  We consider high-dimensional generalized linear models when the covariates
are contaminated by measurement error. Estimates from errors-in-variables
regression models are well-known to be biased in traditional low-dimensional
settings if the error is unincorporated. Such models have recently become of
interest when regularizing penalties are added to the estimation procedure.
Unfortunately, correcting for the mismeasurements can add undue computational
difficulties onto the optimization, which a new tool set for practitioners to
successfully use the models. We investigate a general procedure that utilizes
the recently proposed Imputation-Regularized Optimization algorithm for
high-dimensional errors-in-variables models, which we implement for continuous,
binary, and count response type. Crucially, our method allows for off-the-shelf
linear regression methods to be employed in the presence of contaminated
covariates. We apply our correction to gene microarray data, and illustrate
that it results in a great reduction in the number of false positives whilst
still retaining most true positives.
