B1396
Title: Adaptive high-dimensional 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 impact of the sparsity of change has been actively studied in high-dimensional settings. While many methods have been developed for detecting sparse changes, few are available for a more general alternative where sparse and dense changes exist. It is known that the $L_2$ aggregation performs well in detecting dense and gentle changes, while the $L_infinity$ aggregation is more effective for detecting sparse and strong changes. To achieve robustness against sparsity in detecting changepoints, both $L_2$ and $L_infinity$ aggregations are used by combining their ranks. In a bottom-up way, these aggregations are performed by consecutively merging neighbouring segments of the data starting from the finest level. Compared to many existing variants of binary segmentation, which operate a top-down (i.e. divisive) algorithm, the bottom-up approach performs well for a set of challenging signals, e.g. with frequent changepoints, but tends to underperform in localisation of the estimated change points. A new bottom-up algorithm is proposed, which works well in estimating both the number and locations of changepoints. The practicality of the approach is demonstrated through simulations and real data examples.
