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Online Adaptive Anomaly Thresholding with Confidence Sequences
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Proposes a distribution-free online anomaly thresholding algorithm built on confidence sequences for quantiles, with abstention, change detection, and offline-data warm-starting, with guarantees on FP/FN and abstains.
Problem
Choosing anomaly score thresholds online and unsupervised under distribution shift, with guarantees on false positives, false negatives, and abstentions, and without distributional assumptions.
Approach
Treats thresholding as online quantile estimation and uses confidence sequences on the p-th quantile to abstain inside the CS and flag anomalies/benign outside it; detects shifts via non-intersecting forward/backward CS and uses offline datasets only when their CS intersects the online CS.
Key results
- On synthetic streams without shift and with offline data, the method achieves 0 ± 0 FP+FN with 12.1% abstains, versus 5.3 ± 3.7 for τ 30% and 9.1 ± 3.6 for DSpot in the no-shift setting; with shift and no offline data, 5.2 ± 1.3 FP+FN vs 195 ± 71 for τ 30%.
- On MNIST one-class anomaly detection, NN+A5 under shift yields 8.8 mistakes-level FP+FN (2.3 std) and 210 abstains, versus DSpot 129.5 FP+FN with 150 abstains, in the shift setting.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use confidence-sequence thresholding instead of EQ | Online anomaly thresholding · Synthetic, no shift and no offline data | FP+FN: 3.9 ± 2.1 -> 0 ± 0 | Helped |
| Use adaptive thresholding with change detection instead of τ 30% | Online anomaly thresholding · Synthetic, shift and no offline data | FP+FN: 195 ± 71 -> 5.2 ± 1.3 | Helped |
| Use offline data for warm-starting | Online anomaly thresholding · Synthetic, no shift | Abs. %: 12.1 ± 1.4 -> 9.3 ± 1.2 | Helped |
| Use offline data for warm-starting | Online anomaly thresholding · Synthetic, shift | Abs. %: 32.7 ± 9.1 -> 18.9 ± 4.1 | Helped |
| Use NN+A5 instead of DSpot | MNIST anomaly detection · MNIST, static | FP+FN: 78.1 ± 2.5 -> 2.1 ± 0.2 | Helped |
| Use NN+A5 instead of DSpot | MNIST anomaly detection · MNIST, shift | FP+FN: 129.5 ± 10.2 -> 8.8 ± 2.3 | Helped |
| Use NN+A5 instead of DSpot | MNIST anomaly detection · MNIST, shift | abstains: 150 ± 0 -> 210 ± 8 | Hurt |
Surprising findings
- Any scheme that never abstains incurs order sqrt(T) expected mistakes on an i.i.d. stream, so abstention is necessary for constant mistakes.
Limitations
- Theory assumes temporal independence of samples
- Requires change points to be far apart and detectable (Assumption 5.1)
- Does not handle gradual drift or temporally dependent scores
Experimental setup
Datasets: MNIST synthetic Normal streams Pareto streams two real cloud anomaly score streams (DS1, DS2)
Benchmarks: MNIST one-class anomaly detection synthetic streams real cloud anomaly score streams DS1 and DS2
Metrics: FP+FN mistakes abstain percentage alert volume
Baselines: static threshold tau 30% DSpot EQ empirical quantile with online gradient descent IF+A1 NN+A1
Builds on: Howard and Ramdas 2022 quantile confidence sequences Shekhar and Ramdas 2023 change detection with confidence sequences SPOT/DSpot
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