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Sparse Precision Matrix Estimation with SQUIC

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Eftekhari A., Gaedke-Merzhäuser L., Pasadakis D., Bollhöfer M., Scheidegger S., Schenk O.
Articolo pubblicato in rivista scientifica
in uscita
We present SQUIC, a fast and scalable sparse precision matrix estimation package. The algorithm is a second-order method that solves the ℓ1–regularized maximum likelihood problem using highly optimized linear algebra subroutines, which leverage the underlying sparsity and the intrinsic parallelism in the computation. We provide didactic examples using synthetic datasets where SQUIC consistently outperforms the state-of-the-art packages, with at least up to an order of magnitude faster runtimes and equivalent or higher accuracy. Next, we utilize SQUIC to classify microarray gene expressions and demonstrate that by using the matrix form of the tuning parameter (also called the regularization parameter), SQUIC can use prior bias in the estimation procedure, which can improve classification accuracy with minimal computational overhead. SQUIC is implemented in C++ with interfaces for R and Python.
ACM Transactions on Mathematical Software
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Parole chiave
sparse precision matrix estimation, covariance matrix, matrix factorization, matrix inversion