A Constant-per-Iteration Likelihood Ratio Test for Online Changepoint Detection for Exponential Family Models

TL;DR

This paper introduces an efficient online changepoint detection method for exponential family models that maintains a constant average computational cost per iteration by using pruning techniques similar to the FOCuS algorithm.

Contribution

It extends the pruning approach of FOCuS to general exponential family models, enabling efficient online changepoint detection across various distributions.

Findings

Achieves constant average per-iteration computational cost.

Effective detection of changepoints in diverse exponential family models.

Utilizes adaptive maximization over a small subset of locations.

Abstract

Online changepoint detection algorithms that are based on 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.