Public Thesis Defense - LIDAM

Enhancing Monte Carlo integration by control variates and statistical learning by Aigerim ZHUMAN

Pour l’obtention du grade académique de Doctorat en Sciences

This thesis focuses on enhancing Monte Carlo integration through the use of control variates, a variance reduction technique involving special functions with known integrals. Such techniques become crucial when the sampling process is complex or the integrand is computationally intensive. First, control variates are combined with adaptive importance sampling, another variance reduction method applicable to inference in Bayesian formulations of the linear and logistic regression models. Then the focus is on improving the standard Monte Carlo procedure by constructing control variates using the nearest neighbor approach. The proposed method finds applications in option pricing and optimal transport problems. In the next project, the control variate technique is applied to calculating the Sliced-Wasserstein distance, represented as an integral over the unit sphere, using spherical harmonics as control variates. This approach is applied to the image classification problem. Finally, control variates are built using the random forest method, different types of random forests being compared.

Jury members :

• Prof. Johan Segers (UCLouvain) (Supervisor)
• Prof. Rainer von Sachs (UCLouvain) (Chairperson)
• Prof. Eugen Pircalabelu (UCLouvain)
• Prof. François Portier (ENSAI, France)
• Prof. Philippe Lambert (ULiège)

Pay attention : the public defense of Aigerim ZHUMAN will also take place in the form of a videoconference

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