Un séminaire présenté par les membres de l’équipe SOP aura lieu le jeudi 27 novembre de 14h à 16h30, en salle H218, sur le campus d’Evry.

Vous trouverez ci-dessous le programme du séminaire ainsi que les titres et les résumés des 3 présentations.

Programme

14h00 – Baptiste GOUJAUD
Counter-examples in first-order optimization: a constructive approach and application 
to Heavy-Ball algorithm

Abstract: 
While many approaches were developed for obtaining worst-case complexity bounds for first-order 
optimization methods in the last years, there remain theoretical gaps in cases where no such bound 
can be found. In such cases, it is often unclear whether no such bound exists (e.g., because the 
algorithm might fail to systematically converge) or simply if the current techniques do not allow 
finding them. In this work, we propose an approach to automate the search for cyclic trajectories 
generated by first-order methods.
We then show that the heavy-ball (HB) method provably does not reach an accelerated convergence 
rate on smooth strongly convex problems. More specifically, we show that for any condition number 
and any choice of algorithmic parameters, either the worst-case convergence rate of HB on the class 
of L-smooth and μ-strongly convex quadratic functions is not accelerated (that is, slower than 
1 − O(κ)), or there exists an L-smooth μ-strongly convex function and an initialization such that 
the method does not converge.
To the best of our knowledge, this result closes a simple yet open question on one of the most used 
and iconic first-order optimization technique.
Our approach builds on finding functions for which HB fails to converge and instead cycles over 
finitely many iterates. We analytically describe all parametrizations of HB that exhibit this cycling 
behavior on a particular cycle shape, whose choice is supported by a systematic and constructive 
approach to the study of cycling behaviors of first-order methods. We show the robustness of our 
results to perturbations of the cycle, and extend them to class of functions that also satisfy higher-
order regularity conditions.

14h40 – Stefano FORTUNATI
Finite and infinite dimension nuisance parameters in semiparametric estimation: general framework and some recent results for the elliptical distributions.

Abstract :

In statistics, all the available knowledge about a phenomenon of interest is summarized in the probability distributions of the collected observations from a random experiment. To this end, we define a model as the family of distributions that are able to statistically characterize the observations. The most used class of models are the parametric ones, in which the concept of efficiency is well defined by means of the Fisher Information Matrix (FIM). To relax this unrealistic assumption, a more robust semiparametric model can be adopted. Specifically, a semiparametric model is parameterized by a finite-dimensional parameter vector of interest and by finite and infinite-dimensional nuisance terms that can be used to characterize the lack of knowledge in the functional form the data distributions. The aim of this seminar will be to introduce, in an informal manner, the concepts of semiparametric FIM and semiparametric efficiency. Finally, some recent results obtained in the field of elliptical distributions will be presented.

***  15h20 PAUSE CAFE/THE/…   ***

15h45 – Jean-Pierre DELMAS
Borne de Cramer-Rao pour processus sphériques invariants stationnaires et cyclostationaires

Abstract :
La formule classique de Whittle (1953) donne une expression analytique de la matrice de Fisher asymptotique de processus gaussiens centrés stationnaires purement non déterministes paramétrés.
Cet exposé montrera comment étendre cette formule à des processus sphériques invariants stationnaires en utilisant des propriétés asymptotiques de suites de matrice de Toeplitz à termes absolument sommables. Cette formule de Whittle sera ensuite étendue aux processus sphériques invariants purement cyclostationaires exprimés à l’aide des spectres cycliques.
Un exemple applicatif interprétable sera présenté pour évaluer l’impact des caractéristiques spectrales des  signaux sources sur la borne de Cramer-Rao d’estimation de DOA (direction of arrival).