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\\ ==== Prochaine séance ====
[[seminaires:SemDoc:index|Séminaire doctoral du LPSM]]\\
Jeudi 18 décembre 2025, 17 heures 30, Jussieu - Salle Paul Lévy (16-26 209)\\
**Chloé Hashimoto-Cullen + Emmanuel  Gnabeyeu-Mbiada**  //Time Series Forecasting with Variational Autoencoders: A PAC-Bayesian-driven Algorithm (C. Hashimoto-Cullen) + On Inhomogeneous Fractional Square-Root Process: Microstructural Foundation and Weak Stationarity Theory (E.  Gnabeyeu-Mbiada)//
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Time series forecasting is increasingly important to applications ranging from the medical domain to finance and electricity consumption management, to name but a few. Yet, despite its practical importance, few algorithms come with strong theoretical guarantees, which means that there are no safeguards against sudden performance drops in new implementations. We propose a variational framework for time series forecasting, grounded in a novel PAC-Bayesian bound. Building on this bound, we introduce PAVE, a lightweight VQ-VAE-inspired algorithm. We provide new PAC-Bayesian bounds on the reconstruction error of time series VQ-VAE algorithms alongside a novel empirical framework.


We investigates the asymptotic behavior of time-modulated, renormalized, heavy-tailed,
and nearly unstable Hawkes processes. We show that, under appropriate scaling, both the intensity
processes and the rescaled Hawkes processes converge to a mean-reverting, time-inhomogeneous fractional square-root process and its integrated counterpart, respectively. We further investigate the properties of such limiting scaled time-inhomogeneous Volterra equations, including moment bounds, path regularity and stationarity through the lens of a weaker notion of stationarity referred to as "fake stationary regime" in the sense that all marginal distributions share the same expectation and variance. This offers a tractable proxy to stationarity in the finite horizon and lead to the classical weak L^2-stationarity in the long run (Functional weak asymptotics).
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Organisation : Sacha Quayle, Thomas Le Guerch, Nina Drobac, Pierre Faugere, Maxime Guellil, Eyal Vayness

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\\ ==== Séances passées ====
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