Scalable Multiple Changepoint Detection for Functional Data Sequences

TL;DR

This paper introduces a scalable method for detecting multiple changepoints in functional data sequences, effectively identifying changes in mean and covariance with high accuracy and robustness across various scenarios.

Contribution

The paper presents the Multiple Changepoint Isolation (MCI) method, combining projections and an augmented fused lasso to improve detection accuracy and scalability in functional data.

Findings

Accurately detects number and locations of changepoints in diverse scenarios

Outperforms recent functional changepoint detection methods

Demonstrates robustness and linear scalability with sample size

Abstract

We propose the Multiple Changepoint Isolation (MCI) method for detecting multiple changes in the mean and covariance of a functional process. We first introduce a pair of projections to represent the variability "between" and "within" the functional observations. We then present an augmented fused lasso procedure to split the projections into multiple regions robustly. These regions act to isolate each changepoint away from the others so that the powerful univariate CUSUM statistic can be applied region-wise to identify the changepoints. Simulations show that our method accurately detects the number and locations of changepoints under many different scenarios. These include light and heavy tailed data, data with symmetric and skewed distributions, sparsely and densely sampled changepoints, and mean and covariance changes. We show that our method outperforms a recent multiple functional changepoint detector and several univariate changepoint detectors applied to our proposed projections. We also show that MCI is more robust than existing approaches and scales linearly with sample size. Finally, we demonstrate our method on a large time series of water vapor mixing ratio profiles from atmospheric emitted radiance interferometer measurements.