Un s\u00e9minaire pr\u00e9sent\u00e9 par les membres de l’\u00e9quipe SOP aura lieu le jeudi 27 novembre de 14h30 \u00e0 17h00, en salle G10, sur le campus d’Evry.<\/p>\n\n\n\n
Vous trouverez ci-dessous le programme du s\u00e9minaire ainsi que les titres et les r\u00e9sum\u00e9s des 3 pr\u00e9sentations.<\/p>\n\n\n\n
Programme<\/strong><\/p>\n\n\n\n 14h30 – Baptiste GOUJAUD<\/strong> Abstract: <\/em> 15h10 – Stefano FORTUNATI<\/strong> Abstract :<\/em><\/p>\n\n\n\n In statistics, all the available knowledge about a phenomenon of interest is summarized in the probability<\/em> distributions of the collected observations from a random experiment. To this end, we define a model as<\/em> the family of distributions that are able to statistically characterize the observations.<\/em> The most used class of models are the parametric ones, in which the concept of efficiency is well<\/em> defined by means of the Fisher Information Matrix (FIM). To relax this unrealistic assumption, a more<\/em> robust semiparametric model can be adopted. Specifically, a semiparametric model is parameterized by<\/em> a finite-dimensional parameter vector of interest and by finite and infinite-dimensional nuisance terms that<\/em> can be used to characterize the lack of knowledge in the functional form the data distributions. The aim of<\/em> this seminar will be to introduce, in an informal manner, the concepts of semiparametric FIM and<\/em> semiparametric efficiency. Finally, some recent results obtained in the field of elliptical distributions will be<\/em> presented.<\/em><\/p>\n\n\n\n
Counter-examples in first-order optimization: a constructive approach and application <\/em><\/strong>
to Heavy-Ball algorithm<\/em><\/strong><\/p>\n\n\n\n
While many approaches were developed for obtaining worst-case complexity bounds for first-order <\/em>
optimization methods in the last years, there remain theoretical gaps in cases where no such bound <\/em>
can be found. In such cases, it is often unclear whether no such bound exists (e.g., because the <\/em>
algorithm might fail to systematically converge) or simply if the current techniques do not allow <\/em>
finding them. In this work, we propose an approach to automate the search for cyclic trajectories <\/em>
generated by first-order methods.<\/em>
We then show that the heavy-ball (HB) method provably does not reach an accelerated convergence <\/em>
rate on smooth strongly convex problems. More specifically, we show that for any condition number <\/em>
and any choice of algorithmic parameters, either the worst-case convergence rate of HB on the class <\/em>
of L-smooth and \u03bc-strongly convex quadratic functions is not accelerated (that is, slower than <\/em>
1 \u2212 O(\u03ba)), or there exists an L-smooth \u03bc-strongly convex function and an initialization such that <\/em>
the method does not converge.<\/em>
To the best of our knowledge, this result closes a simple yet open question on one of the most used <\/em>
and iconic first-order optimization technique.<\/em>
Our approach builds on finding functions for which HB fails to converge and instead cycles over <\/em>
finitely many iterates. We analytically describe all parametrizations of HB that exhibit this cycling <\/em>
behavior on a particular cycle shape, whose choice is supported by a systematic and constructive <\/em>
approach to the study of cycling behaviors of first-order methods. We show the robustness of our <\/em>
results to perturbations of the cycle, and extend them to class of functions that also satisfy higher-<\/em>
order regularity conditions.<\/em><\/p>\n\n\n\n
Finite and infinite dimension nuisance parameters in semiparametric estimation:<\/strong><\/em> general framework and some recent results for the elliptical distributions.<\/strong><\/em><\/p>\n\n\n\n