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

• URL: http://arxiv.org/abs/2009.04324v4
• Date: Mon, 29 Nov 2021 12:29:05 GMT
• Title: Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning
• Authors: Vivien Cabannes, Loucas Pillaud-Vivien, Francis Bach, Alessandro Rudi
• Abstract summary: We provide a statistical analysis to overcome drawbacks of Laplacian regularization. We unveil a large body of spectral filtering methods that exhibit desirable behaviors. We provide realistic computational guidelines in order to make our method usable with large amounts of data.
• Score: 80.20302993614594
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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