Journal
BIOSTATISTICS
Volume 18, Issue 3, Pages 422-433Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biostatistics/kxw053
Keywords
Classification; High dimension; Microbiome data; Missing data; Sparsity
Funding
- Intramural Research Program of the NIH, NIEHS [Z01 ES101744-04]
- Israeli Science Foundation [1256/13]
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This paper is motivated by the recent interest in the analysis of high-dimensional microbiome data. A key feature of these data is the presence of structural zeros which are microbes missing from an observation vector due to an underlying biological process and not due to error in measurement. Typical notions of missingness are unable to model these structural zeros. We define a general framework which allows for structural zeros in the model and propose methods of estimating sparse high-dimensional covariance and precision matrices under this setup. We establish error bounds in the spectral and Frobenius norms for the proposed estimators and empirically verify them with a simulation study. The proposed methodology is illustrated by applying it to the global gut microbiome data ofYatsunenko and others (2012. Human gut microbiome viewed across age and geography. Nature 486, 222-227). Using our methodology we classify subjects according to the geographical location on the basis of their gut microbiome.
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