Séminaire PAS

Février 2025

• Jeudi 06 février 2025 - Eddie Aamari
  

Décembre 2024

• Jeudi 05 décembre 2024 - Arthur Stephanovic

  Smooth transport map via diffusion process and applications to generative modelling

  We prove that the Langevin map transporting the d-dimensional
  Gaussian to a k-smooth déformation is (k+1)-smooth. We give applications of this result to functional inequalities as well as generative modelling.

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Novembre 2024

• Jeudi 21 novembre 2024 - Jordan Serre

  Polchinski Renormalization Group, dynamical Gamma-calculus and transportation of measures.

  Renormalization is a set of techniques developed by theoretical physicists to deal with the appearance of divergent quantities in quantum field theory. Highly controversial because they were not mathematically rigorous, these techniques have become increasingly accepted since the work of K. Wilson in the 1970s, showing how they can be used to understand phase transition phenomena in statistical physics, followed by the famous article by J. Polchinski in 1984 on effective Lagrangians.
  Although renormalization is now well accepted and understood in physics, it remains a challenge to provide the appropriate mathematical theory that explains it.
  In this talk, we will focus on the approach of R. Bauerschmidt and T. Bodineau. We will try to explain it through the continuum phi-4 model, then show how certain quantities such as mixing times can be studied along the Renormalization flow, and finally how this flow can be used to construct Lipschitz transport maps.

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• Jeudi 14 novembre 2024 - Valentin Gillet (Université de Lille)

  Propriétés typiques de contractions positives et problème du sous-espace invariant

  Le problème du sous-espace invariant pour les opérateurs positifs, toujours ouvert à ce jour, s'énonce ainsi : étant donné un espace de Banach X complexe de dimension infinie et ayant une base, est-ce que tout opérateur positif sur X admet un sous-espace invariant non trivial ? L'un des résultats fondamentaux à ce sujet, dû à Abramovich, Aliprantis et Burkinshaw, montre l'existence d'un sous-espace invariant non trivial pour tout opérateur positif sur un espace de Banach X ayant une base qui commute avec un opérateur positif non nul et quasinilpotent en un certain vecteur positif non nul.
  
  Dans cet exposé, nous déterminerons, pour les topologies SOT et SOT*, si l'ensemble des contractions positives sur X vérifiant les hypothèses du théorème d'Abramovich, Aliprantis et Burkinshaw est une partie comaigre dans l'ensemble des contractions positives.
  

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Octobre 2024

• Jeudi 03 octobre 2024 - Harouna Kinda

  Natural Resource Revenues and Double Taxation Treaties in Developing Countries: Evidence from A Neural Network Approach

  This paper investigates the effects of double taxation treaties on resource revenue mobilization in 83 resource-rich countries from 2000 to 2019 by applying standard panel fixed effects and methods-of-moments approaches. We calculate countries’ centrality indices by year based on their importance in the tax treaty network and show that centrality indices have a negative relationship with resource revenue mobilization—findings that are robust to alternative centrality indices and government revenue aggregates. We also use the betweenness centrality index to identify countries characterized as intermediate jurisdictions (countries -classified as investment or tax hubs based on their betweenness centrality index, which is above the median), arguing that multinational companies structure their investments to benefit from the low withholding tax rates in these countries. Applying the entropy balancing method, we find evidence of a negative effect on resource revenue mobilization dueto signing tax treaties with country-classified investment or tax hubs

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Septembre 2024

• Jeudi 26 septembre 2024 - Wiliam Kengne

  Robust deep learning from weakly dependent data

  We consider robust deep learning from weakly dependent observations, with unbounded loss function and unbounded input/output. It is only assumed that the output variable has a finite r order moment, with r >1.
  Non asymptotic bounds for the expected excess risk of the deep neural network estimator are established under strong mixing assumptions on the observations.
  We derive a relationship between these bounds and r, and when the data have moments of any order (that is r=\infty), the convergence rate is close to some well-known results.
  When the target predictor belongs to the class of H\"older smooth functions with sufficiently large smoothness index, the rate of the expected excess risk for exponentially strongly mixing data is close to that obtained with i.i.d. samples.
  Application to robust nonparametric regression with heavy-tailed errors shows that, robust estimators with absolute loss and Huber loss outperform the least squares method.

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