Dataset Information

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

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.

SUBMITTER: Song H

PROVIDER: S-EPMC7133715 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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

Song Hyebin H Raskutti Garvesh G

Journal of the American Statistical Association 20190411 529

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 ...[more]

PMID: 32255883

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Project description:BackgroundThe rapid and accurate identification of a minimal-size core set of representative microbial species plays an important role in the clustering of microbial community data and interpretation of clustering results. However, the huge dimensionality of microbial metagenomics datasets is a major challenge for the existing methods such as Dirichlet multinomial mixture (DMM) models. In the approach of the existing methods, the computational burden of identifying a small number of representative species from a large number of observed species remains a challenge.ResultsWe propose a novel approach to improve the performance of the widely used DMM approach by combining three ideas: (i) we propose an indicator variable to identify representative operational taxonomic units that substantially contribute to the differentiation among clusters; (ii) to address the computational burden of high-dimensional microbiome data, we propose a stochastic variational inference, which approximates the posterior distribution using a controllable distribution called variational distribution, and stochastic optimization algorithms for fast computation; and (iii) we extend the finite DMM model to an infinite case by considering Dirichlet process mixtures and estimating the number of clusters as a variational parameter. Using the proposed method, stochastic variational variable selection (SVVS), we analyzed the root microbiome data collected in our soybean field experiment, the human gut microbiome data from three published datasets of large-scale case-control studies and the healthy human microbiome data from the Human Microbiome Project.ConclusionsSVVS demonstrates a better performance and significantly faster computation than those of the existing methods in all cases of testing datasets. In particular, SVVS is the only method that can analyze massive high-dimensional microbial data with more than 50,000 microbial species and 1000 samples. Furthermore, a core set of representative microbial species is identified using SVVS that can improve the interpretability of Bayesian mixture models for a wide range of microbiome studies. Video Abstract.

Dataset Information

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

Publications

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

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