Localizing support-set changepoints in high-dimensional linear models

Existing changepoint localization methods for high-dimensional regression models typically focus on scenarios where the regression coefficients follow a piecewise constant structure over time. However, this assumption can be overly restrictive in many practical applications due to the complex temporal dynamics of the coefficients. Additionally, in sparse regression models, the primary interest sometimes lies not in changes in the magnitudes of the coefficients, but rather in identifying the time points at which covariates transition between inactive and active states. In this paper, we propose a simple yet effective method for detecting changepoints in the support set, allowing the coefficients to vary continuously over time. Theoretically, we establish the minimax lower bound on the localization error that nearly matches the upper bound achieved by the proposed method, and show that the required signal-to-noise condition is essentially the weakest possible based on the impossibility region in a minimax sense. Extensive numerical studies further demonstrate the superior performance of the proposed method. It is also applied in the analysis of real air quality data from Northern Taiwan in 2015. An R package "SCP" is developed to implement the proposed method.