Patricia Reynaud-Bouret


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Laboratoire J.A. Dieudonné
Université Côte d'Azur
CNRS UMR 7351
Parc Valrose, 06108 Nice, Cedex 2, France
+33 (0) 4 89 15 04 96

Patricia.Reynaud-Bouret@univ-cotedazur.fr





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Curriculum Vitae
2021
  CNRS Silver Medal in mathematics
2020 Pierre Faurre prize of the French Academy of Sciences
2019-         Director of the NeuroMod Institute (in charge of the federation of the corresponding scientific community since 2014)
        (Vice-director :Alexandre Muzy)
2019-
 Chair of 3IA Côte d'Azur in Axis 3 (AI for computational biology and Bio-inspired AI)
2016-       
In charge of the construction, then administration of the Master of Science Mod4NeuCog,
        open since September 2018, currently pedagogical coordinator (Director Ingrid Bethus)
2008-         CNRS researcher at Laboratoire JA Dieudonné (Directeur de Recherche since 2014)
2003-2008
CNRS researcher (Chargée de Recherche) at DMA (ENS-Paris).
2002-2003 
Postdoctoral Studies at the  School of Mathematics  (Georgia Institute of Technology, Atlanta, USA)  with  Christian Houdré
1999-2002
PhD Thesis at  Département de Mathématiques d'Orsay (Paris XI)
                     PhD advisor : Pascal Massart

Research interest
Students
Salima El Kolei (2009-2012) also supervised by  Frédéric Patras ex-statistician expert for SAFRAN, currently teacher at ENSAI (Rennes)
Laure Sansonnet (2009-2013) also supervised by  Vincent Rivoirard ex-PostDoc UCL, Belgium, currently MdC at AgroParisTech
Mélisande Albert (2012-2015)
 also supervised by  Magalie Fromont ex-PostDoc Grenoble, LJK/GIPSA, currently MdC at Insa-Toulouse
Julien Chevallier (2013-2016) also supervised by  François Delarue ex-PostDoc Cergy-Pontoise, currently MdC at Grenoble.
Giulia Mezzadri (2016-2020 )
 also supervised by  Fabien Mathy and Thomas Laloë ATER Université Côte d'Azur
Cyrille Mascart (2016- )
 also supervised by  Alexandre Muzy
Laurent Dragoni (2017- ) also supervised by  Karim Lounici and Rémi Flamary
Cuong Tien Phi (2018- )
 also supervised by Eva Löcherbach
Amel Rouis (2011) biostatistician at  CHU - Nice
José Bonnet (2013) research engineer EDF-LJAD on the prediction of sismic activity
Imen Chaarana (2015) computer scientist for Talent Consulting
Valentina Mazzi (2016) Erasmus exchange from Verona University
Hendjy Taraud (2017) in partnership with deligeo
David Maillot (2018)  in partnership with deligeo                 
Sepideh Iranfar (2019)
Jacopo Baldi (2020)  
 
Publications 
[31] Reynaud-Bouret, Patricia ; Muzy, Alexandre;  Bethus, Ingrid Towards a mathematical definition of functional connectivity,  Comptes rendus de l'Académie des Sciences -Series I- Mathematics, In press.

[30] Phi, Tien Cuong; Muzy, Alexandre; Reynaud-Bouret, Patricia Event scheduling algorithms with Kalikow decomposition for simulating potentially infinite neuronal networks, SN Computer Science, 1(35) (2020).

[29] Ost, Guilherme; Reynaud-Bouret, Patricia Sparse space-time models: concentration inequalities and Lasso, Annales de l'IHP, Probabilités et Statistiques, 56(4), 2377-2405 (2020).

[28] Coeurjolly, Jean-François; Reynaud-Bouret, Patricia A concentration inequality for inhomogeneous Neymann-Scott processes, Statistics and Probability Letters, 148, 30-34 (2019).

[27] Hodara, Pierre; Reynaud-Bouret, Patricia Exponential inequality for chaos based on sampling without replacement, Statistics and Probability Letters, 146, 65-69 (2019).

[26] Hunt, Xin Jiang; Reynaud-Bouret, Patricia; Rivoirard, Vincent; Sansonnet, Laure; Willett, Rebecca A data-dependent weighted LASSO under Poisson noise, IEEE Transactions on Information Theory, 65(3), 1589-1613 (2019).

[25] Picard, Franck; Reynaud-Bouret, Patricia; Roquain, Etienne Continuous testing for Poisson process intensities: a new perspective on scanning statistics, Biometrika, 105(4), 931-944 (2018).

[24] Lambert, Régis; Tuleau-Malot, Christine; Bessaih, Thomas; Rivoirard, Vincent; Bouret, Yann; Leresche, Nathalie; Reynaud-Bouret, Patricia Reconstructing the functional connectivity of multiple spike trains using Hawkes models, Journal of Neuroscience Methods, 297, 9-21 (2018) .

[23] Albert, Mélisande ; Bouret, Yann ; Fromont, Magalie ; Reynaud-Bouret , Patricia Surrogate data methods based on a shuffling of the trials for synchrony detection: the centering issue, Neural Computation, 28(11), 2352-2392 (2016).

[22] Fromont, Magalie ; Lerasle, Matthieu ; Reynaud-Bouret, Patricia Family Wise Separation Rates for multiple testing, Annals of Statistics, 44(6), 2533-2563 (2016).

[21] Lerasle, Matthieu ; Magalhães, Nelo ; Reynaud-Bouret, Patricia Optimal kernel selection for density estimation High Dimensional Probability VII : The Cargese Volume, Prog. Probab.  71, Birkhaüser, 425-460 (2016).

[20] Chevallier, Julien ; Cáceres, María José ; Doumic, Marie ; Reynaud-Bouret, Patricia Microscopic approach of a time elapsed neural model, Mathematical Models and Methods in Applied Sciences, 25(14), 2669-2719 (2015).

[19] Albert, Mélisande ; Bouret, Yann ; Fromont, Magalie ; Reynaud-Bouret, Patricia Bootstrap and permutation tests of independence for point processes, Annals of Statistics, 43(6), 2537-2564 (2015).

[18] Tuleau-Malot, Christine ; Rouis, Amel ; Grammont, Franck ; Reynaud-Bouret, Patricia Multiple tests based on a Gaussian approximation of the Unitary Events method with delayed coincidence count, Neural Computation, 26(7), 1408-1454 (2014).

[17] Reynaud-Bouret, Patricia ; Rivoirard, Vincent ; Grammont , Franck ;  Tuleau-Malot, Christine Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis, Journal of Mathematical Neuroscience, 4:3 (2014).

[16] Reynaud-Bouret, Patricia Concentration inequalities, counting processes and adaptive statistics, ESAIM Proc. (proceedings of  "Journées MAS 2012"), 44, 79-98 (2014).

[15] Reynaud-Bouret, Patricia ; Rivoirard, Vincent; Tuleau-Malot, Christine Inference of functional connectivity in Neurosciences via Hawkes processes, 1st IEEE Global Conference on Signal and Information Processing, Austin, Texas (2013).

[14] Hansen, Niels R. ; Reynaud-Bouret, Patricia ; Rivoirard, Vincent Lasso and probabilistic inequalities for multivariate point processes, Bernoulli, 21(1), 83-143 (2015).

[13]  Fromont, Magalie ; Laurent, Béatrice ; Reynaud-Bouret, Patricia The two-sample problem for Poisson processes: adaptive tests with a non-asymptotic wild bootstrap approach, Annals of Statistics, 41(3), 1431-1461 (2013).

[12]  Fromont, Magalie ; Laurent, Béatrice ; Lerasle, Matthieu ; Reynaud-Bouret, Patricia Kernels based tests with non-asymptotic bootstrap approaches for two-sample problems, JMLR : Workshop and Conference Proceedings, 23, 25th Annual Conference on Learning Theory, 23.1–23.22 (2012).

[11]  Doumic -Jauffret, Marie ; Hoffmann, Marc ; Reynaud-Bouret, Patricia ; Rivoirard, Vincent  Nonparametric estimation of the division rate of a size-structured population, SIAM Journal on Numerical Analysis, 50, 925-950 (2012).

[10] Reynaud-Bouret, Patricia ; Rivoirard, Vincent ; Tuleau-Malot, Christine Adaptive density estimation: a curse of support?  J. Statist. Plann. Inference, 141, 115-139 (2011).

[9]  Fromont, Magalie ; Laurent, Béatrice ; Reynaud-Bouret, Patricia  Adaptive test of homogeneity for a Poisson process Ann. Inst. H. Poincaré Probab. Statist. 47 (1), 176-213 (2011).

[8] Reynaud-Bouret, Patricia ;  Schbath, Sophie  Adaptive estimation for Hawkes processes; application to genome analysis  Annals of Statististics, 38(5), 2781-2822 (2010).

[7] Reynaud-Bouret, Patricia ;  Rivoirard, Vincent Near optimal thresholding estimation of a Poisson intensity on the real line  Electronic Journal of Statistics, 4, 172-238 (2010).

[6] Houdré, Christian ; Marchal, Philippe ; Reynaud-Bouret, Patricia Concentration for norms of infinitely divisible vectors with independent components.  Bernoulli, 14(4), 926-948 (2008).

[5] Reynaud-Bouret, Patricia ; Roy, Emmanuel   Some non asymptotic tail estimates for Hawkes processes. Bulletin of the Belgian Mathematical Society-Simon Stevin, 13(5), 883-896 (2007)  (old version here).

[4] Reynaud-Bouret, Patricia   Penalized projection estimators of the Aalen multiplicative intensity.  Bernoulli, 12(4), 633-661 (2006).

[3] Reynaud-Bouret, Patricia   Compensator and exponential inequalities for some suprema of counting processes. Statistics and Probability Letters, 76(14), 1514-1521 (2006).

[2] Houdré, Christian ; Reynaud-Bouret, Patricia   Exponential inequalities, with constants, for U-statistics of order two. Stochastic inequalities and applications, Progr. Probab., 56 Birkhäuser, Basel, 55-69 (2003).

[1] Reynaud-Bouret, Patricia   Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities. Probab. Theory Related Fields 126 (1), 103-153 (2003)


Preprints
[g] Mascart, Cyrille; Muzy, Alexandre; Reynaud-Bouret, Patricia Discrete event simulation of point processes: a computational complexity analysis on sparse graphs, submitted

[f] Albert, Mélisande ; Bouret, Yann ; Fromont, Magalie ; Reynaud-Bouret, Patricia (preliminary work for [23]) A Distribution Free Unitary Events Method based on Delayed Coincidence Count

[e] Reynaud-Bouret, P. ; Tuleau-Malot, C. ; Rivoirard, V. ; Grammont, F. (preliminary work for [17]) Spike trains as (in)homogeneous Poisson processes or Hawkes processes: non-parametric adaptive estimation and goodness-of-fit tests.

[d] Tuleau-Malot, C. ; Rouis, A. ; Reynaud-Bouret, P. ; Grammont, F. (preliminary work for [18]) Multiple Tests Based on a Gaussian Approximation of the Unitary Events.

[c] Reynaud-Bouret, Patricia ;  Rivoirard, Vincent (preliminary work for [7]) Calibration of thresholding rules for Poisson intensity estimation

[b] Reynaud-Bouret, Patricia ;  Rivoirard, Vincent (preliminary work for [7]) Adaptive thresholding estimation of a Poisson intensity with infinite support

[a] Houdré, Christian ; Reynaud-Bouret, Patricia (preliminary work for [6]) Concentration for Infinitely Divisible Vectors with Independent Components

HDR Manuscript :  Adaptive statistical inference for some point processes (Poisson, Aalen, Hawkes)


Material

2017/2018: Course1 Course2 Basic Tests : small review (with typos)


GDT Reinforcement learning LJAD-I3S
[1] Lucile Sassatelli (I3S) 21 Octobre 2020

        An introduction on Reinforcement Learning and Deep RL
        This presentation is meant to provide basics of Reinforcement Learning (RL) and introduce Deep Reinforcement Learning (DRL), for both synthetic and more realistic problems. While applications of RL are typically limited to discrete, low-dimensional constraints, recent advances in Deep RL (DQN for Atari 2600, AlphaGo, and more lately AlphaGo Zero) have demonstrated human-level or super-human performance in complex, high-dimensional spaces. However, DRL remains an active research domain and, as often experienced, is not yet a plug-and-play optimization tool. In this presentation, we will also peek into this challenging aspect of DRL for general control problems such as a robot navigation task, discussing difficulties inherent to RL and most recent approaches to such problems.

        (slides)

[2] Luc Lehéricy (LJAD) 18 Novembre 2020

An introduction to the mathematical proofs of reinforcement learning

Numerous reinforcement learning algorithms have been introduced these last few years to efficiently solve an increasing vast array of problems. Despite their variety, most of them rely on a few well-trodden ideas, the main difficulty being to adapt these ideas to a specific situation. The goal of this presentation is to give the mathematical tools to understand two fundamental and easily generalizable toy-models of reinforcement learning: the stochastic bandits and adversarial bandits.

     (slides)

[3] Oussama Sabri (I3S) 9 Décembre 2020 (10h)

Neural basis of learning

Human beings are born with the fascination gift of learning. With aid of such, they absorb and assimilate knowledge throughout thier entire life. Reinforcement Learning (RL) is one of the computational methods that attempt to simulate such characteristic in a computational environment capable of learning. However, RL carries different meanings for different communities from mathematics, computer science, neuroscience to psychology, etc. In this talk, I will try to clarify in general  the similarities of RL in different domains  and in which ways they differ with a focus on the neuro-cognitive part of the brain to understand the mechanisms behind human/animal learning and decision-making


[4] Giovanni Gatti Pinheiro and Michaël Defoin-Platel (Amadeus) 9 Janvier 2021 (10h)

Airline Revenu Management problem, a general overview on current state-of-the-art systems and possible extensions through the Reinforcement Learning framework.


[5] Athanasios Vasileiadis (LJAD) 27 Janvier 2021 (10h)

Stochastic control and reinforcement learning : How to solve a stochastic control problem using reinforcement learning.

In this series of talks, we are going to study the interaction between stochastic control problem and reinforcement learning. In the first part, we will use reinforcement learning to solve a stochastic control problem, we will deviate from the traditional approximate dynamic programming methods and instead we focus on direct approximation of the feedback function by deep neural networks DNN and stochastic gradient descent SGD. Two algorithms will be proposed by a combination of DNN, sequential dynamic programming DP and MonteCarlo simulation MC.This approach is commonly referred in the literature as deep reinforcement learning.


[6] Mathieu Laurière (Princeton) 8 Avril 2021 (15h)

On Mean-Field Markov Decision Processes and Mean-Field Q-Learning

Mean-field game theory borrows ideas from statistical physics to provide a tractable approximation of very large multi-agent systems. Applications are ubiquitous in today's highly interconnected world, from crowd motion to macroeconomics and distributed robotics. Real-world problems often lead to models which are not fully known to the agents, hence a recent surge of interests for the question of computing solutions with model-free methods. In this talk, we will mainly focus on a framework for reinforcement learning with mean-field interactions. In this talk, we focus on the case where the agents are cooperative and look for a social optimum. We formulate a notion of mean-field Markov Decision Process (MDP), and we prove a dynamic programming principle for the state value function and state-action value function. Based on the latter function, we propose a mean-field Q-learning method. We prove its convergence under suitable conditions and provide numerical examples. Joint work with René Carmona and Zongjun Tan.