Towards A Unified Information Bottleneck Framework for Time Series Explanations
Authors: Xu Zheng, Zichuan Liu, Zhuomin Chen, Mayur Akewar, Janki Bhimani, Jason Liu, Mo Sha, Jingchao Ni, Wei Cheng, Dongsheng Luo
Organizations: Florida International University · Carnegie Mellon University · University of Houston · NEC Labs America · Singapore Management University
Explaining deep learning models operating on time series data is crucial in various applications that require transparent and interpretable insights into model behavior. {Existing explanation methods generally fall into two categories: attribution-based explanations, which identify the temporal regions most responsible for a prediction, and counterfactual explanations, which reveal how an input should be modified to alter the model's decision.} {Despite valuable insights, these two fields are largely studied independently. This disconnect leaves attribution methods lacking causal validation, while counterfactual methods suffer from severe instability, producing adversarial-like noise instead of meaningful explanations.} In this work, we revisit time-series explainability from an information-theoretic perspective and show that existing explainers are vulnerable to trivial solutions and distributional shifts. To address these limitations, we propose a unified objective function for explainable time series learning that bridges attribution and counterfactual reasoning within a single framework. Building upon the Information Bottleneck principle, our formulation explicitly prevents trivial explanations and out-of-distribution counterfactuals. {Based on this objective function, we introduce {\modelname}, a novel explanation framework that learns a parametric transformation network to construct explanation-embedded instances, where preserved information yields attribution explanations and controlled information removal produces stable counterfactual explanations.} We evaluate {\modelname} on synthetic and real-world benchmarks against state-of-the-art baselines. Extensive quantitative and qualitative results show that {\modelname} consistently outperforms competing methods, yielding faithful attributions and stable counterfactual explanations.
Figures & tables
Fig. 1 : A comparison between our model and previous work. For the attribution explanations, the latent embeddings of explanations are learned from the ECG dataset. Our explanations are within the original distribution, whereas the reference model’s explanations are not. For the counterfactual explanations, our framework represents more robust results.
Fig. 2 : The overall architecture of TimeX++, a unified framework for attribution and counterfactual explanations supported by Information Bottleneck. TimeX a ++ and TimeX cf ++ have similar components and loss functions but different implementations.
Dataset
# of Samples
Length
Dimension
Classes
FreqShapes
6,100
50
1
4
SeqComb-UV
6,100
200
1
4
SeqComb-MV
6,100
200
4
4
LowVar
6,100
200
2
4
ECG
92,511
360
1
2
PAM
5,333
600
17
8
TABLE I : The description of synthetic and real-world datasets.
Method
AUPRC
AUP
AUR
AUPRC
AUP
AUR
AUPRC
AUP
AUR
FreqShapes
SeqComb-UV
ECG
IG
0.752 ± 0.003
0.691 ± 0.003
0.598 ± 0.002
0.576 ± 0.002
0.816 ± 0.002
0.287 ± 0.002
0.418 ± 0.001
0.595 ± 0.002
0.320 ± 0.001
Dynamask
0.220 ± 0.001
0.295 ± 0.004
0.504 ± 0.002
0.442 ± 0.002
0.878 ± 0.004
0.103 ± 0.001
0.328 ± 0.001
0.525 ± 0.003
0.108 ± 0.008
WinIT
0.507 ± 0.002
0.555 ± 0.003
0.456 ± 0.002
0.457 ± 0.002
0.787 ± 0.003
0.225 ± 0.002
0.305 ± 0.001
0.443 ± 0.003
0.347 ± 0.001
CoRTX
0.698 ± 0.016
0.494 ± 0.000
0.326 ± 0.001
0.564 ± 0.002
0.824 ± 0.003
0.175 ± 0.001
0.374 ± 0.001
0.497 ± 0.002
0.303 ± 0.001
SGT + Grad
0.531 ± 0.002
0.414 ± 0.001
0.393 ± 0.002
0.573 ± 0.002
0.783 ± 0.001
0.214 ± 0.001
0.314 ± 0.001
0.424 ± 0.002
0.264 ± 0.001
TABLE II : Attribution explanation performance on univariate and multivariate datasets.
Method Substitution
PAM
Epilepsy
Boiler
Wafer
Freezer
Rank
Mean
0.979 ± 0.002
0.939 ± 0.005
0.814 ± 0.056
0.993 ± 0.002
0.772 ± 0.093
7.2
Random
Zero
0.979 ± 0.002
0.940 ± 0.004
0.895 ± 0.012
0.992 ± 0.002
0.775 ± 0.093
7.8
Mean
0.778 ± 0.015
0.816 ± 0.019
0.808 ± 0.036
0.488 ± 0.267
0.452 ± 0.129
4.6
Dynamask
Zero
0.777 ± 0.015
0.361 ± 0.073
0.555 ± 0.146
0.488 ± 0.267
0.355 ± 0.110
3.6
Mean
0.749 ± 0.049
0.852 ± 0.018
0.563 ± 0.041
0.463 ± 0.145
0.469 ± 0.061
4.4
TimeX
Zero
0.754 ± 0.049
0.454 ± 0.077
0.416 ± 0.048
0.465 ± 0.057
0.465 ± 0.057
3.6
TABLE III : Performance report on different real-world datasets by masking the top 10% of salient features. The masked portion is substituted with an average of this feature or with zeros.
Fig. 3 : Occlusion experiments on real-world datasets. Higher values indicate better performance. The x-axis is the Bottom Proportion Perturbed, and the y-axis is the Prediction AUROC.
Method
Validity
Confidence
Sparsity
Prox.-L1
Prox.-L2
Validity
Confidence
Sparsity
Prox.-L1
Prox.-L2
FreqShapes
SeqComb-UV
CoMTE
1.000 ± 0.000
0.965 ± 0.006
1.000 ± 0.000
0.573 ± 0.004
0.828 ± 0.006
1.000 ± 0.000
0.784 ± 0.022
0.999 ± 0.000
0.209 ± 0.002
0.401 ± 0.008
AB-CF
1.000 ± 0.000
0.871 ± 0.008
0.733 ± 0.025
0.441 ± 0.013
0.718 ± 0.011
1.000 ± 0.000
0.911 ± 0.013
0.650 ± 0.037
0.151 ± 0.007
0.348 ± 0.014
M-CELS
0.486 ± 0.053
0.466 ± 0.051
0.061 ± 0.008
0.064 ± 0.011
0.196 ± 0.031
0.361 ± 0.037
0.353 ± 0.036
0.025 ± 0.003
0.016 ± 0.001
0.090 ± 0.007
CONFETTI
0.990 ± 0.003
0.512 ± 0.002
0.349 ± 0.010
0.242 ± 0.011
0.538 ± 0.012
0.894 ± 0.034
0.477 ± 0.017
0.209 ± 0.019
0.059 ± 0.008
0.222 ± 0.021
TimeX cf ++
0.974 ± 0.004
0.964 ± 0.005
0.214 ± 0.005
0.339 ± 0.021
0.757 ± 0.030
0.890 ± 0.053
0.887 ± 0.052
0.516 ± 0.074
0.288 ± 0.085
0.487 ± 0.082
TABLE IV : Targeted counterfactual explanation performance on univariate and multivariate datasets.
Method
Validity
Confidence
Sparsity
Prox.-L1
Prox.-L2
Validity
Confidence
Sparsity
Prox.-L1
Prox.-L2
FreqShapes
SeqComb-UV
CoMTE
1.000 ± 0.000
0.930 ± 0.017
1.000 ± 0.000
0.438 ± 0.016
0.641 ± 0.028
1.000 ± 0.000
0.790 ± 0.023
0.999 ± 0.000
0.196 ± 0.000
0.376 ± 0.001
AB-CF
1.000 ± 0.000
0.826 ± 0.021
0.672 ± 0.006
0.283 ± 0.010
0.486 ± 0.021
1.000 ± 0.000
0.890 ± 0.018
0.513 ± 0.040
0.114 ± 0.004
0.293 ± 0.004
M-CELS
0.612 ± 0.039
0.570 ± 0.034
0.063 ± 0.006
0.040 ± 0.001
0.157 ± 0.002
0.336 ± 0.026
0.319 ± 0.022
0.013 ± 0.001
0.011 ± 0.001
0.083 ± 0.004
CONFETTI
0.621 ± 0.017
0.514 ± 0.019
0.257 ± 0.008
0.117 ± 0.007
0.260 ± 0.017
0.962 ± 0.010
0.519 ± 0.008
0.200 ± 0.005
0.052 ± 0.002
0.208 ± 0.005
TimeX cf ++
1.000 ± 0.000
0.999 ± 0.000
0.233 ± 0.009
0.420 ± 0.016
0.872 ± 0.020
1.000 ± 0.000
0.999 ± 0.001
0.624 ± 0.082
0.393 ± 0.069
0.637 ± 0.076
TABLE V : Untargeted counterfactual explanation performance on univariate and multivariate datasets.
Method
KDE ↑
KL-Divergence ↓
MMD ↓
KDE ↑
KL-Divergence ↓
MMD ↓
FreqShapes
SeqComb-UV
Zero
-36.671 ± 0.275
0.144 ± 0.007
0.077 ± 0.004
-90.093 ± 0.312
0.399 ± 0.005
0.167 ± 0.003
Mean
-36.539 ± 0.194
0.147 ± 0.003
0.078 ± 0.006
-83.038 ± 0.271
0.325 ± 0.009
0.111 ± 0.005
b∼BX
-53.855 ± 0.509
0.289 ± 0.003
0.024 ± 0.000
-100.050 ± 0.658
0.498 ± 0.005
0.009 ± 0.000
TimeX a ++
-28.757 ± 2.658
0.096 ± 0.024
0.016 ± 0.004
-57.932 ± 1.684
0.060 ± 0.018
0.078 ± 0.019
SeqComb-MV
LowVar
TABLE VI : Difference between the distribution of different explanation instances and the distribution of original data.
FreqShapes
SeqComb-MV
ECG
Method
AUPRC
AUP
AUR
AUPRC
AUP
AUR
AUPRC
AUP
AUR
LSTM
IG
0.928 ± 0.002
0.778 ± 0.001
0.693 ± 0.002
0.237 ± 0.002
0.515 ± 0.005
0.321 ± 0.003
0.504 ± 0.002
0.613 ± 0.003
0.403 ± 0.002
Dynamask
0.229 ± 0.001
0.342 ± 0.004
0.517 ± 0.001
0.284 ± 0.002
0.637 ± 0.005
0.182 ± 0.002
0.373 ± 0.001
0.630 ± 0.003
0.110 ± 0.001
WinIT
0.417 ± 0.002
0.511 ± 0.003
0.391 ± 0.002
0.352 ± 0.001
0.655 ± 0.003
0.342 ± 0.002
0.363 ± 0.001
0.381 ± 0.002
0.406 ± 0.001
TimeX
0.990 ± 0.000
0.789 ± 0.001
0.796 ± 0.001
0.130 ± 0.002
0.131 ± 0.002
0.475 ± 0.002
0.606 ± 0.002
0.642 ± 0.002
0.444 ± 0.002
TABLE VII : Explainer results with LSTM and CNN predictors on FreqShapes and SeqComb-MV synthetic datasets.
Method
PAM
Epilepsy
Boiler
IG
5.231 ± 0.247
15.467 ± 0.363
123.556 ± 0.807
Dynamask
105.166 ± 0.610
371.092 ± 4.257
3780.433 ± 468.144
TimeX
0.164 ± 0.219
0.204 ± 0.207
0.918 ± 0.203
TimeX a ++
0.161 ± 0.218
0.201 ± 0.208
0.910 ± 0.177
Method
Wafer
FreezerRegular
IG
15.395 ± 0.305
6.745 ± 0.502
TABLE VIII : Inference runtime of occlusion experiments for IG, Dynamask, TimeX , and TimeX a ++ on all real-world datasets.
Method
FreqShapes
LowVar
Epilepsy
CoMTE
42.245 ± 1.146
64.708 ± 8.603
22.992 ± 0.858
AB-CF
39.042 ± 1.139
37.944 ± 2.479
32.750 ± 2.522
M-CELS
4271.181 ± 55.677
5411.136 ± 63.176
1887.034 ± 69.215
CONFETTI
6628.330 ± 103.100
8397.309 ± 172.012
4519.880 ± 453.902
TimeX cf ++
0.075 ± 0.035
0.287 ± 0.119
0.140 ± 0.012
TABLE IX : Inference runtime of counterfactual explanation experiments for one split.
AUPRC
AUP
AUR
FreqShapes
TimeX a ++
0.891 ± 0.002
0.781 ± 0.001
0.662 ± 0.002
w/o LLC
0.225 ± 0.001
0.196 ± 0.001
0.768 ± 0.002
w/o STE
0.779 ± 0.003
0.732 ± 0.003
0.656 ± 0.002
w/o LKL
0.830 ± 0.003
0.646 ± 0.003
0.703 ± 0.002
w/o Ldr
0.194 ± 0.002
0.139 ± 0.002
0.415 ± 0.002
TABLE X : Ablation of TimeX a ++ considering whether there are different losses in our component.
Fig. 4 : The counterfactual explanations robustness analysis on Freqshape and LowVar.
LSTM
CNN
Method
Validity
Confidence
Sparsity
Prox.-L1
Prox.-L2
Validity
Confidence
Sparsity
Prox.-L1
Prox.-L2
Freqshapes
CoMTE
1.000 ± 0.000
0.935 ± 0.014
1.000 ± 0.000
0.562 ± 0.003
0.821 ± 0.006
1.000 ± 0.000
0.922 ± 0.010
1.000 ± 0.000
0.578 ± 0.002
0.847 ± 0.003
AB-CF
1.000 ± 0.000
0.823 ± 0.017
0.664 ± 0.021
0.424 ± 0.007
0.723 ± 0.005
1.000 ± 0.000
0.790 ± 0.010
0.715 ± 0.015
0.451 ± 0.006
0.760 ± 0.005
M-CELS
0.294 ± 0.029
0.267 ± 0.026
0.057 ± 0.006
0.070 ± 0.008
0.192 ± 0.018
0.405 ± 0.025
0.363 ± 0.022
0.055 ± 0.003
0.072 ± 0.005
0.207 ± 0.013
CONFETTI
0.981 ± 0.008
0.506 ± 0.004
0.361 ± 0.005
0.260 ± 0.004
0.568 ± 0.007
0.984 ± 0.010
0.507 ± 0.005
0.360 ± 0.005
0.275 ± 0.004
0.612 ± 0.006
TABLE XI : Targeted counterfactual explanation performance on LSTM and CNN architectures.
Validity
Confidence
Sparsity
Prox.-L1
Prox.-L2
Freqshapes
TimeX cf ++
0.974 ± 0.004
0.964 ± 0.005
0.214 ± 0.005
0.339 ± 0.021
0.757 ± 0.030
w/o STE
0.769 ± 0.055
0.763 ± 0.055
0.174 ± 0.014
0.281 ± 0.031
0.616 ± 0.059
w/o LLC
0.000 ± 0.000
0.007 ± 0.001
0.091 ± 0.001
0.001 ± 0.000
0.002 ± 0.000
w/o LKL
0.936 ± 0.035
0.928 ± 0.034
0.220 ± 0.012
0.342 ± 0.030
0.730 ± 0.048
w/o Ldr
0.955 ± 0.032
0.946 ± 0.032
0.216 ± 0.014
0.512 ± 0.070
1.107 ± 0.128
TABLE XII : Ablation study Counterfactual explanation performance on LSTM and CNN architectures.
Fig. 5 : Attribution explanation performance varying the sparsity parameter r .
Fig. 6 : The hyperparameter r analysis for counterfactual explanations on Freqshape (univariate), SeqComb-MV (multivariate), and ECG (real-world) datasets.
Fig. 7 : Visualization of two attribution explainers and TimeX a ++ on the FreqShapes dataset.
Fig. 8 : The cases visualization of the FreqShapes dataset for counterfactual explanations. We demonstrate pairs of counterfactual cases with prediction 2 and target label 0.
Explainable time series forecasting makes predictions over time interpretable through attributions, structured models, causal reasoning, and counterfactuals.
Time-series explainability remains challenging because discriminative information is often encoded in latent frequency or time-frequency features rather than in the raw signal itself. Existing attribution methods typically operate either in the time domain or in a fixed transform domain, limiting their ability to capture salient information across different representations. We propose XACT, a general framework that learns sparse attribution masks over coefficients from arbitrary invertible time-frequency transforms. We evaluate the framework on the STFT, the continuous wavelet transform, and the discrete wavelet transform. In addition, we extend the virtual inspection layer approach from the STFT to both wavelet transforms, enabling LRP to generate explanations in these representations. On a synthetic dataset, XACT produces precise explanations and is less prone to highlighting spurious features than the tested baselines. Across two real-world datasets, XACT produces sparse and structured explanations, although no method performs best across all quantitative evaluation criteria. These results demonstrate that learning explanations directly in time-frequency representations offers a flexible approach to interpreting deep-learning models for time series data.
Theresa Dahl Frehr, Francisco Pelayo, Lukas Raad +3
Department of Applied Mathematics and Computer Science Technical University of Denmark
Deep learning models achieve high accuracy in time series classification, yet understanding their class-level decision behaviour remains challenging. Explanations for time series must respect temporal dependencies and identify patterns that recur across instances. Existing approaches face three limitations: model-agnostic XAI methods developed for images and tabular data do not readily extend to time series, global explanation synthesis for time series remains underexplored, and most existing global approaches are model-specific. We propose L2GTX, a model-agnostic framework that generates class-wise global explanations by aggregating local explanations from a representative set of instances. L2GTX extracts clusters of parameterised temporal event primitives, such as increasing or decreasing trends and local extrema, together with their importance scores from instance-level explanations produced by LOMATCE. These clusters are merged across instances to reduce redundancy, and an instance-cluster importance matrix is used to estimate global relevance. Under a user-defined instance selection budget, L2GTX selects representative instances that maximise coverage of influential clusters. Events from the selected instances are then aggregated into concise class-wise global explanations. Experiments on six benchmark time series datasets show that L2GTX produces compact and interpretable global explanations while maintaining stable global faithfulness measured as mean local surrogate fidelity.
Ephrem Tibebe Mekonnen, Luca Longo, Lucas Rizzo +1
School of Computer Science, Technological University Dublin Dublin, Ireland · Artificial Intelligence and Cognitive Load Research Lab, University College Cork Cork, Ireland · School of Computer Science and Information Technology, University College Cork Cork, Ireland +1
Faithful explanations of time-series classifiers should identify subsequences that are not only sufficient to preserve a black-box model's prediction, but also necessary for maintaining it. However, existing sufficiency-oriented methods can assign high importance to spurious subsequences that support the prediction without being essential to the model's decision. We introduce TimePNS, a necessity-aware framework for time-series explanation. Inspired by Pearl's counterfactual notion of necessity, TimePNS assesses whether a temporal factor is necessary by intervening on it and measuring whether the original prediction is disrupted. The framework adopts a two-stage design. Stage I learns an identifiable causal generative process together with a sufficiency-oriented explanation mask. Stage II performs counterfactual interventions on temporal factors to derive necessity signals, which supervise a temporal gate that refines the initial explanation by suppressing non-essential components and emphasizing counterfactually necessary ones. Experiments on synthetic and real-world time-series benchmarks show that TimePNS more accurately identifies decision-critical subsequences and consistently improves sufficiency-necessity trade-offs over strong baselines.
Hongnan Ma, Yiwei Shi, Mengyue Yang +1
School of Computer Science, University of Bristol · School of Engineering Mathematics and Technology, University of Bristol