A1203
Title: High-dimensional sparsity-adaptive multiple change-point detection from the bottom up
Authors: Hyeyoung Maeng - Durham University (United Kingdom) [presenting]
Tengyao Wang - London School of Economics (United Kingdom)
Piotr Fryzlewicz - London School of Economics (United Kingdom)
Abstract: The purpose is to introduce a method for detecting multiple change points in the mean of a high-dimensional data sequence. Unlike existing top-down (i.e., divisive) algorithms, a bottom-up method, where neighbouring segments of data are iteratively merged starting from the finest level. Compared to those top-down approaches, the bottom-up approach has better empirical performance in estimating the number of change points for a set of challenging signals (e.g., with frequent changes) but tends to underperform in the localization of the estimated change points. To remedy this, data is premerged to enhance the signal, and the segmented data is post-processed to improve localization accuracy when passing over the data. This helps the bottom-up algorithm perform well in estimating both the number and locations of change points. Another novelty of the method is the ability to identify both sparse and dense changes in an adaptive fashion. To achieve this, $L_2$ and $L_infinity$ test statistics of neighboring segments are computed and aggregated by combining their respective ranks. This makes the bottom-up algorithm data-adaptive in handling varying sparsity under multiple change-point scenarios. It is shown that the consistency of the estimated number and locations of change-points under both i.i.d. Gaussian and possibly dependent and/or non-Gaussian noise. The practicality of the approach is demonstrated through simulations and a real data example of the UK House Price Index data.
