Robust sparse precision matrix estimation for high-dimensional compositional data

Abstract

Motivated by the rapid development in the high-dimensional compositional data analysis, an ”Approximate-Plug” framework with theoretical justifications is proposed to provide robust precision matrix estimation for this kind of data under the sparsity assumption. To be specific, we first construct a Huber-robustness estimator Γ̃ to approximate the centered log-ratio covariance matrix. Then we plug Γ̃ into a constrained ℓ1-minimization procedure to obtain the final estimator Ω̃. Through imposing some mild conditions, we derive the convergence rate under the entrywise maximum norm and the spectral norm. Given that SpiecEasi in Kurtz et al. (2015) shares same routine with us but lacks of robustness and theoretical guarantees, simulation studies are conducted to show the privileges of our procedure. We also apply the proposed method on a real data.