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.

通过控制变量减少方差的蒙特卡罗积分可以通过对被积函数作为响应、控制变量作为协变量的多元线性回归模型中的截距的普通最小二乘估计来实现。即使没有关于被积函数的特殊知识，如果控制变量空间足够大，也可以获得显着的效率增益。然而，在普通最小二乘程序中并入大量控制变量可能会导致 (i) 普通最小二乘估计器的某些不稳定性和 (ii) 可能的计算时间过长。通过 Lasso 预选适当的控制变量来正则化普通最小二乘估计器，结果证明可以在不增加计算成本的情况下提高准确性。