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Inherently Interpretable Time Series Classification via Multiple Instance Learning
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Proposes MILLET, a framework that reframes deep time series classifiers (FCN, ResNet, InceptionTime) as multiple instance learning with time-point predictions and four pooling variants (including the new Conjunctive pooling), giving inherent interpretability with predictive gains on 85 UCR datasets and a new synthetic WebTraffic dataset.
Problem
Deep learning time series classifiers are black boxes that aggregate time-point representations with global average pooling, providing no inherent localisation of class-discriminatory motifs and limiting trust and adoption.
Approach
Treat each time series as a MIL bag of time points and replace global average pooling with MIL pooling methods (Attention, Instance, Additive, and the new Conjunctive pooling) so each time point yields a class prediction, giving interpretations in a single forward pass; adds positional encoding, replicate padding, and dropout.
Key results
- On WebTraffic, MILLET improves mean accuracy across backbones from 0.850 to 0.874, with Conjunctive InceptionTime reaching 0.940.
- On 85 UCR datasets, Conjunctive InceptionTime reaches mean accuracy 0.856 vs 0.853 for InceptionTime, and is comparable to HC2 and Hydra-MR on balanced accuracy.
- MILLET achieves mean AOPCR of 17.531 on WebTraffic vs 15.415 for CAM and -0.692 for SHAP, and is reported over 800 times faster than SHAP.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace GAP pooling with Conjunctive pooling | FCN · UCR 85 datasets | accuracy: 0.828 -> 0.838 | Helped |
| replace GAP pooling with Conjunctive pooling | ResNet · UCR 85 datasets | accuracy: 0.843 -> 0.845 | Helped |
| replace GAP pooling with Conjunctive pooling | InceptionTime · UCR 85 datasets | accuracy: 0.853 -> 0.856 | Helped |
| replace GAP pooling with Conjunctive pooling | FCN · UCR 85 datasets | NLL: 1.038 -> 0.973 | Helped |
| replace GAP pooling with Conjunctive pooling | ResNet · UCR 85 datasets | NLL: 1.091 -> 1.035 | Helped |
| replace GAP pooling with Conjunctive pooling | InceptionTime · UCR 85 datasets | NLL: 1.078 -> 1.085 | Hurt |
| replace GAP pooling with Conjunctive pooling | FCN · UCR 85 datasets | AUROC: 0.929 -> 0.934 | Helped |
| replace GAP pooling with Conjunctive pooling | ResNet · UCR 85 datasets | AUROC: 0.937 -> 0.939 | Helped |
| replace GAP pooling with Conjunctive pooling | InceptionTime · UCR 85 datasets | balanced accuracy: 0.832 -> 0.834 | Helped |
| replace GAP pooling with MIL pooling | MILLET models across backbones · UCR 85 datasets | AOPCR: 5.71 -> 6.00 | Helped |
| replace GAP pooling with MIL pooling | TSC models across backbones · WebTraffic | accuracy: 0.850 -> 0.874 | Helped |
| use MILLET explanations instead of CAM | WebTraffic explanations · WebTraffic | AOPCR: 15.415 -> 17.531 | Helped |
Surprising findings
- SHAP yields negative AOPCR on several WebTraffic backbones, meaning its explanations are worse than random.
- Attention pooling performs poorly on UCR interpretability because its scores are class-agnostic.
Limitations
- Evaluated only on univariate, equal-length time series with deep learning backbones; other TSC families not explored.
- Hyperparameters were not tuned, and MILLET explanations can lack full coverage of discriminatory regions, lowering NDCG relative to CAM for InceptionTime.
- On UCR, MILLET does not dominate GAP interpretability for ResNet ensembles.
Experimental setup
Datasets: UCR Time Series Classification Archive (85 univariate datasets) WebTraffic (synthetic)
Benchmarks: UCR archive (85 datasets) WebTraffic
Metrics: accuracy balanced accuracy AUROC NLL AOPCR NDCG@n
Baselines: CAM SHAP HC2 Hydra-MR FCN ResNet InceptionTime
Builds on: MI-Net Fully Convolutional Networks ResNet InceptionTime Class activation mapping
Closest papers by meaning
- TimeMIL: Advancing Multivariate Time Series Classification via a Time-aware Multiple Instance Learning (ICML 2024 · similarity 0.87)
- MPTSNet: Integrating Multiscale Periodic Local Patterns and Global Dependencies for Multivariate Time Series Classification (AAAI 2025 · similarity 0.85)
- MSGNet: Learning Multi-Scale Inter-series Correlations for Multivariate Time Series Forecasting (AAAI 2024 · similarity 0.85)
- TAIL-MIL: Time-Aware and Instance-Learnable Multiple Instance Learning for Multivariate Time Series Anomaly Detection (AAAI 2025 · similarity 0.84)
- TSLANet: Rethinking Transformers for Time Series Representation Learning (ICML 2024 · similarity 0.84)
- Abstracted Shapes as Tokens - A Generalizable and Interpretable Model for Time-series Classification (NeurIPS 2024 · similarity 0.84)
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