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Learning with Reproducing Kernel Hilbert spaces: Stochastic Gradient Descent and Laplacian Estimation

Loucas Pillaud-Vivien 1
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : Machine Learning has received a lot of attention during the last two decades both from industry for data-driven decision problems and from the scientific community in general. This recent attention is certainly due to its ability to efficiently solve a wide class of high-dimensional problems with fast and easy- to-implement algorithms. What is the type of problems machine learning tackles ? Generally speaking, answering this question requires to divide it into two distinct topics: supervised and unsupervised learning. The first one aims to infer relationships between a phenomenon one seeks to predict and “explanatory” variables leveraging supervised information. On the contrary, the second one does not need any supervision and aims at extracting some structure, information or significant features of the variables. These two main directions find an echo in this thesis. On the one hand, the supervised learning part theoretically studies the cornerstone of all optimization techniques for these problems: stochastic gradient methods. For their versatility, they are the workhorses of the recent success of ML. However, despite their simplicity, their efficiency is not yet fully understood. Establishing some properties of this algorithm is one of the two important questions of this thesis. On the other hand, the part concerned with unsupervised learning is more problem-specific: we design an algorithm to find reduced order models in physically-based dynamics addressing an crucial question in computational statistical physics (also called molecular dynamics).
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https://hal.inria.fr/tel-03162165
Contributor : Loucas Pillaud-Vivien <>
Submitted on : Monday, March 8, 2021 - 12:32:30 PM
Last modification on : Tuesday, March 9, 2021 - 4:33:35 PM

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  • HAL Id : tel-03162165, version 1

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Loucas Pillaud-Vivien. Learning with Reproducing Kernel Hilbert spaces: Stochastic Gradient Descent and Laplacian Estimation. Machine Learning [stat.ML]. Paris, Science et Lettres; Inria de Paris; Ecole Normale Supérieure, 2020. English. ⟨tel-03162165⟩

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