Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning

• Main Authors: Cabannes, Vivien, Pillaud-Vivien, Loucas, Bach, Francis, Rudi, Alessandro
• Other Authors: Statistical Machine Learning and Parsimony (SIERRA), Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), École des Ponts ParisTech (ENPC), Ecole Polytechnique Fédérale de Lausanne (EPFL), This work was funded in part by the French government under management of Agence Nationale de la Recherche as part of the “Investissements d’avenir” program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute). We also acknowledge support of the European Research Council (grants SEQUOIA 724063 and REAL 94790)., ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), European Project: 724063,ERC-2016-COG,SEQUOIA(2017), European Project: 0947904(2010)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2021
• Subjects: [STAT.ML]Statistics [stat]/Machine Learning [stat.ML]; [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG]; [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; Arctic
• Online Access: https://hal.archives-ouvertes.fr/hal-03454809; https://hal.archives-ouvertes.fr/hal-03454809/document; https://hal.archives-ouvertes.fr/hal-03454809/file/main.pdf

International audience As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of semi-supervised learning. To benefit from the access to unlabelled data, it is natural to diffuse smoothly knowledge of labelled data to unlabelled one. This induces to the use of Laplacian regularization. Yet, current implementations of Laplacian regularization suffer from several drawbacks, notably the well-known curse of dimensionality. In this paper, we provide a statistical analysis to overcome those issues, and unveil a large body of spectral filtering methods that exhibit desirable behaviors. They are implemented through (reproducing) kernel methods, for which we provide realistic computational guidelines in order to make our method usable with large amounts of data.