Séminaire des doctorant·es SO

par Louison Bocquet-Nouaille (ONERA), Sofian Charaabi (IMT), Mathis Deronzier (IMT)

mardi 17 mars 2026, 11:15 → 12:15 Europe/Paris

Salle K. Johnson (1R3, 1er étage)

Louison Bocquet-Nouaille (ONERA)

Control variates for variance-reduced ratio of means estimators: application to Extreme Value Index estimation

Control variates are a classical variance reduction technique for Monte Carlo estimation and can be viewed as a form of transfer learning, where information from a correlated source variable improves inference on a target variable. In many applications the quantity of interest can be expressed as a ratio of expectations. We propose a new variance-reduced estimator for such ratios by applying control variates to both numerator and denominator. We derive jointly optimal control variate coefficients that directly minimize the variance of the ratio estimator and guarantee variance reduction. The method naturally extends to approximate control variates, and fits within a semi-supervised setting where a small set of coupled target and source observations is combined with a large amount of unpaired source data.

We illustrate the practical value of the method on an aerospace reliability case study, achieving significant efficiency gains. We further apply it to the estimation of the Extreme Value Index (EVI), a key parameter in Extreme Value Theory that characterizes tail behavior and governs the frequency of extreme events. Classical EVI estimators, such as the Hill estimator, suffer from high variance due to their reliance on a small number of extreme observations. Rewriting the Hill estimator as a ratio of empirical means allows us to integrate it into our framework, leading to substantial variance reduction when target and source variables exhibit tail dependence. 

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Sofian Charaabi (IMT) 

We establish a central limit theorem for a rank-based estimator of the first-order Sobol sensitivity index. The analysis relies on a strong Gaussian approximation for the underlying empirical processes and ordered statistics, which enables a precise characterization of the estimator’s asymptotic distribution and proves its convergence to a normal law. This framework also supports indexation by a broader class of functions, opening the door to new applications in sensitivity analysis.

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Mathis Deronzier (IMT) 

Gaussian Regression under Fairness Constraint 

Algorithmic fairness has become an ethical and legal concern for artificial intelligence systems. However, while Gaussian processes underpin transparent machine-learning methods with critical applications, the literature has little studied fair Gaussian-process regression. This article contributes to bridging this gap by introducing a Gaussian-process framework that allows to intelligibly control for three objectives: accuracy, statistical parity, and no disparate treatment. We demonstrate how to solve a maximum-of-distribution problem from a specific Gaussian process to obtain a regression function that achieves a trade-off between accuracy and fairness. On this basis, we derive asymptotic results together with a numerical implementation and showcase the performance of our method through experiment and benchmark comparisons.