Séance du 21 octobre 2024

Séance organisée par Guillermo Durand et Thanh Mai Pham Ngoc

Lieu : IHP,  amphi Yvonne Choquet-Bruhat (second étage du bâtiment Perrin)

14.00 : Zacharie Naulet (INRAE)

Titre :  On the impossibility of detecting a late change-point in the preferential attachment random graph model

Résumé : We consider the problem of late change-point detection under the preferential attachment random graph model with time dependent attachment function. This can be formulated  as a hypothesis testing problem where the null hypothesis corresponds to a preferential attachment model with a constant affine attachment parameter $\delta_0$ and the alternative corresponds to a preferential attachment model where the affine attachment parameter changes from $\delta_0$ to $\delta_1$ at a time $\tau_n = n - \Delta_n$ where $0\leq \Delta_n \leq n$ and $n$ is the size of the graph. It was conjectured in Bet et al. that when observing only the unlabeled graph, detection of the change is not possible for $\Delta_n = o(n^{1/2})$. In this work, we make a step towards proving the conjecture by proving the impossibility of detecting the change when $\Delta_n = o(n^{1/3})$. We also study change-point detection in the case where the labelled graph is observed and show that change-point detection is possible if and only if $\Delta_n \to \infty$, thereby exhibiting a strong difference between the two settings.

Joint work with Ibrahim Kaddouri and Elisabeth Gassiat.

15.00 : Sarah Kaakaï (Université Sorbonne Paris Nord )

Titre :  A deep learning scheme for adaptative decision-making using ergodic BSDEs

Résumé :  In this talk, I will present a new numerical method for a class of forward utilities in a stochastic factor model. I will first Strat by giving a brief overview  of forward utilities, which are particularly interesting tools for formulating time-consistent strategies adjusted to the information flow in non-stationary and uncertain environment. In this work, we take advantage of recent results on the representation of forward utilities using  ergodic Backward Stochastic Differential Equations (eBSDEs). By establishing a connection between the solution of the ergodic BSDE and that of an associated BSDE with random terminal time, we develop two new deep learning numerical schemes for both eBSDEs and forward utilities.  Finally, I will present some numerical examples, and more recent developments that extend this  framework  to decision-making in a switching environment. 

16.00 : Yating Liu (Université Paris Dauphine - PSL)

Titre :  A statistical approach for simulating the density solution of a McKean-Vlasov equation

Résumé :  We prove convergence results of the simulation of the density solution to the McKean-Vlasov equation, when the measure variable is in the drift. Our method builds upon adaptive nonparametric results in statistics that enable us to obtain a data-driven selection of the smoothing parameter in a kernel-type estimator. In particular, we give a generalized Bernstein inequality for Euler schemes with interacting particles and obtain sharp deviation inequalities for the estimated classical solution. We complete our theoretical results with a systematic numerical study and gather empirical evidence of the benefit of using high-order kernels and data-driven smoothing parameters. This is a joint work with M. Hoffmann.