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PUlasso: High-Dimensional Variable Selection With Presence-Only Data

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  • Hyebin Song
  • Garvesh Raskutti

Abstract

In various real-world problems, we are presented with classification problems with positive and unlabeled data, referred to as presence-only responses. In this article we study variable selection in the context of presence only responses where the number of features or covariates p is large. The combination of presence-only responses and high dimensionality presents both statistical and computational challenges. In this article, we develop the PUlasso algorithm for variable selection and classification with positive and unlabeled responses. Our algorithm involves using the majorization-minimization framework which is a generalization of the well-known expectation-maximization (EM) algorithm. In particular to make our algorithm scalable, we provide two computational speed-ups to the standard EM algorithm. We provide a theoretical guarantee where we first show that our algorithm converges to a stationary point, and then prove that any stationary point within a local neighborhood of the true parameter achieves the minimax optimal mean-squared error under both strict sparsity and group sparsity assumptions. We also demonstrate through simulations that our algorithm outperforms state-of-the-art algorithms in the moderate p settings in terms of classification performance. Finally, we demonstrate that our PUlasso algorithm performs well on a biochemistry example. Supplementary materials for this article are available online.

Suggested Citation

  • Hyebin Song & Garvesh Raskutti, 2020. "PUlasso: High-Dimensional Variable Selection With Presence-Only Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 334-347, January.
  • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:529:p:334-347
    DOI: 10.1080/01621459.2018.1546587
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    Cited by:

    1. Małgorzata Łazęcka & Jan Mielniczuk & Paweł Teisseyre, 2021. "Estimating the class prior for positive and unlabelled data via logistic regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 1039-1068, December.

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