High-dimensional sparsity-adaptive multiple change-point detection

We 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, we adopt a bottom-up (i.e. agglomerative) approach, whereby we iteratively merge neighboring segments of data starting from the finest level.

This is particularly useful for signals with frequent change-points, since local evidence is assessed before segments are combined into coarser summaries.

We compute $L_2$- and $L_\infty$-aggregated test statistics of neighboring segments and combine the information from their respective ranks, which makes the method adaptive in handling different degrees of change-point sparsity.

We show the consistency of the estimated number and locations of change-points under both iid Gaussian and possibly dependent and/or non-Gaussian noise.

The practicality of our approach is demonstrated through simulations and a real data example involving the UK House Price Index data.