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Building a stable classifier with the inflated argmax
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Proposes selection stability for classifiers and an "inflated argmax" selection rule that, combined with subbagging of any base classifier, gives provable label-stability guarantees without distributional assumptions.
Problem
Argmax-based classifiers are highly unstable: small perturbations of training data can flip the predicted label, even when the underlying probability estimators are algorithmically stable.
Approach
Define selection stability on predicted label sets and propose the inflated argmax, an epsilon-compatible set-valued selection rule that returns all labels that could be the maximum under small perturbations; paired with bagging (tail-stable probability estimates), it yields assumption-free selection stability.
Key results
- Subbagging with inflated argmax reduces maximum instability from 0.966 (subbagged argmax) to 0.000 on Fashion-MNIST across all 10,000 test points.
- Inflated argmax on subbagged model gives correct-singleton rate 0.886 vs 0.893 for subbagged argmax, with average set size 1.018.
- Inflated argmax on the base (non-bagged) model barely changes stability (max instability 1.000 both ways) while costing little accuracy (0.873 vs 0.879).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add inflated argmax to subbagging (ablation) | Subbagging + argmax · Fashion-MNIST test | maximum instability: 0.966 -> 0.000 | Helped |
| Add inflated argmax to subbagging (ablation) | Subbagging + argmax · Fashion-MNIST test | correct-single frequency: 0.893 (0.003) -> 0.886 (0.003) | Hurt |
| Add inflated argmax to subbagging (ablation) | Subbagging + argmax · Fashion-MNIST test | average set size: 1.000 (0.000) -> 1.018 (0.001) | Hurt |
| Add subbagging (ablation) | Argmax · Fashion-MNIST test | maximum instability: 1.000 -> 0.966 | Helped |
| Add subbagging (ablation) | Argmax · Fashion-MNIST test | correct-single frequency: 0.879 (0.003) -> 0.893 (0.003) | Helped |
| Add inflated argmax (ablation) | Argmax · Fashion-MNIST test | maximum instability: 1.000 -> 1.000 | No clear effect |
| Add inflated argmax (ablation) | Argmax · Fashion-MNIST test | correct-single frequency: 0.879 (0.003) -> 0.873 (0.003) | Hurt |
| Add inflated argmax (ablation) | Argmax · Fashion-MNIST test | average set size: 1.000 (0.000) -> 1.015 (0.001) | Hurt |
Surprising findings
- Inflating the argmax alone on a single unbagged model does not improve worst-case stability at all; the bagging step is essential.
Limitations
- Bagging with many bags is computationally intensive.
- Stability is measured on a single benchmark (Fashion-MNIST) with a small LeNet-style model.
- Guarantee is for set-level label consistency (nonempty intersection), a relatively weak notion; stricter measures such as Jaccard are left open.
Experimental setup
Datasets: Fashion-MNIST
Benchmarks: Fashion-MNIST
Metrics: correct singleton frequency average set size maximum instability over test points
Baselines: argmax top-k fixed-margin selection rule thresholding
Builds on: algorithmic stability bagging subbagging tail stability
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