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Abstract:
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In genomics, it is often of interest to study the structural change of a genetic network between two phenotypes. Under Gaussian graphical models, the problem can be transformed to estimating the difference between two precision matrices, and several approaches have been recently developed for this task such as joint graphical lasso and fused graphical lasso. In this work, we consider the problem of directly estimating differential networks under a flexible semiparametric model, namely nonparanormal graphical model, where the random variables are assumed to follow a multivariate Gaussian distribution after a set of monotonically increasing transformations. We propose to use a novel rank-based estimator to directly estimate the differential network, together with a parametric simplex algorithm for fast implementation. Theoretical properties of the new estimator are established under a high-dimensional setting where p grows with n almost exponentially fast. In particular, we show that the proposed estimator is consistent in both parameter estimation and support recovery. Both synthetic data and real genomic data are used to illustrate the promise of the new approach.
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