Change-point estimation in high dimensional linear regression models via sparse group Lasso

In this paper, we consider the problem of estimating change-points in a high dimensional linear regression model. In the model considered, the linear coefficients have high dimensions, are sparse, and undergo multiple changes in the given data samples. Our goal is to estimate the number and locations of change-points and sparse coefficients in each of the intervals between change-points. We develop a sparse group Lasso (SGL) based approach to solve the proposed problem. Under certain assumptions and using a properly chosen regularization parameter, we show that estimation error of linear coefficients and change-point locations can be expressed as a function of the number of data point, the dimension of the model and the sparse level. From the derived error function, we then characterize the conditions under which the proposed estimator is consistent. Numerical simulations are provided to illustrate the performance of our approach.