2019/06/26 by Wang, Daren, Zhao, Zifeng, Lin, Kevin +1 · 1 citation
#Change point detection #FOS: Mathematics #Statistics Theory (math.ST) #high-dimensional regression
paper · doi:10.48550/arxiv.1906.11364
Detecting when the underlying distribution changes for the observed time series is a fundamental problem arising in a broad spectrum of applications. In this paper, we study multiple change-point localization in the high-dimensional regression setting, which is particularly challenging as no direct observations of the parameter of interest is available. Specifically, we assume we observe \ xt, yt\t=1n where \ xt\t=1n are p-dimensional covariates, \yt\t=1n are the univariate responses satisfying 𝔼(yt) = xt^\top βt^* for 1≤ t ≤ n and \βt^*\t=1n are the unobserved regression coefficients that change over time in a piecewise constant manner. We propose a novel projection-based algorithm, Variance Projected Wild Binary Segmentation~(VPWBS), which transforms the original (difficult) problem of change-point detection in p-dimensional regression to a simpler problem of change-point detection in mean of a one-dimensional time series. VPWBS is shown to achieve sharp localization rate Op(1/n) up to a log factor, a significant improvement from the best rate Op(1/√(n)) known in the existing literature for multiple change-point localization in high-dimensional regression. Extensive numerical experiments are conducted to demonstrate the robust and favorable performance of VPWBS over two state-of-the-art algorithms, especially when the size of change in the regression coefficients \βt^*\t=1n is small.