Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A constant-per-iteration likelihood ratio test for online changepoint detection for exponential family models
AU - Ward, Kes
AU - Romano, Gaetano
AU - Eckley, Idris
AU - Fearnhead, Paul
PY - 2024/3/19
Y1 - 2024/3/19
N2 - Online changepoint detection algorithms that are based on (generalised) likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time T, it involves considering O(T) possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to $$O(\log T)$$. This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time T to approximately $$\log T$$. We show that if one wishes to perform the likelihood ratio test for a different one-parameter exponential family model, then exactly the same pruning rule can be used, and again one need only consider approximately $$\log T$$locations at iteration T. Furthermore, we show how we can adaptively perform the maximisation step of the algorithm so that we need only maximise the test statistic over a small subset of these possible locations. Empirical results show that the resulting online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average.
AB - Online changepoint detection algorithms that are based on (generalised) likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time T, it involves considering O(T) possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to $$O(\log T)$$. This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time T to approximately $$\log T$$. We show that if one wishes to perform the likelihood ratio test for a different one-parameter exponential family model, then exactly the same pruning rule can be used, and again one need only consider approximately $$\log T$$locations at iteration T. Furthermore, we show how we can adaptively perform the maximisation step of the algorithm so that we need only maximise the test statistic over a small subset of these possible locations. Empirical results show that the resulting online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average.
KW - Online changepoint
KW - Real-time analysis
KW - Ex-FOCuS
KW - Time series
U2 - 10.1007/s11222-024-10416-6
DO - 10.1007/s11222-024-10416-6
M3 - Journal article
VL - 34
JO - Statistics and Computing
JF - Statistics and Computing
SN - 0960-3174
IS - 3
M1 - 99
ER -