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Large-scale operator-valued kernel regression

Abstract : Many problems in Machine Learning can be cast into vector-valued approximation. Operator-Valued Kernels 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 Operator-Valued Kernels. To achieve this goal, we extend Random Fourier Features, an approximation technique originally introduced for scalar-valued kernels, to Operator-Valued Kernels. 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 (ORFF) to different tasks of Machine learning such as multi-class classification, multi-task learning, time serie modelling, functionnal 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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Contributor : Frédéric Davesne Connect in order to contact the contributor
Submitted on : Monday, April 9, 2018 - 1:44:04 PM
Last modification on : Wednesday, June 15, 2022 - 9:06:38 PM


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  • HAL Id : tel-01761768, version 1


Romain Brault. Large-scale operator-valued kernel regression. Machine Learning [cs.LG]. Université Paris Saclay, 2017. English. ⟨NNT : 2017SACLE024⟩. ⟨tel-01761768⟩



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