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Reducing sequential change detection to sequential estimation
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Proposes repeated-FCS-Detector, a sequential change detector that starts a new forward confidence sequence at each time step and fires when their intersection empties, giving ARL >= 1/alpha under minimal assumptions.
Problem
Sequential change detection of a parameter or functional of a data stream under minimal distributional assumptions (possibly dependent, nonparametric), with false-alarm (ARL) control and small detection delay.
Approach
Reduce change detection to sequential estimation: begin a new (1-alpha) forward confidence sequence at every time step and declare a change when the intersection of all active CSs becomes empty. This needs only forward CSs (unlike BCS-Detector, which needs backward CSs and so independence), and it improves the ARL lower bound by about a factor of 2 while matching BCS-Detector's delay; it also gene
Key results
- Proves the repeated-FCS-Detector achieves ARL at least 1/alpha, improving the BCS-Detector lower bound from 1/(2alpha)-3/2 by roughly a factor of 2.
- Detection delay bound matches BCS-Detector: E_T[(tau-T)^+] <= 3/(1-alpha) * u(theta_0, theta_1, T).
- For bounded mean change with i.i.d. data, delay is O(log(1/(alpha K))/K) where K is a KL-based quantity, which is order optimal (Pinsker gives a weaker O(log(1/(alpha Delta))/Delta^2) bound).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the backward confidence sequences with a new forward confidence sequence at each observation | BCS-Detector · Non-partitioned SCD, no change | average run length (ARL): 1/(2\alpha) - 3/2 -> 1/\alpha | Helped |
| Replace the backward confidence sequences with a new forward confidence sequence at each observation | BCS-Detector · Non-partitioned SCD, change detected | detection delay | No clear effect |
| Use level-$(1-6\alpha/(n^2\pi^2))$ confidence sequences in round n (ablation) | repeated-FCS-Detector · Non-partitioned SCD, no change | probability of false alarms: \mathbb{P}_{\infty}(\tau<\infty) \leq \alpha | Helped |
| Use level-$(1-6\alpha/(n^2\pi^2))$ confidence sequences in round n (ablation) | repeated-FCS-Detector · SCD after a change | detection delay: logarithmic dependence on T | Hurt |
Surprising findings
- A PFA-controlling variant (level 1-6alpha/(n^2 pi^2) at round n) gives ARL infinity but a detection delay that is generally unbounded in the worst case over T.
Limitations
- Detection delay analysis requires an assumption that CS width shrinks deterministically to zero and, for the mean example, i.i.d. data and post-change independence from pre-change data.
- Worst-case delay is not bounded under the PFA-controlling variant.
Experimental setup
Metrics: average run length expected detection delay
Baselines: BCS-Detector empirical-Bernstein CS detector e-detector framework
Builds on: BCS-Detector Lorden's reduction e-detectors betting confidence sequences CUSUM
Closest papers by meaning
- Sequential Changepoint Detection via Backward Confidence Sequences (ICML 2023 · similarity 0.93)
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- Accurate Evaluation of Quickest Changepoint Detectors via Non-parametric Survival Analysis (ICML 2026 · similarity 0.87)
- Optimal Online Change Detection via Random Fourier Features (NeurIPS 2025 · similarity 0.87)
- Fixed-Confidence Multiple Change Point Identification under Bandit Feedback (ICML 2025 · similarity 0.84)
- Conjugate Bayesian Two-step Change Point Detection for Hawkes Process (NeurIPS 2024 · similarity 0.83)
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