Ph.D. Defense of Romain Brault
Monday, July 3rd at 2:00 pm, building IBGBI
23 Boulevard de France -- Évry

Large-Scale Operator-Valued Kernel Regression

Romain Brault.
Date and time
Monday, July 3rd 2017 at 2:00 pm.
23, Boulevard de France -- Évry -- building IBGBI
Jury members
  • Paul Honeine, Professor (Université de Rouen Normandie),
  • Liva Ralaivola, Professor (Université de Aix-Marseille).
  • Aurélien Bellet, Research Fellow (INRIA Lille),
  • Jean Marc Delosme, Professor (Université d'Évry-Val-d'Essonne),
  • Hachem Kadri, Associate Professor (Université de Aix-Marseille),
  • Zoltán Szabó, Associate Professor (École Polytechnique),
  • Marie Szafranski, Associate Professor (ENSIIE Évry).

The presentation will be held in english.


Many problems in Machine Learning can be cast into vector-valued functions approximation. Operator-Valued Kernels (*OVKs*) and vector-valued Reproducing Kernel Hilbert Spaces provide a theoretical and practical framework to address that issue, extending nicely the well-known setting of scalar-valued kernels. However large scale applications are usually not affordable with these tools that require an important computational power along with a large memory capacity. In this thesis, we propose and study scalable methods to perform regression with *OVKs*. To achieve this goal, we extend Random Fourier Features, an approximation technique originally introduced for scalar-valued kernels, to *OVKs*. The idea is to take advantage of an approximated operator-valued feature map in order to come up with a linear model in a finite-dimensional space.

This thesis is structured as follows. First we develop a general framework devoted to the approximation of shift-invariant Mercer kernels on Locally Compact Abelian groups and study their properties along with the complexity of the algorithms based on them. Second we show theoretical guarantees by bounding the error due to the approximation, with high probability. Third, we study various applications of Operator Random Fourier Features (*ORFFs*) to different tasks of Machine learning such as multi-class classification, multi-task learning, time serie modeling, functional regression and anomaly detection. We also compare the proposed framework with other state of the art methods. Fourth, we conclude by drawing short-term and mid-term perspectives of this work.

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