An Efficient Two Step Algorithm for High Dimensional Change Point Regression Models Without Grid Search

We propose a two step algorithm based on \ell_1/\ell_0regularization for the detection and estimation of parameters of a high dimensional change point regression model and provide the corresponding rates of convergence for the change point as well as the regression parameter estimates. Importantly, the computational cost of our estimator is only 2\cdotpasso(n,p) where Lasso(n,p)represents the computational burden of one Lasso...