Patricia
ReynaudBouret
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.ReynaudBouret@univcotedazur.fr


Curriculum
Vitae
Research interest
 Neurosciences and cognition : analysis of
spikes trains and functional connectivity, learning
models.
 Adaptive Statistics : Model selection, Lasso
and multiple testing
 Point processes : Hawkes, Poisson, Aalen
 Concentration inequalities
Students
Amel Rouis
(2011) 
biostatistician at CHU  Nice 
José Bonnet
(2013) 
research
engineer EDFLJAD 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]
ReynaudBouret, 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;
ReynaudBouret, Patricia Event scheduling
algorithms with Kalikow decomposition for simulating
potentially infinite neuronal networks, SN
Computer Science, 1(35) (2020).
[29] Ost, Guilherme; ReynaudBouret, Patricia Sparse spacetime
models: concentration inequalities and Lasso,
Annales de l'IHP, Probabilités et Statistiques, 56(4),
23772405 (2020).
[28] Coeurjolly, JeanFrançois; ReynaudBouret, Patricia A
concentration inequality for inhomogeneous NeymannScott
processes, Statistics and Probability Letters, 148,
3034 (2019).
[27] Hodara, Pierre; ReynaudBouret, Patricia
Exponential
inequality for chaos based on sampling without
replacement, Statistics and Probability Letters,
146, 6569 (2019).
[26] Hunt, Xin Jiang; ReynaudBouret, Patricia; Rivoirard,
Vincent; Sansonnet, Laure; Willett, Rebecca A
datadependent weighted LASSO under Poisson noise, IEEE
Transactions on Information Theory, 65(3), 15891613 (2019).
[25] Picard, Franck; ReynaudBouret, Patricia; Roquain,
Etienne Continuous
testing for Poisson process intensities: a new perspective
on scanning statistics, Biometrika, 105(4),
931944 (2018).
[24] Lambert, Régis; TuleauMalot, Christine; Bessaih, Thomas;
Rivoirard, Vincent; Bouret, Yann; Leresche, Nathalie;
ReynaudBouret, Patricia Reconstructing
the functional connectivity of multiple spike trains using
Hawkes models, Journal of Neuroscience Methods,
297, 921 (2018)
.
[23] Albert, Mélisande ;
Bouret, Yann ; Fromont, Magalie ; ReynaudBouret , Patricia Surrogate data methods based on a shuffling of
the trials for synchrony detection: the centering issue, Neural Computation, 28(11), 23522392 (2016).
[22]
Fromont, Magalie ; Lerasle, Matthieu ; ReynaudBouret,
Patricia Family Wise Separation Rates for multiple testing, Annals of Statistics, 44(6), 25332563 (2016).
[21] Lerasle, Matthieu ;
Magalhães, Nelo ; ReynaudBouret, Patricia Optimal
kernel selection for density estimation High Dimensional
Probability VII : The Cargese Volume, Prog. Probab. 71,
Birkhaüser, 425460 (2016).
[20] Chevallier, Julien ; Cáceres, María José ;
Doumic, Marie ; ReynaudBouret, Patricia Microscopic
approach of a time elapsed neural model, Mathematical Models and Methods in Applied
Sciences, 25(14), 26692719 (2015).
[19]
Albert, Mélisande ; Bouret, Yann ; Fromont, Magalie ;
ReynaudBouret, Patricia Bootstrap and permutation tests
of independence for point processes, Annals of Statistics, 43(6), 25372564 (2015).
[18] TuleauMalot, Christine ; Rouis, Amel ; Grammont,
Franck ; ReynaudBouret, Patricia Multiple tests based on a Gaussian approximation
of the Unitary Events method with delayed coincidence count, Neural Computation, 26(7), 14081454 (2014).
[17] ReynaudBouret, Patricia ; Rivoirard,
Vincent ; Grammont , Franck ; TuleauMalot, Christine Goodnessoffit tests and nonparametric
adaptive estimation for spike train analysis, Journal of Mathematical Neuroscience, 4:3 (2014).
[16] ReynaudBouret, Patricia Concentration inequalities, counting
processes and adaptive statistics, ESAIM
Proc. (proceedings of "Journées MAS 2012"), 44, 7998
(2014).
[15]
ReynaudBouret, Patricia ; Rivoirard, Vincent; TuleauMalot,
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. ; ReynaudBouret, Patricia ; Rivoirard, Vincent Lasso and probabilistic inequalities for
multivariate point processes,
Bernoulli,
21(1), 83143 (2015).
[13] Fromont,
Magalie ; Laurent, Béatrice ; ReynaudBouret, Patricia The twosample problem for Poisson processes:
adaptive tests with a nonasymptotic wild bootstrap approach,
Annals of Statistics, 41(3), 14311461 (2013).
[12]
Fromont,
Magalie ; Laurent, Béatrice ; Lerasle, Matthieu ; ReynaudBouret, Patricia Kernels based tests with
nonasymptotic bootstrap approaches for twosample problems,
JMLR : Workshop and Conference Proceedings, 23, 25th Annual
Conference on Learning Theory, 23.1–23.22 (2012).
[11] Doumic Jauffret,
Marie ; Hoffmann, Marc ; ReynaudBouret, Patricia ; Rivoirard,
Vincent Nonparametric estimation of the
division rate of a sizestructured population, SIAM
Journal on Numerical Analysis, 50, 925950 (2012).
[10] ReynaudBouret, Patricia ; Rivoirard, Vincent ;
TuleauMalot, Christine Adaptive density
estimation: a curse of support?
J. Statist. Plann. Inference, 141, 115139
(2011).
[9] Fromont, Magalie ;
Laurent, Béatrice ; ReynaudBouret, Patricia Adaptive test of
homogeneity for a Poisson process Ann. Inst. H. Poincaré Probab. Statist. 47 (1),
176213 (2011).
[8]
ReynaudBouret,
Patricia ; Schbath,
Sophie Adaptive estimation
for Hawkes processes; application to genome analysis
Annals of Statististics, 38(5), 27812822 (2010).
[7] ReynaudBouret,
Patricia ; Rivoirard,
Vincent Near
optimal thresholding estimation
of a Poisson intensity on the real line
Electronic Journal of Statistics, 4, 172238 (2010).
[6] Houdré, Christian ; Marchal,
Philippe ; ReynaudBouret, Patricia
Concentration
for norms of infinitely divisible vectors with independent
components. Bernoulli, 14(4), 926948 (2008).
[5] ReynaudBouret, Patricia ; Roy,
Emmanuel Some
non
asymptotic tail estimates for Hawkes
processes. Bulletin
of the Belgian Mathematical SocietySimon Stevin,
13(5), 883896 (2007) (old version
here).
[4]
ReynaudBouret,
Patricia Penalized projection estimators of the
Aalen multiplicative intensity. Bernoulli, 12(4), 633661 (2006).
[3]
ReynaudBouret,
Patricia Compensator
and exponential inequalities for some suprema
of counting processes. Statistics and Probability Letters, 76(14),
15141521 (2006).
[2]
Houdré, Christian ; ReynaudBouret,
Patricia Exponential
inequalities, with constants, for Ustatistics of order two. Stochastic
inequalities and applications, Progr.
Probab., 56 Birkhäuser,
Basel, 5569 (2003).
[1]
ReynaudBouret,
Patricia Adaptive estimation of the intensity of
inhomogeneous Poisson processes via concentration
inequalities. Probab.
Theory Related Fields 126 (1), 103153 (2003)
Preprints
[g] Mascart, Cyrille; Muzy, Alexandre; ReynaudBouret,
Patricia Discrete
event simulation of point processes: a computational
complexity analysis on sparse graphs, submitted
[f] Albert, Mélisande ; Bouret, Yann ; Fromont, Magalie ;
ReynaudBouret, Patricia (preliminary work for [23]) A Distribution Free Unitary
Events Method based on Delayed Coincidence Count
[e] ReynaudBouret,
P. ; TuleauMalot, C. ; Rivoirard, V. ; Grammont, F.
(preliminary work for [17]) Spike trains as (in)homogeneous Poisson processes
or Hawkes processes: nonparametric adaptive estimation and
goodnessoffit tests.
[d]
TuleauMalot, C. ; Rouis, A. ; ReynaudBouret, P. ; Grammont,
F. (preliminary work for [18]) Multiple Tests Based on a Gaussian Approximation
of the Unitary Events.
[c]
ReynaudBouret,
Patricia ; Rivoirard,
Vincent (preliminary work for [7])
Calibration of
thresholding rules for Poisson intensity estimation
[b] ReynaudBouret,
Patricia ; Rivoirard,
Vincent (preliminary work for [7]) Adaptive thresholding estimation of a
Poisson intensity with infinite support
[a]
Houdré, Christian ;
ReynaudBouret, 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 LJADI3S
[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, lowdimensional constraints, recent advances in Deep
RL (
DQN for Atari 2600,
AlphaGo, and more
lately
AlphaGo Zero) have
demonstrated humanlevel or superhuman performance in complex,
highdimensional spaces. However, DRL remains an active research
domain and, as often experienced, is not yet a plugandplay
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
welltrodden 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 toymodels 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 neurocognitive part of the brain to understand the
mechanisms behind human/animal learning and decisionmaking
[4]
Giovanni Gatti Pinheiro and Michaël DefoinPlatel (Amadeus) 9
Janvier 2021 (10h)
Airline Revenu Management problem, a general overview on
current stateoftheart 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 MeanField Markov Decision Processes
and MeanField QLearning
Meanfield game theory borrows ideas from statistical physics
to provide a tractable approximation of very large multiagent
systems. Applications are ubiquitous in today's highly
interconnected world, from crowd motion to macroeconomics and
distributed robotics. Realworld 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
modelfree methods. In this talk, we will mainly focus on a
framework for reinforcement learning with meanfield
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 meanfield Markov Decision Process
(MDP), and we prove a dynamic programming principle for the
state value function and stateaction value function. Based on
the latter function, we propose a meanfield Qlearning
method. We prove its convergence under suitable conditions and
provide numerical examples. Joint work with René Carmona and
Zongjun Tan.