Large-Scale Precision Matrix Estimation With SQUIC

15 Pages Posted: 16 Aug 2021

See all articles by Aryan Eftekhari

Aryan Eftekhari

Università della Svizzera italiana - Institute of Computational Science

Lisa Gaedke-Merzhaeuser

Universita della Svizzera italiana (USI Lugano)

Dimosthenis Pasadakis

Universita della Svizzera italiana (USI Lugano)

Matthias Bollhoefer

TU Braunschweig

Simon Scheidegger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne)

Olaf Schenk

Universita della Svizzera italiana (USI Lugano)

Date Written: August 12, 2021

Abstract

High-dimensional sparse precision matrix estimation is a ubiquitous task in multivariate analysis with applications that cross many disciplines. In this paper, we introduce the SQUIC package, which benefits from superior runtime performance and scalability, significantly exceeding the available state-of-the-art packages. This package 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 two sets of numerical tests; the first one consists of didactic examples using synthetic datasets highlighting the performance and accuracy of the package, and the second one is a real-world classification problem of high dimensional medical datasets. The base algorithm is implemented in C++ with interfaces for R and Python.

Keywords: SQUIC, precision matrix, LASSO, maximum likelihood,R,Python

JEL Classification: C02, C10, C13

Suggested Citation

Eftekhari, Aryan and Gaedke-Merzhaeuser, Lisa and Pasadakis, Dimosthenis and Bollhoefer, Matthias and Scheidegger, Simon and Schenk, Olaf, Large-Scale Precision Matrix Estimation With SQUIC (August 12, 2021). Available at SSRN: https://ssrn.com/abstract=3904001 or http://dx.doi.org/10.2139/ssrn.3904001

Aryan Eftekhari

Università della Svizzera italiana - Institute of Computational Science ( email )

Via Giuseppe Buffi 13
Lugano, Ticino 6900
Switzerland

Lisa Gaedke-Merzhaeuser

Universita della Svizzera italiana (USI Lugano) ( email )

Dimosthenis Pasadakis

Universita della Svizzera italiana (USI Lugano) ( email )

Matthias Bollhoefer

TU Braunschweig ( email )

Germany

Simon Scheidegger (Contact Author)

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Internef
Lausanne, 1015
Switzerland

Olaf Schenk

Universita della Svizzera italiana (USI Lugano) ( email )

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