title: A sparse Ising model with covariates.
abstract: There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the binary data, and may influence the dependence relationships. Motivated by such a dataset on genomic instability collected from tumor samples of several types, we propose a sparse covariate dependent Ising model to study both the conditional dependency within the binary data and its relationship with the additional covariates. This results in subject-specific Ising models, where the subject's covariates influence the strength of association between the genes. As in all exploratory data analysis, interpretability of results is important, and we use ℓ1 penalties to induce sparsity in the fitted graphs and in the number of selected covariates. Two algorithms to fit the model are proposed and compared on a set of simulated data, and asymptotic results are established. The results on the tumor dataset and their biological significance are discussed in detail.
authors.affiliation: Department of Statistics, University of Michigan, Ann Arbor, Michigan, U.S.A.
authors.forename: Jie
authors.initials: J
authors.lastname: Cheng
authors.forename: Elizaveta
authors.initials: E
authors.lastname: Levina
authors.forename: Pei
authors.initials: P
authors.lastname: Wang
authors.forename: Ji
authors.initials: J
authors.lastname: Zhu
mesh_terms: D001943:Breast Neoplasms / Q000453:epidemiology* / Q000235:genetics*; D003198:Computer Simulation; D005260:Female; D016147:Genes, Tumor Suppressor; D056726:Genetic Association Studies; D020022:Genetic Predisposition to Disease / Q000453:epidemiology / Q000235:genetics; D006801:Humans; D008280:Magnetics / Q000379:methods; D059346:Magnets; D008390:Markov Chains; D015233:Models, Statistical; D009363:Neoplasm Proteins / Q000235:genetics*; D009664:Norway / Q000453:epidemiology; D015995:Prevalence; D011789:Quantum Theory; D012307:Risk Factors
chemical_list: D009363:Neoplasm Proteins
keywords: Binary Markov network; Graphical model; Ising model; Lasso; Pseudo-likelihood; Tumor suppressor genes
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