  This paper studies the high-dimensional mixed linear regression (MLR) where
the output variable comes from one of the two linear regression models with an
unknown mixing proportion and an unknown covariance structure of the random
covariates. Building upon a high-dimensional EM algorithm, we propose an
iterative procedure for estimating the two regression vectors and establish
their rates of convergence. Based on the iterative estimators, we further
construct debiased estimators and establish their asymptotic normality. For
individual coordinates, confidence intervals centered at the debiased
estimators are constructed.
  Furthermore, a large-scale multiple testing procedure is proposed for testing
the regression coefficients and is shown to control the false discovery rate
(FDR) asymptotically. Simulation studies are carried out to examine the
numerical performance of the proposed methods and their superiority over
existing methods. The proposed methods are further illustrated through an
analysis of a dataset of multiplex image cytometry, which investigates the
interaction networks among the cellular phenotypes that include the expression
levels of 20 epitopes or combinations of markers.
