title: Structural zeros in high-dimensional data with applications to microbiome studies.
abstract: 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 of Yatsunenko 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.
authors.affiliation: Biostatistics and Computational Biology Branch, National Institute of Environmental Health Sciences, RTP, NC 27709, USA.
authors.forename: Abhishek
authors.initials: A
authors.lastname: Kaul
authors.affiliation: Department of Statistics, University of Haifa, Haifa 31905, Israel.
authors.forename: Ori
authors.initials: O
authors.lastname: Davidov
authors.affiliation: Biostatistics and Computational Biology Branch, National Institute of Environmental Health Sciences, RTP, NC 27709, USA.
authors.forename: Shyamal D
authors.initials: SD
authors.lastname: Peddada
mesh_terms: D000069196:Gastrointestinal Microbiome; D005843:Geography; D006801:Humans; D064307:Microbiota; D013223:Statistics as Topic
keywords: Classification; High dimension; Microbiome data; Missing data; Sparsity