  Monte Carlo integration with variance reduction by means of control variates
can be implemented by the ordinary least squares estimator for the intercept in
a multiple linear regression model with the integrand as response and the
control variates as covariates. Even without special knowledge on the
integrand, significant efficiency gains can be obtained if the control variate
space is sufficiently large. Incorporating a large number of control variates
in the ordinary least squares procedure may however result in (i) a certain
instability of the ordinary least squares estimator and (ii) a possibly
prohibitive computation time. Regularizing the ordinary least squares estimator
by preselecting appropriate control variates via the Lasso turns out to
increase the accuracy without additional computational cost. The findings in
the numerical experiment are confirmed by concentration inequalities for the
integration error.
