shapelet encoder—into the main body. Less central implementation details will remain in the appendix for completeness.\n\nAdditionally, we will refine terminology usage by avoiding unnecessary abbreviations and using full spellings for commonly recognized terms (e.g., writing out “Shapley Value” in full). We will also improve the clarity of figure captions. For example:\n- In **Tables 1 and 2**, we will clarify that the color shading reflects the relative magnitude within each column;\n- In **Figure 6(b)**, we will state explicitly that each point corresponds to the best-performing explainer for the respective dataset at a given perturbation ratio."}, {"review_id": "kpPNDXh9H0", "reviewer": "Reviewer_DZ2U", "summary": "The paper focuses on explaining a time series predictive model. This is based only on shapelet (time series segments)-driven methods, which makes sense since the focus is on explainable models. Given a set of initial shapelets: For each time series X, the method compares each shapelet S_n with all segments in the time series X and computes alignment scores (descriptors), identifying the most similar segment from X (most strongly aligned) (detectors). The set of shapelets is learnable (although I have questions about this) and optimized to enforce diversity among shapelets and their predictive power. After learning shapelets that can discriminate between classes, a post-hoc analysis is performed to explain the model. This is done by computing Shapley-value attribution. The saliency scores are computed by finding the most strongly aligned segments between all learned shapelets and the time series from the test data. A subset of these segments (g') is perturbed using a mask as in equation 14, and the scores are computed to measure how each segment influences the predictive power of the classifier (equation 12).", "questions": "Method: \n- not sure why the authors in line 119 define the time series as multivariate (X_t \\in R^D) although the method works only on univariate time series.\n- how did you obtain the initial set of shapelets? Line 145\n- not quite sure how shapelets are learned. Each shapelet is divided into patches and each patch goes through a linear transformation along with multi-head attention across all patches. The question is whether the outcome of the encoder is a representation for each patch or a representation for the entire shapelet? In each case, how does the original set of shapelets get updated? I think what gets updated is how to transform the initial set of shapelets into a useful learnable representation. This needs to be clarified in the manuscript. Additionally, does this depend on the quality of the initial set of shapelets? Does it hinder the explainability of the model? Because initially I thought the explanation would be based on the learned shapelets, but it seems that the initial shapelets are random and it might not be easy to explain the learned transformation of shapelets.\n- in equations 7 and 8, what if these time points t are not continuous? For example, for a given shapelet S_n, what if the high activation regions are say 5, 16, 52? These three time points are not contiguous.\n- bit confused about the suffix 'i' in equation 23: is it an index for heads or patches?\n- it seems from Table 3 that removing the shapelet encoder significantly hinders the performance of the model; AUPRC drops from 72% to 21%. How is the learned transformation of the shapelets used in detecting the most strongly aligned segment? My understanding is that the strongly aligned segments are detected using the initial shapelets**,** not their learned transformation?\n- equation 2: Isn't the difference between |g'| and |g| always one? g' is basically g but without shapelet n?\n- Equation 11 is not quite clear to me. It needs more explanation.\n- what is P(X,M) in line 194? \n\nExperiments: \n- all experiments are performed on binary classification problems, although the method was proposed to be general for multi-class classification.\n- from Figure 4, it seems that dyna is more robust to highly perturbed segments than ShapeX. Is there any explanation?\n- Fails to compare against published post-hoc explainers for shapelet-based methods such as\n\t- Bahri, Omar, Soukaina Filali Boubrahimi, and Shah Muhammad Hamdi. \"Shapelet-based counterfactual explanations for multivariate time series.\" arXiv preprint arXiv:2208.10462 (2022).\n\t- Mochaourab, Rami, et al. \"Post hoc explainability for time series classification: Toward a signal processing perspective.\" IEEE signal processing magazine 39.4 (2022): 119-129.\n\t- Huang, Qi, et al. \"Shapelet-based model-agnostic counterfactual local explanations for time series classification.\" arXiv preprint arXiv:2402.01343 (2024).\n\t- Meng, Fanyu, et al. \"Implet: A Post-hoc Subsequence Explainer for Time Series Models.\" arXiv preprint arXiv:2505.08748 (2025).\n\nI do not think that shapelet-based methods need any post-hoc explanation as shapelets are inherently interpretable. The proposed method fits in the area of attribution more than post-hoc explaination.", "limitations": "No", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength: \n- Explainable AI models are of utmost importance, especially for time series analysis \n- Based on well known shapelet-driven time series framework\n\nWeakness: \n- If I'm not mistaken the main contribution of the paper is basically in equation 12, which is minor and incremental. \n- Proving shapelet-value is equivalent to model-level CATE is straight-forward. \n- Fail to compare against other post-hoc explainer that are based on shapelet-driven methods.", "was_revised": true, "final_justification": "Authors replied to my concerns.", "rebuttal": "We sincerely thank you for your careful reading of our work and the constructive comments provided. Your feedback has significantly helped us improve the clarity and positioning of our manuscript.\n\n> **Q1: Ambiguity in Defining Time Series as Multivariate While Focusing on Univariate Case**\n\nA1: We agree that this may appear confusing. Our intention was to present a general formulation in the methodology section to maintain future extensibility to multivariate time series. However, as explicitly stated in line 125, this paper focuses solely on the univariate setting ($D = 1$). We will revise the manuscript to make this restriction clearer earlier in the main text to avoid misunderstanding. In addition, we **have included new experiments during the rebuttal phase to demonstrate that ShapeX can be easily extended to multivariate time series**. For the specific experimental setup and results, please refer to our response to Reviewer NMJu’s Q2.\n\n---\n\n> **Q2: Clarification on How the Initial Shapelet Set Is Obtained**\n\nA2: The initial shapelets are **randomly initialized**. The detailed initialization process is described in Appendix C. We acknowledge that this is a critical design detail and should have been clearly stated in the main text. We sincerely apologize for this oversight and will make sure to highlight it explicitly in the revised manuscript.\n\n---\n\n> **Q3: How Are Shapelets Learned and Are They Sensitive to Initialization Quality?** \n\nA3: The shapelets are learned via a self-attention-based encoder, following a structure similar to PatchTST. Each shapelet is divided into patches, passed through linear transformations, and processed by multi-head attention to produce a unified representation for the entire shapelet—not for individual patches.\n\nThis design is briefly described in Appendix C, but we acknowledge that it deserves clearer exposition in the main text and will revise accordingly.\n\nTo examine whether the initial shapelet quality impacts the results, we conducted a robustness study using three different random seeds for initialization. As shown below, the **explanation quality exhibit negligible variation, suggesting that the learned shapelets are stable and insensitive to initialization**. \n\n\n\n| Seed       | MCC-E         |             |             | ECG       |             |             |\n|-|-|-|-|-|-|-|\n|            | AUPRC          | AUP         | AUR         |AUPRC           | AUP         | AUR         |\n| seed=44| 0.6407±0.0036  |0.5614±0.0076  |  0.3679±0.0050 |   0.7228±0.0028    |   0.8395±0.0030   | 0.6961±0.0032 |\n| seed=22| 0.6443±0.0012  |0.5623±0.0004  |  0.3716±0.0069 |   0.7205±0.0012    |   0.8320±0.0059   | 0.6924±0.0009 |\n| seed=5 | 0.6402±0.0030  |0.5604±0.0054  |  0.3681±0.0043 |   0.7340±0.0031    |   0.8334±0.0049   | 0.6956±0.0045 |\n\n---\n\n> **Q4: Concern About Discontinuity in Activated Time Steps in Equations 7 and 8**\n\nA4: This is an excellent observation. In practice, the high-activation regions of a shapelet $S_n$ are often non-contiguous. Therefore, $X(S_n)$ does not necessarily refer to a continuous segment—it may consist of disjoint time indices that align strongly with $S_n$.\n\nThis does not affect our downstream steps, such as perturbation and Shapley value calculation. However, we agree that the current form of Equations (7) and (8) may imply continuity and thus be misleading. We will revise the manuscript to explicitly clarify that non-contiguous activations are valid and expected.\n\n---\n\n> **Q5: Clarification on the Meaning of Index 'i' in Equation 23**\n\nA5: In Equation 23, the index $i$ refers to different attention heads. We will clarify this explicitly in the revised manuscript to avoid potential ambiguity.\n\n---\n\n> **Q6: Are Strongly Aligned Segments Based on Initial or Learned Shapelets?**\n\nA6: This is a very reasonable concern. The misunderstanding may stem from our lack of clarity in explaining that the shapelets are initially random and are then learned through the encoder. If we used the initial untrained shapelets, they would have no meaningful structure and could not align with any relevant segments.\n\nThe encoder is crucial—it transforms randomly initialized sequences into meaningful shapelets that can align with semantically important regions in the input. Thus, the strongly aligned segments are based on the learned shapelets, not the initial ones.\n\n---\n\n> **Q7: Does the Difference Between $|G'|$ and $|G|$ Always One?**\n\nA7: We believe you are referring to Equation 12. In this context, $G'$ is defined as an arbitrary subset of $G \\setminus \\{n\\}$—that is, any subset of $G$ excluding the element $n$—and is not necessarily of size $|G| - 1$. This definition is indicated below the summation symbol in the equation. We acknowledge that this notation may be unintuitive at first glance, and we will revise the manuscript to make the definition of $G'$ more explicit and accessible.\n\n---\n\n> **Q8: Lack of Clarity in Equation 11**\n\nA8: The goal of Equation 11 is to apply linear interpolation between $X_{\\text{start}}$ and $X_{\\text{end}}$ so that the pertubation is smooth. This design helps prevent introducing abrupt, unrealistic changes during perturbation. We will add a more detailed explanation of this operation and its intent in the revised manuscript.\n\n---\n\n> **Q9: What Is $P(X, M)$ in Line 194?**\n\nA9: $P(X, M)$ refers to the perturbation function defined in Equation 14 and elaborated in the appendix. We will add a clear reference in the main text to avoid confusion.\n\n---\n\n> **Q10: All Experiments Use Binary Classification**\n\nA10: Thank you for pointing this out. In fact, 85 of the UCR Archive datasets used in our experiments are multi-class classification tasks. **This was not explicitly annotated in Table 4, and we will correct this oversight in the revised manuscript to avoid misinterpretation.**\n\n---\n\n> **Q11: From Figure 4, it seems that dyna is more robust to highly perturbed segments than SHAPEX. Is there any explanation?**\n\nA11: You have a very keen observation. Figure 4 indeed shows results from two randomly selected datasets in the UCR Archive. However, as shown in **Figure 6 and Figure 8–11** in the appendix, the complete evaluation across all 112 datasets reveals that it is difficult to conclude that dyna is consistently more robust.\n\nThat said, in certain datasets, dyna does show smoother performance degradation curves than ShapeX. We suspect this is because dyna computes saliency scores at the single timestep level, which leads to more scattered and discrete saliency regions. When perturbed, these regions result in more gradual degradation. However, as shown in Figure 6, although Dyna’s curve appears smoother, its performance at nearly every perturbation ratio is worse than ShapeX, and it degrades more sharply in early perturbation stages.\n\n---\n\n> **Q12: Fails to Compare Against Published Shapelet-Based Methods**\n\nA12: Thank you very much for providing these valuable references. We **have included Implet [Meng et al., 2025] as a baseline in our comparative experiments—results are reported below**. Unfortunately, we were unable to include the other cited methods due to the lack of publicly available code. If these works release their implementations in the future, we would be glad to incorporate them into future evaluations.\n\nFrom the experimental results, ShapeX consistently outperforms Implet.\n\n---\n\n| Model         | MCC-E          |              |              | MCC-H          |              |              |\n|-|--|-|-|--|-|-|\n|               | AUPRC          | AUP          | AUR          | AUPRC          | AUP          | AUR          |\n| ShapeX        | 0.6407±0.0036  | 0.5614±0.0076| 0.3679±0.0050| 0.8110±0.0003  | 0.6838±0.0054| 0.7431±0.0055|\n| Implet        | 0.3701±0.0025  | 0.5184±0.0020| 0.4901±0.0029| 0.5103±0.0079  | 0.4801±0.0038| 0.5501±0.0028|\n\n| Model         | MTC-E          |              |              | MTC-H          |              |              |\n|-|--|-|-|--|-|-|\n|               | AUPRC          | AUP          | AUR          | AUPRC          | AUP          | AUR          |\n| ShapeX        | 0.6100±0.0048  | 0.3962±0.0067| 0.5472±0.0082| 0.6792±0.0014  | 0.4255±0.0024| 0.9019±0.0041|\n| Implet        | 0.1740±0.0023  | 0.1802±0.0009| 0.5082±0.0011| 0.3922±0.0062  | 0.5024±0.0012| 0.4502±0.0035|\n\n| Model         | ECG            |              |              |\n|-|--|-|-|\n|               | AUPRC          | AUP          | AUR          |\n| ShapeX        | 0.7228±0.0028  | 0.8395±0.0030| 0.6961±0.0032|\n| Implet        | 0.5385±0.0035  | 0.5092±0.0024| 0.4845±0.0042|\n\n---\n\n> **Q13: Whether Post-Hoc Explanations Are Necessary for Shapelet-Based Methods, and Whether the Proposed Method Is Better Categorized as Attribution**\n\nA13: We sincerely appreciate this thoughtful and insightful comment. Indeed, our method relies on shapelets, which are inherently interpretable. However, in ShapeX, **shapelets serve purely as an intermediate representation to facilitate the computation of saliency scores**, and are not used for classification or as an interpretability tool themselves.\n\nThe goal of ShapeX is to explain the behavior of a black-box model, which aligns with the spirit of post-hoc explanation. In fact, our use of the term “post-hoc” follows the convention established in TimeX++ under the phrase “Post-hoc Instance-level Time Series Explanation.” However, we agree with the reviewer that the overall design of ShapeX—especially its emphasis on saliency estimation and perturbation analysis—fits naturally within the attribution literature.\n\nThus, **ShapeX can reasonably be viewed as both a post-hoc explanation tool and an attribution method**. To better clarify its position to readers, we **will categorize ShapeX under the umbrella of attribution methods in the revised manuscript**, particularly in the introduction and methodology sections."}, {"review_id": "pisrEBgmfe", "reviewer": "Reviewer_NMJu", "summary": "The paper introduces SHAPEX, a post-hoc explanation framework for time-series classifiers.\nKey steps: (i) a Shapelet Describe-and-Detect (SDD) module jointly learns a small, diverse set of representative shapelets; (ii) test series are segmented at the points where those shapelets fire; (iii) Shapley values are computed over the resulting shapelet-aligned segments, using a carefully smoothed perturbation baseline, to yield saliency scores.\nThe authors prove that, under standard causal-inference assumptions, these segment-level Shapley values approximate the model-level Conditional Average Treatment Effect, giving a causal reading to the explanations.\nExperiments span four new synthetic motif datasets and 112 real UCR datasets plus ECG, multiple black-box architectures, occlusion tests, and ablations. Code is released for reproducibility.", "questions": "1. Multivariate extension: do you foresee any obstacles beyond memory to applying SDD + segment SV when D > 1? A small multivariate benchmark in the rebuttal could strengthen impact.\n2. Threshold $\\Omega$: how is it chosen per dataset? Please report sensitivity; fixed global values may split or merge segments incorrectly.\n3. Give average explanation time per instance for UCR lengths; if real-time limits practical use, can the local-coalition trick be further approximated (e.g., Monte-Carlo)?\n4. SUTVA/ignorability rely on independent perturbations, yet overlapping shapelet segments may violate this. Any empirical evidence that causal conclusions remain stable when overlaps are large?\n5. Have cardiologists or other domain experts assessed the ECG explanations? Even a small pilot would bolster claims of practical fidelity.\n6. Why did you leave out some related work like TimeSHAP, WindowSHAP and ShapTST? It would also be good to include a discussion on counter-factual explanation methods as they offer complementary explanations and use similar methods (such as TX-Gen, ContraLSP, SubSpacE)", "limitations": "The paper openly notes that SHAPEX is currently univariate and that segment granularity hinges on learned shapelets. I would add two more: (i) causal interpretation depends on strong independence assumptions; (ii) Shapley computation may become prohibitive for long series. Addressing these would help.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Qaulity**\n\n*Strengths*:  \n-  joint learning of shapelets with matching + diversity losses improves fidelity; thorough ablations isolate each component’s impact\n- Extensive evaluation\n\n*Weaknesses*:  \n- No human or domain-expert study to gauge interpretability usefulness.\n- Computational cost of Shapley sampling (even with local coalition restriction) is not reported in wall-clock terms\n- Some of the related literature should be added in the discussions (or even as baselines in experiments), these include other SHAP methods such as TimeSHAP, WindowSHAP and ShapTST (2025). In addition it would be good to add a section about counterfactual and constrastive explainers as these serve a similar purpose in the TS domain and are based on the same building blocks, such as TX-Gen, ContraLSP. and Sub-SpaCE. See references below:\n\n1. Bento, J., Saleiro, P., Cruz, A. F., Figueiredo, M. A., & Bizarro, P. (2021, August). Timeshap: Explaining recurrent models through sequence perturbations. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining (pp. 2565-2573).\n2. Nayebi, A., Tipirneni, S., Reddy, C. K., Foreman, B., & Subbian, V. (2023). WindowSHAP: An efficient framework for explaining time-series classifiers based on Shapley values. Journal of biomedical informatics, 144, 104438.\n3. Cheng, Q., Xing, J., Xue, C., & Yang, X. (2025). Unifying Prediction and Explanation in Time-Series Transformers via Shapley-based Pretraining. arXiv preprint arXiv:2501.15070.\n4. Huang, Q., Kitharidis, S., Bäck, T., & van Stein, N. (2024). TX-Gen: Multi-Objective Optimization for Sparse Counterfactual Explanations for Time-Series Classification. arXiv preprint arXiv:2409.09461.\n5. Refoyo, M., & Luengo, D. (2024, July). Sub-SpaCE: Subsequence-Based Sparse Counterfactual Explanations for Time Series Classification Problems. In World Conference on Explainable Artificial Intelligence (pp. 3-17). Cham: Springer Nature Switzerland. \n\n**Clarity**  \n- Paper is well-structured\n\n- Some notation is heavy. Threshold $\\Omega$ for segment extraction is introduced but its tuning is unclear\n\n**Significance**\n\n- Large-scale benchmark (entire UCR), demonstrates generalisation; the causal justification is novel. Synthetic datasets address bias problem in prior work\n\n- Impact limited to univariate series; many real problems are multivariate\n- Potential users still need to trust the surrogate causal assumptions\n\n**Originality**\n\n- Combining learned shapelets specifically trained for explanation with segment-level Shapley attribution is new\n\n- Uses standard building blocks (1-D conv, attention, Shapley sampling); novelty mostly in integrating them.", "was_revised": true, "final_justification": "Thank you, no further questions.", "rebuttal": "We sincerely thank you for recognizing the significance and novelty of our work. Your comments are highly constructive, and we believe that addressing your concerns will substantially improve the quality of our manuscript.\n\n> **Q1: Lack of Human or Domain-Expert Evaluation to Assess Explanation Usefulness**\n\nA1: Thank you for the helpful comment. We acknowledge that our current version lacks formal quantitative evaluations by domain experts. However, to partially address this gap, **we conducted qualitative visual assessments in Appendix G.3 to evaluate the plausibility of ShapeX explanations using semantically meaningful regions in real-world datasets**.\n\nSpecifically, from Figures 14 to 16, we observe that only ShapeX successfully highlights the following class-discriminative regions:\n- the **growth plate** in *PhalangesOutlinesCorrect*\n- the **facial contour regions** in *FaceAll*\n- the **gesture transitions** in *UWaveGestureLibraryAll*\n\nThese **regions are aligned with human-intuitive features and offer promising qualitative evidence of the usefulness of ShapeX explanations.**\n\nThat said, we fully agree that future work would benefit from formal domain expert studies. For example, we plan to collaborate with cardiologists to evaluate the interpretability of ShapeX explanations on ECG datasets, thereby further validating the real-world trustworthiness of our framework.\n\n---\n\n> **Q2: Interest in Multivariate Extension of ShapeX**\n\nA2: We appreciate your interest in extending ShapeX to multivariate time series. To explore this direction, we implemented a multivariate version of ShapeX: ShapeX-M during the rebuttal period and designed a corresponding synthetic dataset with ground-truth saliency labels to assess its feasibility.\n\nSpecifically, we merged the two univariate synthetic datasets defined in Appendix E.1—MCC-E and MTC-E—into a new multivariate dataset where each input $X \\in \\mathbb{R}^{800 \\times 2}$ contains two variables. We refer to this dataset as **MCC-MTC**, which comprises four classes defined by different motif combinations across the two dimensions.\n\nFrom a model structure perspective, we adopt a **parallel variable-wise architecture**, where each variable is assigned its own Shapelet Describe-and-Detect (SDD) module, learning variable-specific shapelets. For saliency attribution, we compute the Shapley Values jointly over the **entire multivariate input**, allowing cross-variable influence to be captured in the final attribution scores.\n\nDetailed evaluation results on MCC-MTC are included in the table below, demonstrating that **ShapeX can be naturally extended to multivariate settings and maintain strong attribution performance**.\n\n\n| Model         | MCC-MTC        |              |              | \n|-|-|-|-|\n|               | AUPRC          | AUP          | AUR          | \n| TimeX         | 0.4135±0.0051  | 0.4813±0.0041| 0.2351±0.0093| \n| TimeX++       | 0.2903±0.0030  | 0.4601±0.0015| 0.1529±0.0008| \n| ShapeX-M      | 0.5301±0.0041  | 0.5041±0.0076| 0.4135±0.0043| \n\n\n---\n\n> **Q3: Request for Hyperparameter Configurations**\n\nA3: Thank you for your interest in implementation details. We provide the complete set of hyperparameter configurations in the table below. These include:\n\n- the number and length of shapelets,\n- the threshold $\\Omega$ for activation,\nThese configurations reflect the settings used across our experiments and are reported to ensure reproducibility.\n\n| Parameter                          | MCC-E, MCC-H,MTC-E,MTC-H         | ECG         | UCR                   |\n|-|-|-|-|\n| Number of shapelets               | 5                      | 4                      | 5                     |\n| Length of shapelets               | 100                    | 40                     |10% of input length    |\n| Threshold $\\Omega$ for activation | 0.5                    | 0.5                    | 0.5                   |\n\n---\n\n> **Q4: Request for Runtime Statistics on UCR Datasets**\n\nA4: We have recorded the average runtime of ShapeX across all UCR datasets, which is **58.51 seconds** per dataset. For comparison, the average runtime of DynaMask under the same settings is **470.34 seconds**. This indicates that ShapeX achieves a favorable trade-off between explanation quality and computational efficiency.\n\nIn addition, we provided runtime statistics on synthetic datasets to further assess scalability. These results are summarized in **Table 10** of the appendix.\n\n---\n\n> **Q5: Concern About Violating SUTVA/Ignorability Due to Overlapping Shapelet Segments—Is There Empirical Evidence That Causal Conclusions Remain Stable?**\n\nA5: We appreciate this thoughtful and technically grounded question. To empirically assess the impact of overlapping shapelet segments on the robustness of our causal explanations, we designed a synthetic dataset called **MCC-H (overlap)**. In this variant, the motifs across samples are allowed to **overlap by up to 30%** of their length, introducing nontrivial dependency across saliency regions.\n\nThe experimental results (see table below) show that ShapeX achieves **comparable performance** on MCC-H (overlap) to its performance on the original non-overlapping MCC-H dataset. This provides empirical support for the robustness of our method under moderate overlap, suggesting that the resulting saliency scores and causal attributions remain stable in such settings.\n\nHowever, we agree that this empirical evidence does not constitute a formal theoretical guarantee. We consider a more rigorous investigation into the causal implications of overlapping shapelets—particularly with respect to assumptions like SUTVA and ignorability—an important direction for future work.\n\n\n| Model         | MCC-H (overlap)|              |              | \n|-|-|-|-|\n|               | AUPRC          | AUP          | AUR          | \n| ShapeX        | 0.8083±0.0014  | 0.6304±0.0031| 0.7531±0.0027| \n\n---\n\n> **Q6: Have Cardiologists or Other Domain Experts Assessed the ECG Explanations? Even a Small Pilot Would Strengthen the Practical Claims**\n\nA6: The ECG dataset we use—**PTB-XL**—is annotated by clinical domain experts, and we believe that ShapeX’s strong performance on this dataset indirectly supports the alignment between our method’s explanations and cardiologist-level diagnostic knowledge.\n\nThat said, we fully agree that direct expert evaluation would provide more concrete evidence of practical fidelity. Moving forward, we plan to involve **cardiologists** in reviewing and validating the saliency outputs produced by ShapeX. This human-in-the-loop process will enable us to more formally assess the clinical plausibility and trustworthiness of our explanations.\n\n---\n\n> **Q7: Request for a Summary of Related Works**\n\nA7: Thank you for the helpful suggestion. In the revised manuscript, we will expand the **Related Work** section to provide a more systematic summary of recent time series attribution and explanation methods."}, {"review_id": "bOkXrAy3aC", "reviewer": "Reviewer_zzMH", "summary": "This paper proposes SHAPEX, a shapelet-driven segmentation method for explaining time-series classifiers, integrating shapelets with Shapley attribution to enhance interpretability and causal grounding. Experimental results demonstrate its effectiveness compared to existing baselines.", "questions": "1. You use valid-width convolution yet later treat the activations as length T. Did you apply padding or another strategy? This seems missing from the paper.\n\n2. In occlusion experiments, SHAPEX masks whole segments rather than single timesteps. How exactly do you ensure fairness (matching the exact p% of timesteps) across methods?\n\n3. The segmentation strongly depends on threshold Ω and shapelet count N. Could you briefly clarify how sensitive your results are to these choices?", "limitations": "yes", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n\t1. The idea of combining shapelet-based segmentation with Shapley attribution is compelling, neatly bridging the gap between shapelet extraction methods and post-hoc explanations.\n\n\t2. The overall structure, figures, and description of the pipeline (especially the SDD module) are concise and easy to follow.\n\n\t3. The paper goes beyond typical benchmarks, covering the entire UCR archive as well as labeled ECG and synthetic datasets, clearly demonstrating the effectiveness of the proposed approach.\n\nWeaknesses\n\n\t1.  All experiments focus exclusively on single-channel time series; it’s unclear how readily this method scales to real-world multivariate or multidimensional scenarios.\n\n\t2. Lack of sensitivity analysis for key hyperparameters: The segmentation quality strongly depends on the activation threshold (Ω) and the predefined number of shapelets. The authors haven’t provided a sensitivity or robustness analysis for these crucial choices.", "was_revised": true, "final_justification": "Thank you for your reply. I have no other questions and will keep my recommendation", "rebuttal": "We sincerely thank you for recognizing the significance and novelty of our work. Your comments are highly constructive, and we believe that addressing your concerns will substantially improve the quality of our manuscript.\n\n> **Q1: Valid-Width Convolution Appears Inconsistent with Later Use of Length $T$ Activations—Was Padding Applied?**\n\nA1: Thank you for your careful observation. In our implementation, we apply **symmetric padding** to the output of the 1D convolution to ensure that the activation map has the same temporal length $T$ as the input time series. This padding operation was omitted in the current manuscript, and we will explicitly clarify this step in the revised version to avoid confusion.\n\n---\n\n> **Q2: Fairness in Occlusion Experiments—How Do You Match the Exact $p\\%$ of Masked Timesteps if ShapeX Operates on Segments?**\n\nA2: We greatly appreciate this thoughtful question. As you correctly point out, ShapeX generates segment-level saliency scores, which could result in coarse masking granularity when compared to timestep-level attribution methods. This may lead to unfair comparisons in occlusion experiments, where precise control over the proportion of masked timesteps is critical.\n\nTo address this, we add **small Gaussian noise** to the saliency scores within each segment. Specifically, we sample the noise from a normal distribution $\\mathcal{N}(0,1)$ and scale it by a factor of $10^{-6}$ before adding it to each timestep within a segment. This strategy ensures that:\n- The **relative ranking between segments** is preserved;\n- **Slight variations within each segment** allow per-timestep ranking and precise masking percentages.\n\nThis ensures that the masking procedure can fairly match the exact $p\\%$ of timesteps across all methods, including those based on segment-wise scores. We will include this implementation detail in the revised Occlusion Evaluation section.\n\n> **Q3: Sensitivity to Hyperparameters—How Do the Results Depend on the Threshold $\\Omega$ and the Number of Shapelets $N$?**\n\nA3: Thank you for raising this important question. We have conducted a sensitivity analysis of ShapeX with respect to the number and length of shapelets on ECG datasets. The results are presented in **Figure 12**.\n\nAdditionally, we provide per-dataset hyperparameter configurations in the table below to enhance transparency. In the revised manuscript, we will expand the sensitivity experiments to cover more datasets beyond ECG, to better characterize the effect of $\\Omega$ and $N$ in broader settings.\n\n| Parameter                          | MCC-E, MCC-H,MTC-E,MTC-H         | ECG         | UCR                   |\n|-|-|-|-|\n| Number of shapelets               | 5                      | 4                      | 5                     |\n| Length of shapelets               | 100                    | 40                     |10% of input length    |\n| Threshold $\\Omega$ for activation | 0.5                    | 0.5                    | 0.5                   |\n---\n\n> **Q4: Generalizability to Multivariate Time Series—Can the Method Scale Beyond Single-Channel Inputs?**\n\nA4: Thank you for this valuable observation. While our main experiments focus on univariate time series, we conducted a **preliminary multivariate extension of ShapeX** during the rebuttal phase. The design, implementation, and evaluation of this multivariate version are described in **our response to Reviewer NMJu, Q2**.\n\nIn brief, we constructed a multivariate synthetic dataset and adapted ShapeX to use variable-specific shapelet modules with joint saliency attribution across channels. Initial results demonstrate that ShapeX can be extended to multivariate inputs with promising results, and we plan to explore this direction further in future work."}]

Author rebuttal:

Meta-review: **Summary**  
Existing post-hoc time series explanation methods primarily focus on timestep-level feature attribution, and overlook the fundamental prior that classification outcomes are predominantly driven by key shapelets. This paper presents ShapeX, which first segments time series into shapelet-driven segments and then employs Shapley values to assess their saliency. On both synthetic and real-world datasets, ShapeX produces explanations revealing causal relationships instead of just correlations.

**Strengths**  
- The premise of this paper (that the impact of shapelets are more significant for explaining classification models than individual timesteps) is novel, interesting and important.
- The authors evaluated their approach on 100+ datasets from UCR archive.
- The joint learning of shapelets with matching + diversity losses improves fidelity, and there are thorough ablations that isolate each component's impact.

**Weaknesses**  
- In the shaplet describe and detect (SDD) framework, shapelets are self-identified and generated independently from the black-box classification model. 
- The comparison of ShapeX to traditional step-level explanation might have unfair advantage to ShapeX, considering that the attribution scores of ShapeX aggregates over multiple timesteps. However, the authors point out that the attribution scores of multiple step-level explanations also utilize cross-timestep dependencies.
- Human-evaluated interpretability usefulness would be good-to-have.
- The computational cost of Shapley sampling in wall-clock terms would be good-to-have.
- More discussions of related works, and improvements on the writing would improve the presentation of this paper.
Decision: Accept (poster)