Differentiable Unsupervised Feature Selection based on a Gated Laplacian

Ofir Lindenbaum, Uri Shaham, Erez Peterfreund, Jonathan Svirsky, Nicolas Casey, Yuval Kluger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


Scientific observations may consist of a large number of variables (features). Selecting a subset of meaningful features is often crucial for identifying patterns hidden in the ambient space. In this paper, we present a method for unsupervised feature selection, and we demonstrate its advantage in clustering, a common unsupervised task. We propose a differentiable loss that combines a graph Laplacian-based score that favors low-frequency features with a gating mechanism for removing nuisance features. Our method improves upon the naive graph Laplacian score by replacing it with a gated variant computed on a subset of low-frequency features. We identify this subset by learning the parameters of continuously relaxed Bernoulli variables, which gate the entire feature space. We mathematically motivate the proposed approach and demonstrate that it is crucial to compute the graph Laplacian on the gated inputs rather than on the full feature space in the high noise regime. Using several real-world examples, we demonstrate the efficacy and advantage of the proposed approach over leading baselines.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
EditorsMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
PublisherNeural information processing systems foundation
Number of pages13
ISBN (Electronic)9781713845393
StatePublished - 2021
Event35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
Duration: 6 Dec 202114 Dec 2021

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference35th Conference on Neural Information Processing Systems, NeurIPS 2021
CityVirtual, Online

Bibliographical note

Funding Information:
The authors thank Stefan Steinerberger, Boaz Nadler and Ronen Basri for helpful discussions. The work of OL and YK was supported by the National Institutes of Health R01GM131642, UM1PA05141, P50CA121974, and U01DA053628.

Publisher Copyright:
© 2021 Neural information processing systems foundation. All rights reserved.


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