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Control variate selection for Monte Carlo integration

Author

Listed:
  • Leluc, Rémi
  • Portier, François
  • Segers, Johan

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

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.

Suggested Citation

  • Leluc, Rémi & Portier, François & Segers, Johan, 2021. "Control variate selection for Monte Carlo integration," LIDAM Reprints ISBA 2021024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2021024
    DOI: https://doi.org/10.1007/s11222-021-10011-z
    Note: In: Statistics and Computing, Vol. 31, 50 (2021)
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    Cited by:

    1. Leluc, Rémi & Portier, François & Zhuman, Aigerim & Segers, Johan, 2023. "Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence," LIDAM Discussion Papers ISBA 2023019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Leluc, Rémi & Portier, François & Segers, Johan & Zhuman, Aigerim, 2022. "A Quadrature Rule combining Control Variates and Adaptive Importance Sampling," LIDAM Discussion Papers ISBA 2022018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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