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Rare Event Detection in Imbalanced Multi-Class Datasets Using an Optimal MIP-Based Ensemble Weighting Approach
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Proposes a mixed integer programming weighting scheme with elastic net regularization that selects K classifiers from a pool and assigns per-class weights to a weighted voting ensemble for imbalanced multi-class rare event detection in CPS.
Problem
Weighted voting ensembles for imbalanced multi-class rare event detection in cyber-physical systems lack an optimal, adaptable way to assign per-class classifier weights and select a fixed number of classifiers.
Approach
Formulates classifier-class weight assignment and K-classifier selection as a MIP that maximizes validation-accuracy-weighted ensemble accuracy with an elastic net penalty, plus constraints ensuring weighted accuracy exceeds uniform-weight accuracy per class and overall.
Key results
- MIP improves balanced accuracy by 0.99% to 7.31% over six weighting schemes, averaging 4.53% across datasets and ensemble sizes K=2 to 8.
- Average macro precision, recall, and F1 gains are 4.63%, 4.60%, and 4.61% respectively.
- For K=3 and n=8 on D2, MIP computes weights in 0.35 s versus 1 to 3.12 s for other approaches.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MIP-based classifier-class weighting instead of the six existing weighting schemes | Ensembles on D1–D4 across K=2–8 · D1–D4, K=2–8 | Balanced accuracy: 4.53% | Helped |
| Use MIP-based classifier-class weighting instead of the six existing weighting schemes | Ensembles on D1–D4 across K=2–8 · D1–D4, K=2–8 | Macro-averaged precision: 4.63% | Helped |
| Use MIP-based classifier-class weighting instead of the six existing weighting schemes | Ensembles on D1–D4 across K=2–8 · D1–D4, K=2–8 | Macro-averaged recall: 4.60% | Helped |
| Use MIP-based classifier-class weighting instead of the six existing weighting schemes | Ensembles on D1–D4 across K=2–8 · D1–D4, K=2–8 | Macro-averaged F1-score: 4.61% | Helped |
| Increase ensemble size K | MIP relative to other weighting schemes · D1–D4 | Performance improvement | Helped |
| Use MIP weighting | Ensembles on D1–D4 · D1–D4, K=2–8 | Macro-averaged AUPRC | Helped |
Surprising findings
- Gains over other schemes were lower on the highly imbalanced datasets D1 and D2 than on the moderately imbalanced D3 and D4.
- A classifier with below-average overall accuracy (SVM) received high MIP weights for classes where it performed well.
Limitations
- Performance gains are smaller on highly imbalanced datasets (D1, D2).
- MIP solver time complexity cannot be derived analytically; relies on proprietary Gurobi solver.
- Hyperparameters lambda and alpha were tuned by incremental search per dataset.
Experimental setup
Datasets: LeakDB NSL-KDD SG-MITM CIC-IDS2017
Benchmarks: LeakDB NSL-KDD SG-MITM CIC-IDS2017
Metrics: balanced accuracy macro-averaged precision macro-averaged recall macro-averaged F1-score AUPRC runtime speedup
Baselines: UW-PC UW-PCC WA-PC WA-PCC DE BMA
Builds on: elastic net regularization Bayesian model averaging differential evolution
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